From 8c0e36ed04a30378884ec48ec74106e24e025bbd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jo=C3=A3o=20Capucho?= <jcapucho7@gmail.com>
Date: Thu, 25 Jan 2024 14:08:21 +0000
Subject: [PATCH] MPEI: Add files

---
 .gitmodules                                   |      3 +
 2ano1/MPEI/aula01/analyticProbCoinToss.m      |      3 +
 2ano1/MPEI/aula01/ex02_ex05.m                 |      2 +
 2ano1/MPEI/aula01/ex02_v1.m                   |     20 +
 2ano1/MPEI/aula01/ex02_v2.m                   |     10 +
 2ano1/MPEI/aula01/ex03.m                      |     10 +
 2ano1/MPEI/aula01/ex03_ex05.m                 |      2 +
 2ano1/MPEI/aula01/ex04.m                      |     12 +
 2ano1/MPEI/aula01/ex04_ex05.m                 |      7 +
 2ano1/MPEI/aula01/ex05.m                      |     36 +
 2ano1/MPEI/aula01/ex07.m                      |     27 +
 2ano1/MPEI/aula01/probCoinToss.m              |      5 +
 2ano1/MPEI/aula02/ex01.m                      |     82 +
 2ano1/MPEI/aula02/ex02.m                      |     89 +
 2ano1/MPEI/aula02/ex03.m                      |     68 +
 2ano1/MPEI/aula02/ex04.m                      |     28 +
 2ano1/MPEI/aula02/ex05.m                      |     35 +
 2ano1/MPEI/aula02/ex06.m                      |     28 +
 2ano1/MPEI/aula02/ex07.m                      |     69 +
 2ano1/MPEI/aula03/Binomial.m                  |      3 +
 2ano1/MPEI/aula03/NPPoisson.m                 |      4 +
 2ano1/MPEI/aula03/Poisson.m                   |      4 +
 2ano1/MPEI/aula03/ex01.m                      |     20 +
 2ano1/MPEI/aula03/ex02.m                      |     17 +
 2ano1/MPEI/aula03/ex03.m                      |     76 +
 2ano1/MPEI/aula03/ex04.m                      |     71 +
 2ano1/MPEI/aula03/ex05.m                      |     21 +
 2ano1/MPEI/aula03/ex06.m                      |      7 +
 2ano1/MPEI/aula03/ex07.m                      |     17 +
 2ano1/MPEI/aula03/ex08.m                      |      3 +
 2ano1/MPEI/aula03/ex09.m                      |     22 +
 2ano1/MPEI/aula04/ex01.asv                    |     21 +
 2ano1/MPEI/aula04/ex01.m                      |     22 +
 2ano1/MPEI/aula04/ex02.m                      |     30 +
 2ano1/MPEI/aula04/ex03.m                      |     33 +
 2ano1/MPEI/aula05/ex01.m                      |     32 +
 2ano1/MPEI/aula05/ex02.m                      |     33 +
 2ano1/MPEI/aula05/ex03.m                      |     16 +
 2ano1/MPEI/aula05/ex04.m                      |     38 +
 2ano1/MPEI/aula05/ex05.m                      |     76 +
 2ano1/MPEI/aula05/ex06.m                      |     68 +
 2ano1/MPEI/aula05/ex06_suplementar.m          |    106 +
 2ano1/MPEI/aula06/ex07.m                      |     51 +
 .../exame-pratico-2022-2023/BloomFilter.m     |     51 +
 .../CalculateSignaturesWithShingles.m         |     16 +
 .../SignatureForText.m                        |     28 +
 2ano1/MPEI/exame-pratico-2022-2023/crawl.m    |     37 +
 2ano1/MPEI/exame-pratico-2022-2023/ex01.m     |     44 +
 2ano1/MPEI/exame-pratico-2022-2023/ex02.m     |     36 +
 2ano1/MPEI/exame-pratico-2022-2023/ex03.m     |     20 +
 2ano1/MPEI/exame-pratico-2022-2023/hf1.m      |     37 +
 .../MPEI/exame-pratico-2022-2023/rand_keys.m  |     48 +
 .../exame-pratico-2022-2023/string2hash.m     |     48 +
 .../CalculateMinHash.m                        |     17 +
 .../CountingBloomFilter.m                     |     34 +
 2ano1/MPEI/exame-pratico-2023-2024/cars3.xlsx |    Bin 0 -> 10454 bytes
 2ano1/MPEI/exame-pratico-2023-2024/ex01.m     |     35 +
 2ano1/MPEI/exame-pratico-2023-2024/ex02.m     |     29 +
 2ano1/MPEI/exame-pratico-2023-2024/ex03.m     |     15 +
 2ano1/MPEI/exame-pratico-2023-2024/hf24.m     |     50 +
 2ano1/MPEI/exame-pratico-2023-2024/input.mat  |    Bin 0 -> 33591 bytes
 .../exame-pratico-2023-2024/kHashValues.m     |     17 +
 2ano1/MPEI/guiao04/Hashtable/hashtable.m      |     36 +
 .../MPEI/guiao04/Hashtable/hashtable_entry.m  |     30 +
 .../guiao04/Hashtable/hashtable_examples.m    |     36 +
 2ano1/MPEI/guiao04/Hashtable/hashtable_kv.m   |     26 +
 .../guiao04/Sec\303\247\303\243o 1/DJB31MA.m" |     14 +
 .../Sec\303\247\303\243o 1/RandKeys_A.mat"    |    Bin 0 -> 1407740 bytes
 .../Sec\303\247\303\243o 1/RandKeys_B.mat"    |    Bin 0 -> 1182788 bytes
 .../guiao04/Sec\303\247\303\243o 1/ex01.m"    |     20 +
 .../guiao04/Sec\303\247\303\243o 1/ex02.m"    |     42 +
 .../guiao04/Sec\303\247\303\243o 1/ex03.m"    |     65 +
 .../Sec\303\247\303\243o 1/hashstring.m"      |     15 +
 .../Sec\303\247\303\243o 1/prob_pt.txt"       |     26 +
 .../Sec\303\247\303\243o 1/rand_keys.m"       |     42 +
 .../Sec\303\247\303\243o 1/string2hash.m"     |     48 +
 .../Sec\303\247\303\243o 2/BloomFilter.m"     |     51 +
 .../guiao04/Sec\303\247\303\243o 2/DJB31MA.m" |     14 +
 .../guiao04/Sec\303\247\303\243o 2/ex05.m"    |     51 +
 .../wordlist-preao-20201103.txt"              | 994898 +++++++++++++++
 .../CalculateJaccardDistance.m"               |     15 +
 .../CalculateJaccardDistanceMinHash.m"        |     17 +
 .../CalculateMinHash.m"                       |     21 +
 .../Sec\303\247\303\243o 3/CreateMoviesSet.m" |     10 +
 .../Ex01UserPairsDistance.mat"                |    Bin 0 -> 2552794 bytes
 .../Ex02UserPairsDistance.mat"                |    Bin 0 -> 2552794 bytes
 .../Ex04UserPairsDistance.mat"                |    Bin 0 -> 763166 bytes
 .../Sec\303\247\303\243o 3/SimilarPairs.m"    |     14 +
 .../guiao04/Sec\303\247\303\243o 3/ex01.m"    |     56 +
 .../guiao04/Sec\303\247\303\243o 3/ex02.m"    |     32 +
 .../guiao04/Sec\303\247\303\243o 3/ex04.m"    |     33 +
 .../Sec\303\247\303\243o 3/muxDJB31MA.m"      |     12 +
 .../guiao04/Sec\303\247\303\243o 3/u.data"    | 100000 ++
 .../trabalho-pratico-1-2022-2023/Folha 1.jpeg |    Bin 0 -> 110888 bytes
 .../trabalho-pratico-1-2022-2023/Folha 2.jpeg |    Bin 0 -> 102051 bytes
 2ano1/MPEI/trabalho-pratico-1-2022-2023/L.mat |    Bin 0 -> 1168 bytes
 .../MPEI/trabalho-pratico-1-2022-2023/crawl.m |     34 +
 2ano1/MPEI/trabalho-pratico-1-2022-2023/ex1.m |     40 +
 2ano1/MPEI/trabalho-pratico-1-2022-2023/ex2.m |     52 +
 2ano1/MPEI/trabalho-pratico-1-2022-2023/ex3.m |    108 +
 .../Exemplo_cod_Cadeia_Markov.m               |     50 +
 2ano1/MPEI/trabalho-pratico-1-2023-2024/L.mat |    Bin 0 -> 1585 bytes
 .../MPEI/trabalho-pratico-1-2023-2024/ex01.m  |     32 +
 .../MPEI/trabalho-pratico-1-2023-2024/ex02.m  |     37 +
 .../MPEI/trabalho-pratico-1-2023-2024/ex03.m  |    105 +
 .../CalculateSignatures.m                     |     23 +
 .../CalculateSignaturesWithShingles.m         |     34 +
 .../CountingBloomFilter.m                     |     34 +
 .../folha 1.jpg                               |    Bin 0 -> 1686927 bytes
 .../folha 2.jpg                               |    Bin 0 -> 1860646 bytes
 .../folha 3.jpg                               |    Bin 0 -> 1421332 bytes
 .../muxDJB31MA.m                              |     12 +
 .../trabalho-pratico-2-2023-2023-v2/parte1.m  |     37 +
 .../trabalho-pratico-2-2023-2023-v2/parte2.m  |     37 +
 .../processed.mat                             |    Bin 0 -> 533889 bytes
 .../restaurantes.txt                          |    215 +
 .../turistas1.data                            |  11533 +
 2ano1/MPEI/trabalho-pratico-2-2023-2024-v1    |      1 +
 118 files changed, 1109897 insertions(+)
 create mode 100644 2ano1/MPEI/aula01/analyticProbCoinToss.m
 create mode 100644 2ano1/MPEI/aula01/ex02_ex05.m
 create mode 100644 2ano1/MPEI/aula01/ex02_v1.m
 create mode 100644 2ano1/MPEI/aula01/ex02_v2.m
 create mode 100644 2ano1/MPEI/aula01/ex03.m
 create mode 100644 2ano1/MPEI/aula01/ex03_ex05.m
 create mode 100644 2ano1/MPEI/aula01/ex04.m
 create mode 100644 2ano1/MPEI/aula01/ex04_ex05.m
 create mode 100644 2ano1/MPEI/aula01/ex05.m
 create mode 100644 2ano1/MPEI/aula01/ex07.m
 create mode 100644 2ano1/MPEI/aula01/probCoinToss.m
 create mode 100644 2ano1/MPEI/aula02/ex01.m
 create mode 100644 2ano1/MPEI/aula02/ex02.m
 create mode 100644 2ano1/MPEI/aula02/ex03.m
 create mode 100644 2ano1/MPEI/aula02/ex04.m
 create mode 100644 2ano1/MPEI/aula02/ex05.m
 create mode 100644 2ano1/MPEI/aula02/ex06.m
 create mode 100644 2ano1/MPEI/aula02/ex07.m
 create mode 100644 2ano1/MPEI/aula03/Binomial.m
 create mode 100644 2ano1/MPEI/aula03/NPPoisson.m
 create mode 100644 2ano1/MPEI/aula03/Poisson.m
 create mode 100644 2ano1/MPEI/aula03/ex01.m
 create mode 100644 2ano1/MPEI/aula03/ex02.m
 create mode 100644 2ano1/MPEI/aula03/ex03.m
 create mode 100644 2ano1/MPEI/aula03/ex04.m
 create mode 100644 2ano1/MPEI/aula03/ex05.m
 create mode 100644 2ano1/MPEI/aula03/ex06.m
 create mode 100644 2ano1/MPEI/aula03/ex07.m
 create mode 100644 2ano1/MPEI/aula03/ex08.m
 create mode 100644 2ano1/MPEI/aula03/ex09.m
 create mode 100644 2ano1/MPEI/aula04/ex01.asv
 create mode 100644 2ano1/MPEI/aula04/ex01.m
 create mode 100644 2ano1/MPEI/aula04/ex02.m
 create mode 100644 2ano1/MPEI/aula04/ex03.m
 create mode 100644 2ano1/MPEI/aula05/ex01.m
 create mode 100644 2ano1/MPEI/aula05/ex02.m
 create mode 100644 2ano1/MPEI/aula05/ex03.m
 create mode 100644 2ano1/MPEI/aula05/ex04.m
 create mode 100644 2ano1/MPEI/aula05/ex05.m
 create mode 100644 2ano1/MPEI/aula05/ex06.m
 create mode 100644 2ano1/MPEI/aula05/ex06_suplementar.m
 create mode 100644 2ano1/MPEI/aula06/ex07.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/BloomFilter.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/CalculateSignaturesWithShingles.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/SignatureForText.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/crawl.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/ex01.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/ex02.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/ex03.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/hf1.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/rand_keys.m
 create mode 100644 2ano1/MPEI/exame-pratico-2022-2023/string2hash.m
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/CalculateMinHash.m
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/CountingBloomFilter.m
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/cars3.xlsx
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/ex01.m
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/ex02.m
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/ex03.m
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/hf24.m
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/input.mat
 create mode 100644 2ano1/MPEI/exame-pratico-2023-2024/kHashValues.m
 create mode 100644 2ano1/MPEI/guiao04/Hashtable/hashtable.m
 create mode 100644 2ano1/MPEI/guiao04/Hashtable/hashtable_entry.m
 create mode 100644 2ano1/MPEI/guiao04/Hashtable/hashtable_examples.m
 create mode 100644 2ano1/MPEI/guiao04/Hashtable/hashtable_kv.m
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/DJB31MA.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/RandKeys_A.mat"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/RandKeys_B.mat"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex01.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex02.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex03.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/hashstring.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/prob_pt.txt"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/rand_keys.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/string2hash.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/BloomFilter.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/DJB31MA.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/ex05.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/wordlist-preao-20201103.txt"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistance.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistanceMinHash.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateMinHash.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CreateMoviesSet.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex01UserPairsDistance.mat"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex02UserPairsDistance.mat"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex04UserPairsDistance.mat"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/SimilarPairs.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex01.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex02.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex04.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/muxDJB31MA.m"
 create mode 100644 "2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/u.data"
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2022-2023/Folha 1.jpeg
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2022-2023/Folha 2.jpeg
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2022-2023/L.mat
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2022-2023/crawl.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2022-2023/ex1.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2022-2023/ex2.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2022-2023/ex3.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2023-2024/Exemplo_cod_Cadeia_Markov.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2023-2024/L.mat
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2023-2024/ex01.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2023-2024/ex02.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-1-2023-2024/ex03.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignatures.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignaturesWithShingles.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CountingBloomFilter.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/folha 1.jpg
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/folha 2.jpg
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/folha 3.jpg
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/muxDJB31MA.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte1.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte2.m
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/processed.mat
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/restaurantes.txt
 create mode 100644 2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/turistas1.data
 create mode 160000 2ano1/MPEI/trabalho-pratico-2-2023-2024-v1

diff --git a/.gitmodules b/.gitmodules
index a8dd3b8..80a7583 100644
--- a/.gitmodules
+++ b/.gitmodules
@@ -7,3 +7,6 @@
 [submodule "excalidraw"]
 	path = excalidraw
 	url = https://github.com/excalidraw/excalidraw.git
+[submodule "2ano1/MPEI/trabalho-pratico-2-2023-2024-v1"]
+	path = 2ano1/MPEI/trabalho-pratico-2-2023-2024-v1
+	url = https://github.com/JCapucho/Trabalho-MPEI-2.git
diff --git a/2ano1/MPEI/aula01/analyticProbCoinToss.m b/2ano1/MPEI/aula01/analyticProbCoinToss.m
new file mode 100644
index 0000000..0a50cb8
--- /dev/null
+++ b/2ano1/MPEI/aula01/analyticProbCoinToss.m
@@ -0,0 +1,3 @@
+function [probAnalitica] = analyticProbCoinToss(probCara, numLancamentos, numCaras)
+    probAnalitica = nchoosek(numLancamentos, numCaras) * (probCara^numCaras) * (1 - probCara)^(numLancamentos - numCaras);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex02_ex05.m b/2ano1/MPEI/aula01/ex02_ex05.m
new file mode 100644
index 0000000..d85c14b
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex02_ex05.m
@@ -0,0 +1,2 @@
+probSimulacao = probCoinToss(0.5, 3, 2, 1e5)
+probAnalitico = analyticProbCoinToss(0.5, 3, 2)
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex02_v1.m b/2ano1/MPEI/aula01/ex02_v1.m
new file mode 100644
index 0000000..2fc30fe
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex02_v1.m
@@ -0,0 +1,20 @@
+%% Codigo 1
+% Gerar uma matriz com 3 linhas e 10000 colunas de n´umeros aleat´orios
+% entre 0.0 e 1.0 (ou seja, cada coluna representa uma experiˆencia):
+experiencias = rand(3,10000);
+% Gerar uma matriz com 3 linhas e 10000 colunas com o valor 1 se o valor
+% da matriz anterior for superior a 0.5 (ou seja, se saiu cara) ou com o
+% valor 0 caso contr´ario (ou seja, saiu coroa):
+lancamentos = experiencias > 0.5; % 0.5 corresponde a 1 - prob. de caras
+% Gerar um vetor linha com 10000 elementos com a soma dos valores de cada
+% coluna da matriz anterior (ou seja, o n´umero de caras de cada experiˆencia):
+resultados = sum(lancamentos);
+% Gerar um vetor linha com 10000 elementos com o valor 1 quando o valor do
+% vetor anterior ´e 2 (ou seja, se a experiˆencia deu 2 caras) ou 0 quando ´e
+% diferente de 2:
+sucessos = resultados == 2;
+% Determinar o resultado final dividindo o n´umero de experiˆencias com 2
+% caras pelo n´umero total de experiˆencias:
+probSimulacao = sum(sucessos)/10000;
+
+fprintf("probSimulacao = %f\n", probSimulacao);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex02_v2.m b/2ano1/MPEI/aula01/ex02_v2.m
new file mode 100644
index 0000000..effa027
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex02_v2.m
@@ -0,0 +1,10 @@
+%% Codigo 2
+N= 1e5; %n´umero de experiˆencias
+p = 0.5; %probabilidade de cara
+k = 2; %n´umero de caras
+n = 3; %n´umero de lanc¸amentos
+lancamentos = rand(n,N) > 1-p;
+sucessos= sum(lancamentos)==k;
+probSimulacao= sum(sucessos)/N;
+
+fprintf("probSimulacao = %f\n", probSimulacao);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex03.m b/2ano1/MPEI/aula01/ex03.m
new file mode 100644
index 0000000..09bb9f0
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex03.m
@@ -0,0 +1,10 @@
+%% Codigo 3
+N= 1e5; %n´umero de experiˆencias
+p = 0.5; %probabilidade de cara
+k = 6; %n´umero de caras
+n = 15; %n´umero de lanc¸amentos
+lancamentos = rand(n,N) > 1-p;
+sucessos= sum(lancamentos)==k;
+probSimulacao= sum(sucessos)/N;
+
+fprintf("probSimulacao = %f\n", probSimulacao);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex03_ex05.m b/2ano1/MPEI/aula01/ex03_ex05.m
new file mode 100644
index 0000000..e9590db
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex03_ex05.m
@@ -0,0 +1,2 @@
+probSimulacao = probCoinToss(0.5, 15, 6, 1e5)
+probAnalitico = analyticProbCoinToss(0.5, 15, 6)
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex04.m b/2ano1/MPEI/aula01/ex04.m
new file mode 100644
index 0000000..8c98632
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex04.m
@@ -0,0 +1,12 @@
+%% Codigo 4
+N= 1e5; %n´umero de experiˆencias
+p = 0.5; %probabilidade de cara
+k = 6; %n´umero de caras
+n = 15; %n´umero de lanc¸amentos
+lancamentos = rand(n,N) > 1-p;
+% Pelos menos k lançamentos, o que signficia que
+% mais do que k e um caso favoravel.
+sucessos= sum(lancamentos)>=k;
+probSimulacao= sum(sucessos)/N;
+
+fprintf("probSimulacao = %f\n", probSimulacao);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex04_ex05.m b/2ano1/MPEI/aula01/ex04_ex05.m
new file mode 100644
index 0000000..475ada0
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex04_ex05.m
@@ -0,0 +1,7 @@
+probSimulacao = 0;
+
+for k = 6:15
+    probSimulacao = probSimulacao + probCoinToss(0.5, 15, k, 1e5);
+end
+
+fprintf("probSimulacao = %f\n", probSimulacao);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex05.m b/2ano1/MPEI/aula01/ex05.m
new file mode 100644
index 0000000..9fc5dda
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex05.m
@@ -0,0 +1,36 @@
+throws = 20;
+probSimulacao20 = zeros(1, throws + 1);
+for k = 0:throws
+    probSimulacao20(k + 1) = probCoinToss(0.5, throws, k, 1e4);
+end
+
+hold on
+stem(0:throws, probSimulacao20)
+stem(0:throws, arrayfun(@(k) analyticProbCoinToss(0.5, throws, k), 0:throws))
+hold off
+
+%%
+
+throws = 40;
+probSimulacao40 = zeros(1, throws + 1);
+for k = 0:throws
+    probSimulacao40(k + 1) = probCoinToss(0.5, throws, k, 1e4);
+end
+
+hold on
+stem(0:throws, probSimulacao40)
+stem(0:throws, arrayfun(@(k) analyticProbCoinToss(0.5, throws, k), 0:throws))
+hold off
+
+%%
+
+throws = 100;
+probSimulacao100 = zeros(1, throws + 1);
+for k = 0:throws
+    probSimulacao100(k + 1) = probCoinToss(0.5, throws, k, 1e4);
+end
+
+hold on
+stem(0:throws, probSimulacao100)
+stem(0:throws, arrayfun(@(k) analyticProbCoinToss(0.5, throws, k), 0:throws))
+hold off
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/ex07.m b/2ano1/MPEI/aula01/ex07.m
new file mode 100644
index 0000000..85c6cca
--- /dev/null
+++ b/2ano1/MPEI/aula01/ex07.m
@@ -0,0 +1,27 @@
+%% Parte a)
+probSimulacao = probCoinToss(0.3, 5, 3, 1e4)
+probAnalitico = analyticProbCoinToss(0.3, 5, 3)
+
+%% Parte b)
+
+probSimulacao = 0;
+probAnalitico = 0;
+
+for k = 0:2
+    probSimulacao = probSimulacao + probCoinToss(0.3, 5, k, 1e4)
+    probAnalitico = probAnalitico + analyticProbCoinToss(0.3, 5, k)
+end
+
+probSimulacao
+probAnalitico
+
+%% Parte c)
+
+
+probSimulacao = zeros(1, 6);
+
+for k = 0:5
+    probSimulacao(k + 1) = probCoinToss(0.3, 5, k, 1e4);
+end
+
+bar(0:5, probSimulacao)
\ No newline at end of file
diff --git a/2ano1/MPEI/aula01/probCoinToss.m b/2ano1/MPEI/aula01/probCoinToss.m
new file mode 100644
index 0000000..9b55ef2
--- /dev/null
+++ b/2ano1/MPEI/aula01/probCoinToss.m
@@ -0,0 +1,5 @@
+function [probSimulacao] = probCoinToss(probCara, numLancamentos, numCaras, numExperiencias)
+    lancamentos = rand(numLancamentos, numExperiencias) > (1 - probCara);
+    sucessos= sum(lancamentos) == numCaras;
+    probSimulacao= sum(sucessos) / numExperiencias;
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/aula02/ex01.m b/2ano1/MPEI/aula02/ex01.m
new file mode 100644
index 0000000..37c438e
--- /dev/null
+++ b/2ano1/MPEI/aula02/ex01.m
@@ -0,0 +1,82 @@
+%% a)
+N = 1e5;
+p = 0.5;
+
+nascimentos = rand(2, N);
+rapazes = nascimentos < p;
+numrapazes = sum(rapazes);
+
+A = numrapazes >= 1; % Pelo menos um rapaz
+
+prob = sum(A)/N
+
+%% b)
+
+% probabiliaded de nascer um filho
+%               +
+% probabilidade de nascerem dois filhos
+prob = 0.5 + 0.5 * 0.5
+
+%% c)
+
+N = 1e5;
+p = 0.5;
+
+nascimentos = rand(2, N);
+rapazes = nascimentos < p;
+numrapazes = sum(rapazes);
+
+A = numrapazes == 2; % Nasceram dois rapazes
+B = numrapazes >= 1; % Pelo menos um rapaz
+
+AB = A&B;
+
+prob = sum(AB)/sum(B)
+
+%% d)
+
+N = 1e5;
+p = 0.5;
+
+nascimentos = rand(2, N);
+rapazes = nascimentos < p;
+numrapazes = sum(rapazes);
+
+A = numrapazes == 2; % Nasceram dois rapazes
+B = rapazes(1,:) == 1; % Primeiro e rapaz
+
+AB = A&B;
+
+prob = sum(AB)/sum(B)
+
+%% e)
+
+N = 1e5;
+p = 0.5;
+
+nascimentos = rand(5, N);
+rapazes = nascimentos < p;
+numrapazes = sum(rapazes);
+
+A = numrapazes == 2; % Nasceram dois rapazes
+B = numrapazes >= 1; % Pelo menos um rapaz
+
+AB = A&B;
+
+prob = sum(AB)/sum(B)
+
+%% f)
+
+N = 1e5;
+p = 0.5;
+
+nascimentos = rand(5, N);
+rapazes = nascimentos < p;
+numrapazes = sum(rapazes);
+
+A = numrapazes >= 2; % Nasceram dois rapazes
+B = numrapazes >= 1; % Pelo menos um rapaz
+
+AB = A&B;
+
+prob = sum(AB)/sum(B)
\ No newline at end of file
diff --git a/2ano1/MPEI/aula02/ex02.m b/2ano1/MPEI/aula02/ex02.m
new file mode 100644
index 0000000..e479b18
--- /dev/null
+++ b/2ano1/MPEI/aula02/ex02.m
@@ -0,0 +1,89 @@
+%% a)
+
+n = 20;
+m = 100;
+
+N = 1e5;
+
+lancamentos = randi(m, n, N);
+
+A = false(1, N); 
+
+for i=1:N
+    diferentes = unique(lancamentos(:,i));
+    A(i) = length(diferentes) == n;
+end
+
+prob = sum(A)/N
+
+%% b)
+
+n = 20;
+m = 100;
+
+N = 1e5;
+
+lancamentos = randi(m, n, N);
+
+A = false(1, N);
+
+for i=1:N
+    diferentes = unique(lancamentos(:,i));
+    A(i) = length(diferentes) < n;
+end
+
+prob = sum(A)/N
+
+%% c)
+
+N = 1e5;
+x = 10:10:100;
+m = [1000 100000];
+
+for m_idx = 1:length(m)
+    alvos = m(m_idx);
+
+    y = zeros(1, length(x));
+
+    for x_idx=1:length(x)
+        n = x(x_idx);
+        lancamentos = randi(alvos, n, N);
+        
+        A = false(1, N);
+    
+        for i=1:N
+            diferentes = unique(lancamentos(:,i));
+            A(i) = length(diferentes) < n;
+        end
+
+        y(x_idx) = sum(A)/N;
+    end
+
+    subplot(1, length(m), m_idx);
+    plot(x, y);
+    title(sprintf("Alvos = %d", alvos));
+end
+
+%% d)
+
+N = 1e5;
+n = 100;
+m = [200 500 1000 2000 5000 10000 20000 50000 100000];
+
+y = zeros(1, length(m));
+
+for x_idx=1:length(m)
+    alvos = m(x_idx);
+    lancamentos = randi(alvos, n, N);
+    
+    A = false(1, N);
+
+    for i=1:N
+        diferentes = unique(lancamentos(:,i));
+        A(i) = length(diferentes) < n;
+    end
+
+    y(x_idx) = sum(A)/N;
+end
+
+plot(m, y);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula02/ex03.m b/2ano1/MPEI/aula02/ex03.m
new file mode 100644
index 0000000..7e43ad5
--- /dev/null
+++ b/2ano1/MPEI/aula02/ex03.m
@@ -0,0 +1,68 @@
+%% a)
+
+N = 1e5;
+T = 1000;
+keys = 10;
+
+distribution = randi(T, keys, N);
+
+A = false(1, N); 
+
+for i=1:N
+    diferentes = unique(distribution(:,i));
+    A(i) = length(diferentes) < keys;
+end
+
+prob = sum(A) / N
+
+%% b)
+
+N = 1e3;
+T = 1000;
+keys_array = 10:10:1000;
+
+A = false(1, N);
+
+y = zeros(1, length(keys_array));
+
+for x_idx=1:length(keys_array)
+    keys = keys_array(x_idx);
+    distribution = randi(T, keys, N);
+    
+    A = false(1, N);
+
+    for i=1:N
+        diferentes = unique(distribution(:,i));
+        A(i) = length(diferentes) < keys;
+    end
+
+    y(x_idx) = sum(A)/N;
+end
+
+plot(keys_array, y);
+
+%% c)
+
+N = 1e4;
+T_array = 100:100:1000;
+keys = 50;
+
+A = false(1, N);
+
+y = zeros(1, length(T_array));
+
+for x_idx=1:length(T_array)
+    T = T_array(x_idx);
+    distribution = randi(T, keys, N);
+    
+    A = false(1, N);
+
+    for i=1:N
+        diferentes = unique(distribution(:,i));
+        A(i) = length(diferentes) < keys;
+    end
+
+    y(x_idx) = sum(A)/N;
+end
+
+plot(T_array, y);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula02/ex04.m b/2ano1/MPEI/aula02/ex04.m
new file mode 100644
index 0000000..18e8427
--- /dev/null
+++ b/2ano1/MPEI/aula02/ex04.m
@@ -0,0 +1,28 @@
+N = 1e5;
+people_array = 20:50;
+
+A = false(1, N);
+
+y = zeros(1, length(people_array));
+
+for x_idx=1:length(people_array)
+    people = people_array(x_idx);
+    distribution = randi(365, people, N);
+    
+    A = false(1, N);
+
+    for i=1:N
+        diferentes = unique(distribution(:,i));
+        A(i) = length(diferentes) < people;
+    end
+
+    y(x_idx) = sum(A)/N;
+end
+
+n50 = find(y > 0.5, 1) + people_array(1) - 1;
+n90 = find(y > 0.9, 1) + people_array(1) - 1;
+
+fprintf("a) P > 0.5: n=%d\n", n50);
+fprintf("b) P > 0.9: n=%d\n", n90);
+
+plot(people_array, y);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula02/ex05.m b/2ano1/MPEI/aula02/ex05.m
new file mode 100644
index 0000000..5015d88
--- /dev/null
+++ b/2ano1/MPEI/aula02/ex05.m
@@ -0,0 +1,35 @@
+% a)
+sides = 6;
+tries = 2;
+
+N = 1e5;
+
+lancamentos = randi(sides, tries, N);
+
+A = sum(lancamentos) == 9;
+B = rem(lancamentos(2,:), 2) == 0;
+C = sum(lancamentos == 5) >= 1;
+D = sum(lancamentos == 1) == 0;
+
+A_prob = sum(A)/N;
+B_prob = sum(B)/N;
+C_prob = sum(C)/N;
+D_prob = sum(D)/N;
+
+fprintf("P(A) = %f | P(B) = %f | P(C) = %f | P(D) = %f\n", ...
+    A_prob, B_prob, C_prob, D_prob);
+
+% b)
+% P(A) = 4/36 = 1/9
+% P(B) = 1/2
+% - `P(AB)`: Probabilidade da soma dos dois valores ser 9
+%            e o segundo valor ser possivel, casos possiveis:
+%              3 6 | 5 4
+% P(AB) = 1/18 = 1/2 * 1/9 = P(A)P(B)
+
+% c)
+% P(C) = 11/36
+% P(D) = 25/36
+% - `P(CD)`: Probabilidade de pelo menos um dos valores ser
+%            5 e nenhum dos valores ser 1.
+% P(CD) = 9/36 != P(A)P(B) = 11/36 * 25/36 = 275/1296
\ No newline at end of file
diff --git a/2ano1/MPEI/aula02/ex06.m b/2ano1/MPEI/aula02/ex06.m
new file mode 100644
index 0000000..7ffec68
--- /dev/null
+++ b/2ano1/MPEI/aula02/ex06.m
@@ -0,0 +1,28 @@
+% a)
+% Existem 3^2 = 9 possiveis sequencias o que
+% significa que a possibilidade de uma dada
+% sequencia e de 1/9.
+
+% b)
+% "um" pode aparecer em 5 sequencias distintas, se
+% assumirmos que aparece na primeira posicao entao
+% existem tres sequencias, porque existem 3 possibilidades
+% para a segunda palavra, se depois assumirmos que
+% aparece na segunda posicao existem mais outra duas
+% posicoes, uma com cada palavra possivel exceto "um"
+% na primeira possivel.
+% Logo a probabilidade e de 5/9.
+
+% c)
+% Aplicando a mesma logica do exercicio anterior,
+% existem 6 casos favoraveis se uma destas palavras
+% tiver na primeira posicao, depois mais dois se
+% estiver na segunda posicao.
+% A probabilidade sera de 8/9.
+
+% d)
+% "sequencia incluir a palavra um" | "sequencia inclui palavra dois"
+% A probabilidade da sequencia incluir a palavra dois e de 5/9 (ver
+% alinea b). P("sequencia incluir a palavra um" & "sequencia inclui palavra dois")
+% e igual a 2/9.
+% Logo temos que a probabilidade sera igual a (2/9)/(5/9) = 2/5.
\ No newline at end of file
diff --git a/2ano1/MPEI/aula02/ex07.m b/2ano1/MPEI/aula02/ex07.m
new file mode 100644
index 0000000..f4e9ccc
--- /dev/null
+++ b/2ano1/MPEI/aula02/ex07.m
@@ -0,0 +1,69 @@
+N = 1e6;
+total = 100;
+
+programas = zeros(total, N);
+
+% Andre
+programas(1:20, :) = rand(20, N) < 0.01;
+% Bruno
+programas(21:50, :) = rand(30, N) < 0.05;
+% Carlos
+programas(51:end, :) = rand(50, N) < 0.001;
+
+select = randi(total, 1, N);
+
+% a)
+possiveis = zeros(1, N);
+carlos = zeros(1, N);
+
+% b)
+andre = zeros(1, N);
+bruno = zeros(1, N);
+
+for k=1:N
+    idx = select(k);
+    defeito = programas(idx, k);
+    possiveis(k) = defeito;
+    % a)
+    carlos(k) = defeito & idx > 50;
+    % b)
+    andre(k) = defeito & idx < 21;
+    bruno(k) = defeito & idx > 20 & idx < 51;
+end
+
+prob_carlos = sum(carlos&possiveis)/sum(possiveis);
+prob_andre = sum(andre&possiveis)/sum(possiveis);
+prob_bruno = sum(bruno&possiveis)/sum(possiveis);
+
+% a)
+fprintf("P(C|E) = %f\n", prob_carlos);
+% b)
+fprintf("P(A|E) = %f\n", prob_andre);
+fprintf("P(B|E) = %f\n", prob_bruno);
+
+[~, I] = max([prob_andre, prob_bruno, prob_carlos]);
+names = ["Andre", "Bruno", "Carlos"];
+worst = names(I);
+
+fprintf("%s e o mais provavel\n", worst);
+
+%% Teorico
+% a)
+%
+% P(E) = P(E|A)P(A) + P(E|B)P(B) + P(E|C)P(C)
+%      = 0.01*(1/5) + 0.05*(3/10) + 0.001*(1/2)
+%      = 0.0175
+%
+% P(C&E) = P(E|C)P(C) = 0.001*(1/2) = 0.0005
+%
+% P(C|E) = P(C&E)/P(E) = 0.0005/0.0175 ~= 0.02857
+%
+% b)
+%
+% P(A&E) = P(E|A)P(A) = 0.01*(1/5) = 0.002
+% P(A|E) = P(A&E)/P(E) = 0.002/0.0175 ~= 0.11428
+%
+% P(B&E) = P(E|B)P(B) = 0.05*(3/10) = 0.015
+% P(B|E) = P(B&E)/P(E) = 0.015/0.0175 ~= 0.85714
+%
+% P(C|E) < P(A|E) < P(B|E) - O Bruno e o mais provavel
diff --git a/2ano1/MPEI/aula03/Binomial.m b/2ano1/MPEI/aula03/Binomial.m
new file mode 100644
index 0000000..dc95c9f
--- /dev/null
+++ b/2ano1/MPEI/aula03/Binomial.m
@@ -0,0 +1,3 @@
+function [dist_prob] = Binomial(n, k, p)
+    dist_prob = nchoosek(n, k) * p^k * (1-p)^(n-k);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/NPPoisson.m b/2ano1/MPEI/aula03/NPPoisson.m
new file mode 100644
index 0000000..8060c53
--- /dev/null
+++ b/2ano1/MPEI/aula03/NPPoisson.m
@@ -0,0 +1,4 @@
+function [dist_prob] = NPPoisson(n, k, p)
+    lambda = n * p;
+    dist_prob = Poisson(lambda, k);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/Poisson.m b/2ano1/MPEI/aula03/Poisson.m
new file mode 100644
index 0000000..4534fdd
--- /dev/null
+++ b/2ano1/MPEI/aula03/Poisson.m
@@ -0,0 +1,4 @@
+% Regra prática: n > 20 e np <= 7
+function [dist_prob] = Poisson(lambda, k)
+    dist_prob = (lambda.^k) ./ factorial(k) .* exp(-lambda);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex01.m b/2ano1/MPEI/aula03/ex01.m
new file mode 100644
index 0000000..4ebe567
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex01.m
@@ -0,0 +1,20 @@
+% a)
+lados = [1 2 3 4 5 6];
+probs = zeros(length(lados), 1) + 1/length(lados);
+
+subplot(2, 1, 1);
+bar(probs);
+title("Funcao massa probabilidade");
+xlabel("lado");
+ylabel("p(x)");
+
+% b)
+accum_probs = cumsum(probs);
+
+subplot(2, 1, 2);
+stairs(accum_probs);
+title("Funcao distribuicao acumulada");
+xlabel("lado");
+ylabel("F(x)");
+xlim([0 7]);
+ylim([0 1.1]);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex02.m b/2ano1/MPEI/aula03/ex02.m
new file mode 100644
index 0000000..b005944
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex02.m
@@ -0,0 +1,17 @@
+
+%% c)
+notas_5 = 90;
+notas_50 = 9;
+notas_100 = 1;
+
+total = notas_5 + notas_50 + notas_100;
+
+p5 = notas_5 / total;
+p50 = notas_50 / total;
+p100 = notas_100 / total;
+
+notas = [0 5 50 100 120];
+accum_probs = cumsum([0 p5 p50 p100 0]);
+
+stairs(notas, accum_probs);
+ylim([0 1.1])
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex03.m b/2ano1/MPEI/aula03/ex03.m
new file mode 100644
index 0000000..408e1a5
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex03.m
@@ -0,0 +1,76 @@
+% a)
+p = 0.5;
+N = 1e5;
+
+lancamentos = rand(4, N);
+coroas = sum(lancamentos < p);
+
+[gc, grps] = groupcounts(coroas');
+
+probs = gc/N;
+
+stem(grps, probs);
+title("Funcao massa probabilidade");
+xlabel("coroas");
+ylabel("p(x)");
+
+fprintf("a)\n");
+
+for i = 1:length(grps)
+    fprintf("\tp(%d) = %f\n", grps(i), probs(i))
+end
+
+% b)
+esperado = sum(probs .* grps);
+variancia = sum((grps - esperado).^2 .* probs);
+desvio = sqrt(variancia);
+
+fprintf("b)\n");
+
+fprintf("\tMedia = %f\n", esperado);
+fprintf("\tVariancia = %f\n", variancia);
+fprintf("\tDesvio = %f\n", desvio);
+
+% c)
+
+n = max(grps);
+fprintf("c)\n");
+fprintf("\tDistribuicao binomial p=%f e n=%d\n", p, n);
+
+% d)
+
+fprintf("d)\n")
+
+dist_probs = zeros(1, n + 1);
+
+for k=0:n
+    dist_prob = nchoosek(n, k) * p^k * (1-p)^(n-k);
+    dist_probs(k + 1) = dist_prob;
+    fprintf("\tp(%d) = %f\n", k, dist_prob);
+end
+
+% e)
+
+grps = 0:n;
+esperado = sum(dist_probs .* grps);
+variancia = sum((grps - esperado).^2 .* dist_probs);
+desvio = sqrt(variancia);
+
+fprintf("e)\n");
+
+fprintf("\tMedia = %f\n", esperado);
+fprintf("\tVariancia = %f\n", variancia);
+fprintf("\tDesvio = %f\n", desvio);
+
+% f)
+
+caso_i = sum(dist_probs(3:end));
+caso_ii = sum(dist_probs(1:2));
+caso_iii = sum(dist_probs(2:4));
+
+fprintf("f)\n");
+
+fprintf("\ti. a probabilidade de obter pelo menos 2 coroas = %f\n", caso_i);
+fprintf("\tii. a probabilidade de obter at´e 1 coroa = %f\n", caso_ii);
+fprintf("\tiii. a probabilidade de obter entre 1 e 3 coroas = %f\n", caso_iii);
+
diff --git a/2ano1/MPEI/aula03/ex04.m b/2ano1/MPEI/aula03/ex04.m
new file mode 100644
index 0000000..ebdff3c
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex04.m
@@ -0,0 +1,71 @@
+%% a)
+p = 0.3;
+N = 1e5;
+
+lancamentos = rand(5, N);
+defeituosas = sum(lancamentos < p);
+
+[gc, grps] = groupcounts(defeituosas');
+
+probs = gc/N;
+
+subplot(2, 2, 1);
+stem(grps, probs);
+title("Funcao massa probabilidade");
+xlabel("defeituosas");
+ylabel("p(x)");
+
+fprintf("a)\ni)\n");
+
+for i = 1:length(grps)
+    fprintf("\tp(%d) = %f\n", grps(i), probs(i))
+end
+
+accum_probs = cumsum(probs);
+
+subplot(2, 2, 3);
+stairs([-1; grps; 6], [0; accum_probs; 1]);
+ylim([0 1.1]);
+title("Funcao distribuicao acumulada");
+xlabel("defeituosas");
+ylabel("F(x)");
+
+idx2 = find(grps == 2, 1);
+
+max_2_prob = sum(probs(1:idx2));
+
+fprintf("iii)\n");
+fprintf("\tprobabilidade de, no maximo, 2 das pecas de uma amostra serem defeituosas = %f\n", max_2_prob)
+
+%% b)
+p = 0.3;
+n = 5;
+fprintf("b)\ni)\n");
+
+dist_probs = zeros(1, n + 1);
+
+for k=0:n
+    dist_prob = nchoosek(n, k) * p^k * (1-p)^(n-k);
+    dist_probs(k + 1) = dist_prob;
+    fprintf("\tp(%d) = %f\n", k, dist_prob);
+end
+
+subplot(2, 2, 2);
+stem(0:n, dist_probs);
+title("Funcao massa probabilidade (analitico)");
+xlabel("defeituosas");
+ylabel("p(x)");
+
+accum_dist_probs = cumsum(dist_probs);
+
+subplot(2, 2, 4);
+stairs([-1 0:n 6], [0 accum_dist_probs 1]);
+ylim([0 1.1]);
+title("Funcao distribuicao acumulada (analitico)");
+xlabel("defeituosas");
+ylabel("F(x)");
+
+max_2_dist_prob = sum(dist_probs(1:3));
+
+fprintf("ii)\n");
+fprintf("\tprobabilidade de, no maximo, 2 das pecas de uma amostra serem defeituosas = %f\n", max_2_dist_prob)
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex05.m b/2ano1/MPEI/aula03/ex05.m
new file mode 100644
index 0000000..74ae61b
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex05.m
@@ -0,0 +1,21 @@
+N = 1e5;
+
+p = logspace(-3, log10(1/2) ,100);
+
+y_aviao2 = zeros(1, length(p));
+y_aviao4 = zeros(1, length(p));
+
+for k = 1:length(p)
+    prob_falha_aviao2 = rand(2, N);
+    falhas_aviao2 = sum(prob_falha_aviao2 < p(k));
+    y_aviao2(k) = sum(falhas_aviao2 > 1) / N;
+    
+    prob_falha_aviao4 = rand(4, N);
+    falhas_aviao4 = sum(prob_falha_aviao4 < p(k));
+    y_aviao4(k) = sum(falhas_aviao4 > 2) /N;
+end
+
+loglog(p, y_aviao2, "r")
+hold on
+loglog(p, y_aviao4, "g")
+hold off
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex06.m b/2ano1/MPEI/aula03/ex06.m
new file mode 100644
index 0000000..8fa360e
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex06.m
@@ -0,0 +1,7 @@
+p = 1/1000;
+
+% a)
+dist_prob = Binomial(8000, 7, p)
+
+% b)
+dist_prob = NPPoisson(8000, 7, p)
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex07.m b/2ano1/MPEI/aula03/ex07.m
new file mode 100644
index 0000000..1f1d6c4
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex07.m
@@ -0,0 +1,17 @@
+lambda = 15;
+% a)
+dist_prob0 = Poisson(15, 0)
+
+% b)
+k = 11;
+dist_prob11 = 0;
+while true
+    k_prob = Poisson(15, k);
+    dist_prob11 = dist_prob11 + k_prob;
+    if k_prob < 1/1e5
+        break
+    end
+    k = k + 1;
+end
+
+dist_prob11
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex08.m b/2ano1/MPEI/aula03/ex08.m
new file mode 100644
index 0000000..296349e
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex08.m
@@ -0,0 +1,3 @@
+lambda = 0.02 * 100;
+
+prob = sum(Poisson(lambda, 0:1))
\ No newline at end of file
diff --git a/2ano1/MPEI/aula03/ex09.m b/2ano1/MPEI/aula03/ex09.m
new file mode 100644
index 0000000..6a8ee13
--- /dev/null
+++ b/2ano1/MPEI/aula03/ex09.m
@@ -0,0 +1,22 @@
+N = 1e5;
+media = 14;
+desvio = 2;
+
+X = desvio * randn(1, N) + media;
+
+% a)
+p = sum(X >= 12 & X <= 16) / N;
+fprintf("Probabilidade evento A: %f\n", p);
+% b)
+p = sum(X >= 10 & X <= 18) / N;
+fprintf("Probabilidade evento B: %f\n", p);
+% c)
+p = sum(X >= 10) / N;
+fprintf("Probabilidade evento C: %f\n", p);
+% d)
+pc_A = normcdf(16, media, desvio) - normcdf(12, media, desvio);
+fprintf("Correcao evento A: %f\n", pc_A);
+pc_B = normcdf(18, media, desvio) - normcdf(10, media, desvio);
+fprintf("Correcao evento B: %f\n", pc_B);
+pc_C = normcdf(10, media, desvio, 'upper');
+fprintf("Correcao evento C: %f\n", pc_C);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula04/ex01.asv b/2ano1/MPEI/aula04/ex01.asv
new file mode 100644
index 0000000..d86a704
--- /dev/null
+++ b/2ano1/MPEI/aula04/ex01.asv
@@ -0,0 +1,21 @@
+N = 1e5;
+n = 8;
+
+p_1 = 0.002;
+p_2 = 0.005;
+p_a = 0.01;
+
+defeito_1 = rand(n, N) <= p_1;
+defeito_2 = rand(n, N) <= p_2;
+defeito_a = rand(n, N) <= p_a;
+
+defeito = defeito_1 | defeito_2 | defeito_a;
+
+% a)
+caixa_defeito = sum(defeito) > 0;
+prob = sum(caixa_defeito) / N
+printf("Evento A")
+
+% b)
+AB = sum(defeito_a & caixa_defeito);
+prob = sum(AB) / sum(caixa_defeito);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula04/ex01.m b/2ano1/MPEI/aula04/ex01.m
new file mode 100644
index 0000000..5e54750
--- /dev/null
+++ b/2ano1/MPEI/aula04/ex01.m
@@ -0,0 +1,22 @@
+N = 1e5;
+n = 8;
+
+p_1 = 0.002;
+p_2 = 0.005;
+p_a = 0.01;
+
+defeito_1 = rand(n, N) <= p_1;
+defeito_2 = rand(n, N) <= p_2;
+defeito_a = rand(n, N) <= p_a;
+
+defeito = defeito_1 | defeito_2 | defeito_a;
+
+% a)
+caixa_defeito = sum(defeito) > 0;
+prob = sum(caixa_defeito) / N;
+fprintf("Probabilidade evento A: %f\n", prob);
+
+% b)
+AB = sum(defeito_a & caixa_defeito);
+num_defeito_montagem = sum(AB) / sum(caixa_defeito);
+fprintf("Numero medio de defeito na montagem: %f\n", num_defeito_montagem);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula04/ex02.m b/2ano1/MPEI/aula04/ex02.m
new file mode 100644
index 0000000..fb7cfd7
--- /dev/null
+++ b/2ano1/MPEI/aula04/ex02.m
@@ -0,0 +1,30 @@
+N = 1e5;
+n = 8;
+
+p_1 = 0.002;
+p_2 = 0.005;
+p_a = 0.01;
+
+defeito_1 = rand(n, N) <= p_1;
+defeito_2 = rand(n, N) <= p_2;
+defeito_a = rand(n, N) <= p_a;
+
+defeito = defeito_1 | defeito_2 | defeito_a;
+
+% a)
+caixa_sem_defeito = sum(defeito) == 0;
+prob = sum(caixa_sem_defeito) / N;
+fprintf("Probabilidade evento B: %f\n", prob);
+
+% b)
+teorico = ((1-p_1) * (1 - p_2) * (1 - p_a))^8;
+fprintf("Probabilidade evento B (teorico): %f\n", teorico);
+
+% c)
+x = 2:20;
+y = ((1-p_1) * (1 - p_2) * (1 - p_a)).^x;
+plot(x, y, "-o");
+
+% d)
+maximo = find(y >= 0.9, 1, 'last') + 1;
+fprintf("Tamanho maximo caixa: %d\n", maximo);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula04/ex03.m b/2ano1/MPEI/aula04/ex03.m
new file mode 100644
index 0000000..476649c
--- /dev/null
+++ b/2ano1/MPEI/aula04/ex03.m
@@ -0,0 +1,33 @@
+N = 1e5;
+n = 16;
+
+p_1 = 0.002;
+p_2 = 0.005;
+p_a = 0.01;
+
+defeito_1 = rand(n, N) <= p_1;
+defeito_2 = rand(n, N) <= p_2;
+defeito_a = rand(n, N) <= p_a;
+
+defeito = defeito_1 | defeito_2 | defeito_a;
+
+% a)
+[gc, grps] = groupcounts(sum(defeito)');
+
+probs = gc/N;
+
+stem(grps, probs);
+
+% b)
+favoraveis = sum((grps >= 2) .* gc);
+prob = favoraveis / N;
+fprintf("Probabilidade de X >= 2: %f\n", prob);
+
+% c)
+esperado = sum(probs .* grps);
+variancia = sum((grps - esperado).^2 .* probs);
+desvio = sqrt(variancia);
+
+fprintf("Media = %f\n", esperado);
+fprintf("Variancia = %f\n", variancia);
+fprintf("Desvio = %f\n", desvio);
diff --git a/2ano1/MPEI/aula05/ex01.m b/2ano1/MPEI/aula05/ex01.m
new file mode 100644
index 0000000..d5be3b9
--- /dev/null
+++ b/2ano1/MPEI/aula05/ex01.m
@@ -0,0 +1,32 @@
+% Coluna 1 - Nao esteve presente na anterior
+% Coluna 2 - Esteve presente na anterior
+% Linha 1 - Nao vai a aula
+% Linha 2 - Vai a aula
+T = [0.2, 0.3; 0.8, 0.7];
+
+% a)
+I = [0; 1];
+probs = T^2*I;
+fprintf("a) P = %f\n", probs(2));
+
+% b)
+I = [1; 0];
+probs = T^2*I;
+fprintf("b) P = %f\n", probs(2));
+
+% c)
+I = [0; 1];
+probs = T^30*I;
+fprintf("c) P = %f\n", probs(2));
+
+% d)
+I = [0.15; 0.85];
+x = 0:1:30;
+
+y = zeros(1, length(x));
+for i=x
+    probs = T^i*I;
+    y(i + 1) = probs(1);
+end
+
+plot(x, y, "+-", "Color", [0, 0, 1, 0.3]);
diff --git a/2ano1/MPEI/aula05/ex02.m b/2ano1/MPEI/aula05/ex02.m
new file mode 100644
index 0000000..4d8ebac
--- /dev/null
+++ b/2ano1/MPEI/aula05/ex02.m
@@ -0,0 +1,33 @@
+% Coluna - Estado anterior
+% Linha - Estado atual
+% Linha/Coluna 1 - Grupo A
+% Linha/Coluna 2 - Grupo B
+% Linha/Coluna 3 - Grupo C
+T = [1/3, 1/4, 0;
+     1/3, 11/20, 1/2;
+     1/3, 1/5, 1/2];
+
+% a)
+estocastica = all(sum(T) == [1, 1, 1]);
+fprintf("a) Estocastica? = %s\n", string(estocastica));
+
+% b)
+alunos = 90;
+I = [2/3; 1/6; 1/6];
+
+% c)
+dist = T^30*I;
+grupos = alunos * dist;
+
+fprintf("c) Grupo A = %f\n", grupos(1));
+fprintf("   Grupo B = %f\n", grupos(2));
+fprintf("   Grupo C = %f\n", grupos(3));
+
+% d)
+I = [1/3; 1/3; 1/3];
+dist = T^30*I;
+grupos = alunos * dist;
+
+fprintf("d) Grupo A = %f\n", grupos(1));
+fprintf("   Grupo B = %f\n", grupos(2));
+fprintf("   Grupo C = %f\n", grupos(3));
\ No newline at end of file
diff --git a/2ano1/MPEI/aula05/ex03.m b/2ano1/MPEI/aula05/ex03.m
new file mode 100644
index 0000000..98d8b79
--- /dev/null
+++ b/2ano1/MPEI/aula05/ex03.m
@@ -0,0 +1,16 @@
+N = 20;
+T = rand(N);
+T = T ./ sum(T);
+
+% a)
+estocastica = all(abs(1 - sum(T)) < 1e-15);
+fprintf("a) Estocastica? = %s\n", string(estocastica));
+
+% b)
+I = zeros(N, 1);
+I(1) = 1;
+
+for k=[2, 5, 10, 100]
+    probs = T^k*I;
+    fprintf("b) Prob. em %d transicoes: %.5f%%\n", k, probs(20) * 100);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/aula05/ex04.m b/2ano1/MPEI/aula05/ex04.m
new file mode 100644
index 0000000..103e458
--- /dev/null
+++ b/2ano1/MPEI/aula05/ex04.m
@@ -0,0 +1,38 @@
+p = 0.4;
+q = 0.6;
+
+% Coluna - Estado anterior
+% Linha - Estado atual
+% Estados: A B C D
+T = [p^2,     0, 0, q^2;
+     (1-p)^2, 0, 0, q*(1-q);
+     p*(1-p), 0, 0, q*(1-q);
+     p*(1-p), 1, 1, (1-q)^2];
+
+% a)
+estocastica = all(abs(1 - sum(T)) < 1e-15);
+fprintf("a) Estocastica? = %s\n", string(estocastica));
+
+% b)
+I = [1; 0; 0; 0];
+
+for k=[5, 10, 100, 200]
+    probs = T^k*I;
+    fprintf("b) %d transicoes\n", k);
+    fprintf("  Prob. estado A: %.5f%%\n", probs(1) * 100);
+    fprintf("  Prob. estado B: %.5f%%\n", probs(2) * 100);
+    fprintf("  Prob. estado C: %.5f%%\n", probs(3) * 100);
+    fprintf("  Prob. estado D: %.5f%%\n", probs(4) * 100);
+end
+
+% c)
+N = length(T);
+M=[T - eye(N); ones(1, N)];
+x = [zeros(N, 1); 1];
+u = M\x;
+
+fprintf("c)\n");
+fprintf("  Prob. estado A: %.5f%%\n", u(1) * 100);
+fprintf("  Prob. estado B: %.5f%%\n", u(2) * 100);
+fprintf("  Prob. estado C: %.5f%%\n", u(3) * 100);
+fprintf("  Prob. estado D: %.5f%%\n", u(4) * 100);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula05/ex05.m b/2ano1/MPEI/aula05/ex05.m
new file mode 100644
index 0000000..9d9e1dd
--- /dev/null
+++ b/2ano1/MPEI/aula05/ex05.m
@@ -0,0 +1,76 @@
+% a)
+
+% Coluna - Estado anterior
+% Linha - Estado atual
+% Estados: Sol Nuvens Chuva
+T = [0.7, 0.2, 0.3;
+     0.2, 0.3, 0.3;
+     0.1, 0.5, 0.4];
+
+estocastica = all(abs(1 - sum(T)) < 1e-15);
+fprintf("a) Estocastica? = %s\n", string(estocastica));
+
+I = [1; 0; 0];
+seguinte = T*I;
+
+% b)
+prob = seguinte(1)^2;
+fprintf("b) Prob. dois dias = %.5f%%\n", prob * 100);
+
+% c)
+I_nao_chuva = seguinte;
+I_nao_chuva(3) = 0;
+I_nao_chuva = I_nao_chuva ./ sum(I_nao_chuva);
+
+nao_chuva_seguinte = T*I_nao_chuva;
+prob = (1 - seguinte(3)) * (1 - nao_chuva_seguinte(3));
+fprintf("c) Prob. dois dias = %.5f%%\n", prob * 100);
+
+% d)
+I = [1; 0; 0];
+dias = 31;
+medio = I;
+
+for k=1:dias- 1
+    x=T^k * I;
+    medio = medio + x;
+end
+
+fprintf("d)\n");
+fprintf("  Medio dias sol = %f\n", medio(1));
+fprintf("  Medio dias nuvens = %f\n", medio(2));
+fprintf("  Medio dias chuva = %f\n", medio(3));
+
+% e)
+I = [0; 0; 1];
+dias = 31;
+medio = I;
+
+for k=1:dias- 1
+    x=T^k * I;
+    medio = medio + x;
+end
+
+fprintf("e)\n");
+fprintf("  Medio dias sol = %f\n", medio(1));
+fprintf("  Medio dias nuvens = %f\n", medio(2));
+fprintf("  Medio dias chuva = %f\n", medio(3));
+
+% f)
+probs = [0.1; 0.3; 0.5];
+I_sol = [1; 0; 0];
+I_chuva = [0; 0; 1];
+dias = 31;
+medio_sol = sum(probs .* I_sol);
+medio_chuva = sum(probs .* I_chuva);
+
+for k=1:dias- 1
+    x_sol = T^k * I_sol;
+    medio_sol = medio_sol + sum(probs .* x_sol);
+    x_chuva = T^k * I_chuva;
+    medio_chuva = medio_chuva + sum(probs .* x_chuva);
+end
+
+fprintf("f)\n");
+fprintf("  N medio dias com dores, se primeiro dia for sol = %f\n", medio_sol);
+fprintf("  N medio dias com dores, se primeiro dia for chuva = %f\n", medio_chuva);
\ No newline at end of file
diff --git a/2ano1/MPEI/aula05/ex06.m b/2ano1/MPEI/aula05/ex06.m
new file mode 100644
index 0000000..01ef878
--- /dev/null
+++ b/2ano1/MPEI/aula05/ex06.m
@@ -0,0 +1,68 @@
+% a)
+% Coluna - Estado anterior
+% Linha - Estado atual
+% Estados: 1 2 4 3 5
+%          Estados absorventes no final
+T = [0.8 0   0.3 0   0;
+     0.2 0.6 0.2 0   0;
+     0   0.1 0.4 0   0;
+     0   0.3 0   1   0;
+     0   0   0.1 0   1];
+
+estocastica = all(abs(1 - sum(T)) < 1e-15);
+fprintf("a) Estocastica? = %s\n", string(estocastica));
+
+% b)
+fprintf("b) grafico 1\n");
+x = 1:100;
+y = zeros(1, length(x));
+
+inicial = [1 0 0 0 0]';
+
+for k=x
+    estado = T^k * inicial;
+    y(k) = estado(2);
+end
+
+plot(x, y)
+
+% c)
+fprintf("c) grafico 2\n");
+x = 1:100;
+y1 = zeros(1, length(x));
+y2 = zeros(1, length(x));
+
+inicial = [1 0 0 0 0]';
+
+for k=x
+    estado = T^k * inicial;
+    y1(k) = estado(4);
+    y2(k) = estado(5);
+end
+
+figure
+plot(x, y1, "red")
+hold on
+plot(x, y2, "blue")
+hold off
+
+% d)
+fprintf("d)\n");
+Q = T(1:3, 1:3)
+
+% e)
+fprintf("e)\n");
+F = (eye(length(Q)) - Q)^-1
+
+% f)
+fprintf("f)\n");
+t = F' * ones(length(F), 1)
+
+% g)
+fprintf("g)\n");
+
+R = T(4:5, 1:3);
+B = R * F;
+
+fprintf("Prob. absorcacao 1 -> 3: %f\n", B(1, 1))
+fprintf("Prob. absorcacao 1 -> 5: %f\n", B(2, 1))
\ No newline at end of file
diff --git a/2ano1/MPEI/aula05/ex06_suplementar.m b/2ano1/MPEI/aula05/ex06_suplementar.m
new file mode 100644
index 0000000..5ef767b
--- /dev/null
+++ b/2ano1/MPEI/aula05/ex06_suplementar.m
@@ -0,0 +1,106 @@
+T = [0.8 0   0.3 0   0;
+     0.2 0.6 0.2 0   0;
+     0   0.1 0.4 0   0;
+     0   0.3 0   1   0;
+     0   0   0.1 0   1];
+
+%% a)
+N = 1e5;
+
+start1 = zeros(1, N);
+start2 = zeros(1, N);
+start4 = zeros(1, N);
+
+for k=1:N
+    state = crawl(T, 1, [4 5]);
+    start1(k) = length(state) - 1;
+    state = crawl(T, 2, [4 5]);
+    start2(k) = length(state) - 1;
+    state = crawl(T, 3, [4 5]);
+    start4(k) = length(state) - 1;
+end
+
+fprintf("f)\n")
+fprintf("Passos medios comecando em 1: %f\n", sum(start1) / N);
+fprintf("Passos medios comecando em 2: %f\n", sum(start2) / N);
+fprintf("Passos medios comecando em 4: %f\n", sum(start4) / N);
+
+%% a-g)
+N = 1e5;
+
+end3 = 0;
+end5 = 0;
+
+for k=1:N
+    state = crawl(T, 1, [4 5]);
+    if state(end) == 4
+        end3 = end3 + 1;
+    else
+        end5 = end5 + 1;
+    end
+end
+
+fprintf("g)\n")
+fprintf("Prob. absorcacao por 3: %f\n", end3 / N);
+fprintf("Prob. absorcacao por 5: %f\n", end5 / N);
+
+%% b)
+
+N = 10000;
+C = cell(1, N);
+
+for k=1:N
+    initial = randi([1, 3]);
+    C{k} = crawl(T, initial, [4 5]);
+end
+
+fprintf("b)\n")
+fprintf("Tamanho minimo: %f\n", min(cellfun(@length, C)));
+fprintf("Tamanho maximo: %f\n", max(cellfun(@length, C)));
+
+% Note:
+% if the Markov chain has more than 1 absorbing state the third argument
+% must be a vector with the absorbing states
+% for example in a chain with 5 states and considering that
+% states 4 and 5 are absorbing states:
+% state = crawl(H5, 1, [4 5])
+%
+% Random walk on the Markov chain
+% Inputs:
+% H - state transition matrix
+% first - initial state
+% last - terminal or absorving state
+function [state] = crawl(H, first, last)
+    % the sequence of states will be saved in the vector "state"
+    % initially, the vector contains only the initial state:
+    state = [first];
+    % keep moving from state to state until state "last" is reached:
+    while (1)
+        state(end+1) = nextState(H, state(end));
+        if ismember(state(end), last) % verifies if state(end) is absorbing
+            break;
+        end
+    end
+end
+
+% Returning the next state
+% Inputs:
+% H - state transition matrix
+% currentState - current state
+function state = nextState(H, currentState)
+    % find the probabilities of reaching all states starting at the current one:
+    probVector = H(:,currentState)'; % probVector is a row vector
+    n = length(probVector); %n is the number of states
+    % generate the next state randomly according to probabilities probVector:
+    state = discrete_rnd(1:n, probVector);
+end
+
+% Generate randomly the next state.
+% Inputs:
+% states = vector with state values
+% probVector = probability vector
+function state = discrete_rnd(states, probVector)
+    U=rand();
+    i = 1 + sum(U > cumsum(probVector));
+    state= states(i);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/aula06/ex07.m b/2ano1/MPEI/aula06/ex07.m
new file mode 100644
index 0000000..7787098
--- /dev/null
+++ b/2ano1/MPEI/aula06/ex07.m
@@ -0,0 +1,51 @@
+% a)
+% Coluna - Estado anterior
+% Linha - Estado atual
+% Estados: A B C D E F
+H = [0 0 0 0 1 0;
+     1 0 0 0 1 0;
+     0 1 0 1 0 0;
+     0 0 1 0 0 0;
+     0 1 0 0 0 0;
+     0 0 0 0 1 0];
+
+sites = length(H);
+links_saida = sum(H);
+H = H./(links_saida + (abs(links_saida)<eps));
+
+I = ones(sites, 1);
+I = I/sum(I);
+
+P = H^10 * I
+
+% b)
+% F e um dead end
+% O conjunto C e D e uma spider trap
+
+% c)
+dead_ends = find(links_saida == 0);
+H(:, dead_ends) = ones(sites, length(dead_ends))/sites;
+
+P_no_dead_end = H^10 * I
+
+% d)
+beta = 0.8;
+A = beta*H + (1-beta)*(ones(sites)/sites);
+
+P_google = A^10 * I
+
+passos = 1;
+prev_P = I;
+P = A*prev_P;
+
+while any(abs(P - prev_P) > 1e-4)
+    prev_P = P;
+    P = A*prev_P;
+
+    passos = passos + 1;
+end
+
+% Limite ou vetor estacionario
+M=[A - eye(sites); ones(1, sites)];
+x = [zeros(sites, 1); 1];
+u = M\x;
\ No newline at end of file
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/BloomFilter.m b/2ano1/MPEI/exame-pratico-2022-2023/BloomFilter.m
new file mode 100644
index 0000000..90a459b
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/BloomFilter.m
@@ -0,0 +1,51 @@
+classdef BloomFilter < handle
+    properties (Access = private)
+        members,
+        filter_array,
+        number_of_hashes,
+        hash_function
+    end
+    
+    methods
+        function obj = BloomFilter(n, k, hash)
+            obj.members = 0;
+            obj.filter_array = false(1, n);
+            obj.number_of_hashes = k;
+            obj.hash_function = hash;
+        end
+        
+        function [] = insert(obj, key)
+            key = convertStringsToChars(key);
+            n = length(obj.filter_array);
+            
+            for i=1:obj.number_of_hashes
+                key = [key num2str(i)];
+                h = obj.hash_function(key, n) + 1;
+                obj.filter_array(h) = true;
+            end
+            
+            obj.members = obj.members + 1;
+        end
+        
+        function [contained] = contains(obj, key)
+            key = convertStringsToChars(key);
+            n = length(obj.filter_array);
+            
+            for i=1:obj.number_of_hashes
+                key = [key num2str(i)];
+                h = obj.hash_function(key, n) + 1;
+                if ~obj.filter_array(h)
+                    contained = false;
+                    return
+                end
+            end
+            
+            contained = true;
+        end
+        
+        function [members] = get_members(obj)
+            members = obj.members;
+        end
+    end
+end
+
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/CalculateSignaturesWithShingles.m b/2ano1/MPEI/exame-pratico-2022-2023/CalculateSignaturesWithShingles.m
new file mode 100644
index 0000000..df7c2e1
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/CalculateSignaturesWithShingles.m
@@ -0,0 +1,16 @@
+function [assinaturas] = CalculateSignaturesWithShingles(Corpus, k_hashes)
+N = length(Corpus);
+
+assinaturas = zeros(N, k_hashes);
+
+h = waitbar(0,"Calculating signatures (with shingles)");
+
+for i=1:N
+    waitbar(i/N,h);
+    
+    assinaturas(i, :) = SignatureForText(Corpus{i}, k_hashes);
+end
+
+delete (h)
+end
+
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/SignatureForText.m b/2ano1/MPEI/exame-pratico-2022-2023/SignatureForText.m
new file mode 100644
index 0000000..fc39169
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/SignatureForText.m
@@ -0,0 +1,28 @@
+function [assinatura] = SignatureForText(text, k_hashes)
+assinatura = inf(1, k_hashes);
+
+k_grams = 3;
+
+text_length = length(text);
+
+% If the text is smaller than the shingle size, then consider the
+% full text as a shingle, there are some titles that are only 1 char
+% long, so independent of `k_grams` (except for 1) we need this.
+if text_length < k_grams
+	for hashFuncN=1:k_hashes
+		hash = hf1(text, hashFuncN);
+		assinatura(hashFuncN) = min(hash, assinatura(hashFuncN));
+	end
+end
+
+for shingle_start=1:(text_length - k_grams + 1)
+	shingle_end = shingle_start + k_grams - 1;
+	shingle = text(shingle_start:shingle_end);
+	
+	for hashFuncN=1:k_hashes
+		hash = hf1(shingle, hashFuncN);
+		assinatura(hashFuncN) = min(hash, assinatura(hashFuncN));
+	end
+end
+end
+
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/crawl.m b/2ano1/MPEI/exame-pratico-2022-2023/crawl.m
new file mode 100644
index 0000000..35501b4
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/crawl.m
@@ -0,0 +1,37 @@
+% Random walk on the Markov chain
+% Inputs:
+% H - state transition matrix
+% first - initial state
+% last - terminal or absorving state
+function [state] = crawl(H, first, last)
+% the sequence of states will be saved in the vector "state"
+% initially, the vector contains only the initial state:
+state = [first];
+% keep moving from state to state until state "last" is reached:
+while (1)
+	state(end+1) = nextState(H, state(end));
+	if ismember(state(end), last) % verifies if state(end) is absorbing
+		break;
+	end
+end
+end
+% Returning the next state
+% Inputs:
+% H - state transition matrix
+% currentState - current state
+function state = nextState(H, currentState)
+% find the probabilities of reaching all states starting at the current one:
+probVector = H(:,currentState)'; % probVector is a row vector
+n = length(probVector); %n is the number of states
+% generate the next state randomly according to probabilities probVector:
+state = discrete_rnd(1:n, probVector);
+end
+% Generate randomly the next state.
+% Inputs:
+% states = vector with state values
+% probVector = probability vector
+function state = discrete_rnd(states, probVector)
+U=rand();
+i = 1 + sum(U > cumsum(probVector));
+state= states(i);
+end
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/ex01.m b/2ano1/MPEI/exame-pratico-2022-2023/ex01.m
new file mode 100644
index 0000000..8dfa7bb
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/ex01.m
@@ -0,0 +1,44 @@
+% Considere um jogo de tabuleiro para crianças muito simples e que envolve 2
+% jogadores de cada vez. Neste jogo, cada jogador parte da casa 1 e ganha o que
+% chegar mais depressa a casa /Meta/.
+%
+% O percurso de cada jogador desde a casa 1 até à casa /Meta/ segue o diagrama
+% a seguir que indica as casas para onde o jogador se pode mover durante o jogo.
+% A escolha do percurso depende do resultado do lançamento de uma moeda ao ar
+% que não é equilibrada (moeda diferente em cada casa). O resultado do
+% lançamento em cada casa depende de um parâmetro /alpha_i/, sendo /i/ o
+% número da casa. Nas alíneas seguintes assuma
+alpha = [0.2, 0, 0.3, 0.1, 0.45];
+
+% Parte A
+
+% Coluna - Estado anterior
+% Linha - Estado atual
+T = [
+	0              0 0              0              0              0;
+	alpha(1)       0 0              0              0              0;
+	0              0 0              alpha(4)       alpha(5)       0;
+	0              0 alpha(3)       0              (1 - alpha(5)) 0;
+	(1 - alpha(1)) 1 (1 - alpha(3)) 0              0              0;
+	0              0 0              (1 - alpha(4)) 0              1;
+	];
+
+estocastica = all(abs(1 - sum(T)) < 1e-15);
+fprintf("(Sanity Check) Estocastica? = %s\n", string(estocastica));
+
+% Parte B
+% O caminho mais curto até a meta é 1 -> 5 -> 4 -> Meta
+
+P = T(5, 1) * T(4, 5) * T(6, 4);
+fprintf("b) Probabilidade = %f\n", P);
+
+% Parte C
+N_estados_absorventes = 1;
+Q = T(1:end-N_estados_absorventes, 1:end-N_estados_absorventes);
+
+F = (eye(length(Q)) - Q)^-1;
+
+% Tempo médio até absorção
+t = F' * ones(length(F), 1);
+
+fprintf("c) Número de passos médios até meta = %f\n", t(1) + 1);
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/ex02.m b/2ano1/MPEI/exame-pratico-2022-2023/ex02.m
new file mode 100644
index 0000000..0385403
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/ex02.m
@@ -0,0 +1,36 @@
+%% Parte A
+
+% P_fp ≈ (1 - e^(-km/n))^k
+k = 1;
+m = 300;
+
+P_fp = @(n) (1 - exp(-k*m ./ n)) .^ k;
+
+n = round(fzero(@(n) P_fp(n) - 0.03, [100, 10000]));
+
+fprintf("a) Número de elementos N = %f\n", n);
+
+% Manualmente
+% n = -m / ln(1 - P_fp) (para k = 1)
+
+%% Parte B
+
+words = rand_keys(10000, [5 8], 'a':'z', [0.4, 0.6]);
+
+filter = BloomFilter(n, k, @(key, size) mod(string2hash(key), size));
+
+for i=1:m
+	filter.insert(words{i});
+end
+
+false_positives = 0;
+test_words = (m + 1):length(words);
+for i=test_words
+	if filter.contains(words{i})
+		false_positives = false_positives + 1;
+	end
+end
+
+false_positive_rate = false_positives / length(test_words);
+
+fprintf("b) Taxa de falsos positivos = %f\n", false_positive_rate);
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/ex03.m b/2ano1/MPEI/exame-pratico-2022-2023/ex03.m
new file mode 100644
index 0000000..b818bbc
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/ex03.m
@@ -0,0 +1,20 @@
+Frases = {
+	'Lisboa e Porto são duas cidades importantes de Portugal.'
+	'Lisboa é a capital de Portugal.'
+	'Porto é a capital do Norte de Portugal.'
+	'Portugal não é só Lisboa e Porto.'
+	};
+
+k = 4;
+
+assinaturas = CalculateSignaturesWithShingles(Frases, k);
+
+Nf = length(Frases);
+
+J = zeros(Nf);
+for n1= 1:Nf
+	for n2 = n1+1:Nf
+		diff = sum(assinaturas(n1, :) ~= assinaturas(n2, :));
+		J(n1, n2) = diff / k;
+	end
+end
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/hf1.m b/2ano1/MPEI/exame-pratico-2022-2023/hf1.m
new file mode 100644
index 0000000..317d4b6
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/hf1.m
@@ -0,0 +1,37 @@
+function hashCode = hf1(shingle,nhf)
+% USAGE EXAMPLE: hc=hf1('abcd',3)
+% input : shingle  - string (of length 3)
+%         nhf      - number of the hash function to apply (1 to 5)
+% output: hashCode - from 0 to 1012 (M-1)
+
+l = 3;  % shingle length, don't change
+n = 5;  % max number of hash function
+
+M = 1013; % to limit hashcode to M-1
+
+if length(shingle) ~= l
+	fprintf(1,'ERROR! 1st parameter must have %d characters\n',l);
+	
+	hashCode = -1;
+	return
+end
+
+if nhf <1 || nhf > n
+	fprintf(1,'ERROR! hf number must be between 1 and %d\n',n);
+	hashCode = -1;
+	return
+end
+
+R =[15761,14189,65576,75776;
+	97062,42177, 3571,74315;
+	95719,91576,84915,39223;
+	48539,79223,93402,65549;
+	80030,95952,67875,17119];
+
+R=R(:,1:l);
+
+% each line of R defines a different hash function
+r=R(nhf,:);
+
+%   (\sum r * x ) mode M
+hashCode=mod(sum (r.*  double(shingle)),M);
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/rand_keys.m b/2ano1/MPEI/exame-pratico-2022-2023/rand_keys.m
new file mode 100644
index 0000000..41bb656
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/rand_keys.m
@@ -0,0 +1,48 @@
+function [keys] = rand_keys(N, lenghts,  alphabet, lenghts_probs, probs)
+arguments
+	N {mustBeInteger, mustBeNonnegative}
+	lenghts (1, :) {mustBeInteger, mustBeNonnegative}
+	alphabet (1, :)
+	lenghts_probs (:, 1) = ones(length(lenghts), 1) / length(lenghts)
+	% If the probabilities aren't passed to the function assume a uniform distribution
+	probs (:, 1) = ones(length(alphabet), 1) / length(alphabet)
+end
+% Helper function for generating N unique random strings that use the provided
+% alphabet with the probability distribution specified in probs and have lengths
+% as defined in the `lenghts` parameter which follows the probability distribution
+% specified in `length_probs`.
+
+% Pre allocate the result cell array
+keys = cell(1, N);
+
+% Do a first pass generating the N keys
+for i=1:N
+	keys{i} = generate_one_key(lenghts, lenghts_probs, alphabet, probs);
+end
+
+% Filter out duplicate keys
+keys = unique(keys);
+
+% Generate unique keys until the size of the cell array equals N
+while length(keys) ~= N
+	key = generate_one_key(lenghts, lenghts_probs, alphabet, probs);
+	if ~ismember(key, keys)
+		keys{length(keys) + 1} = key;
+	end
+end
+end
+
+function [key] = generate_one_key(lenghts, lenghts_probs, alphabet, probs)
+% Helper function to generate a random key
+
+% Randomize the key size
+U = rand();
+i = 1 + sum(U  > cumsum(lenghts_probs));
+tamanho = lenghts(i);
+
+% Generate random indices for the alphabet array based on the probabilities
+U = rand(1, tamanho);
+positions = 1 + sum(U > cumsum(probs));
+
+key = alphabet(positions);
+end
diff --git a/2ano1/MPEI/exame-pratico-2022-2023/string2hash.m b/2ano1/MPEI/exame-pratico-2022-2023/string2hash.m
new file mode 100644
index 0000000..efc8f0a
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2022-2023/string2hash.m
@@ -0,0 +1,48 @@
+function hash=string2hash(str,type)
+% This function generates a hash value from a text string
+%
+% hash=string2hash(str,type);
+%
+% inputs,
+%   str : The text string, or array with text strings.
+% outputs,
+%   hash : The hash value, integer value between 0 and 2^32-1
+%   type : Type of has 'djb2' (default) or 'sdbm'
+%
+% From c-code on : http://www.cse.yorku.ca/~oz/hash.html 
+%
+% djb2
+%  this algorithm was first reported by dan bernstein many years ago 
+%  in comp.lang.c
+%
+% sdbm
+%  this algorithm was created for sdbm (a public-domain reimplementation of
+%  ndbm) database library. it was found to do well in scrambling bits, 
+%  causing better distribution of the keys and fewer splits. it also happens
+%  to be a good general hashing function with good distribution.
+%
+% example,
+%
+%  hash=string2hash('hello world');
+%  disp(hash);
+%
+% Function is written by D.Kroon University of Twente (June 2010)
+
+
+% From string to double array
+str=double(str);
+if(nargin<2), type='djb2'; end
+switch(type)
+    case 'djb2'
+        hash = 5381*ones(size(str,1),1); 
+        for i=1:size(str,2), 
+            hash = mod(hash * 33 + str(:,i), 2^32-1); 
+        end
+    case 'sdbm'
+        hash = zeros(size(str,1),1);
+        for i=1:size(str,2), 
+            hash = mod(hash * 65599 + str(:,i), 2^32-1);
+        end
+    otherwise
+        error('string_hash:inputs','unknown type');
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/exame-pratico-2023-2024/CalculateMinHash.m b/2ano1/MPEI/exame-pratico-2023-2024/CalculateMinHash.m
new file mode 100644
index 0000000..6845111
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2023-2024/CalculateMinHash.m
@@ -0,0 +1,17 @@
+function [assinaturas] = CalculateMinHash(Set, Nl, k)
+assinaturas = inf(Nl, k);
+
+for u=1:Nl
+    items = Set(u, :);
+    
+    for item_idx=1:length(items)
+        item = items{item_idx};
+        
+        for hashFuncN=1:k
+            hash = hf24(item, hashFuncN);
+            assinaturas(u, hashFuncN) = min(hash, assinaturas(u, hashFuncN));
+        end
+    end
+end
+end
+
diff --git a/2ano1/MPEI/exame-pratico-2023-2024/CountingBloomFilter.m b/2ano1/MPEI/exame-pratico-2023-2024/CountingBloomFilter.m
new file mode 100644
index 0000000..f0202a5
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2023-2024/CountingBloomFilter.m
@@ -0,0 +1,34 @@
+classdef CountingBloomFilter < handle
+    properties (Access = private)
+        filter_array,
+        number_of_hashes,
+    end
+    
+    methods
+        function obj = CountingBloomFilter(n, k)
+            obj.filter_array = zeros(1, n);
+            obj.number_of_hashes = k;
+        end
+        
+        function [] = insert(obj, key)
+            n = length(obj.filter_array);
+            
+            hashes = kHashValues(key, obj.number_of_hashes);
+            positions = mod(hashes, n) + 1;
+            
+            for pos=positions
+                obj.filter_array(pos) = obj.filter_array(pos) + 1;
+            end
+        end
+        
+        function res = getInsertedAssured(obj, key)
+            n = length(obj.filter_array);
+            
+            hashes = kHashValues(key, obj.number_of_hashes);
+            positions = mod(hashes, n) + 1;
+            
+            res = min(obj.filter_array(positions));
+        end
+    end
+end
+
diff --git a/2ano1/MPEI/exame-pratico-2023-2024/cars3.xlsx b/2ano1/MPEI/exame-pratico-2023-2024/cars3.xlsx
new file mode 100644
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diff --git a/2ano1/MPEI/exame-pratico-2023-2024/ex01.m b/2ano1/MPEI/exame-pratico-2023-2024/ex01.m
new file mode 100644
index 0000000..e0ef4c8
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2023-2024/ex01.m
@@ -0,0 +1,35 @@
+% Parte A
+% Coluna - Estado anterior
+% Linha - Estado atual
+T = [
+	0 0   0.8 0 0;
+	1 0   0   0 0;
+	0 0.9 0   0 0;
+	0 0.1 0   1 0;
+	0 0   0.2 0 1
+	];
+
+estocastica = all(abs(1 - sum(T)) < 1e-15);
+fprintf("(Sanity Check) Estocastica? = %s\n", string(estocastica));
+
+% Parte B
+P = T^12 * [1 0 0 0 0]';
+fprintf("b) Probabilidade = %f\n", P(1));
+
+% Parte C
+N_estados_absorventes = 2;
+Q = T(1:end-N_estados_absorventes, 1:end-N_estados_absorventes);
+
+F = (eye(length(Q)) - Q)^-1;
+
+% Tempo médio até absorção
+t = F' * ones(length(F), 1);
+
+fprintf("c) Número médio de iterações até estado absorvente = %f\n", t(1));
+
+% Parte D
+R = T(end - N_estados_absorventes + 1:end, 1:end-N_estados_absorventes);
+
+B = R * F;
+
+fprintf("d) Prob. absorção 1 -> 4 = %f\n", B(1, 1));
diff --git a/2ano1/MPEI/exame-pratico-2023-2024/ex02.m b/2ano1/MPEI/exame-pratico-2023-2024/ex02.m
new file mode 100644
index 0000000..292f256
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2023-2024/ex02.m
@@ -0,0 +1,29 @@
+load input.mat
+
+Np = length(list);
+Na = sum(strcmp(list, 'Adão'));
+
+fprintf("a) Número de pessoas no universo = %f\n", Np);
+fprintf("a) Número de pessoas chamadas Adão = %f\n", Na);
+
+filter = CountingBloomFilter(500, 4);
+
+for i=1:Np
+	filter.insert(list{i});
+end
+
+fprintf("a) Número de pessoas chamadas Adão no bloom filter = %f\n", filter.getInsertedAssured('Adão'));
+
+% Parte B
+
+n = [0 0 0 0];
+
+for i=1:length(extra)
+	num = filter.getInsertedAssured(extra{i});
+	num = min(num, 3) + 1;
+	n(num) = n(num) + 1;
+end
+
+P = n / length(extra);
+
+fprintf("b) Prob. de 0: = %.5f\n Prob. de 1: = %.5f\n Prob. de 2: = %.5f\n Prob. de 3: = %.5f\n", P);
diff --git a/2ano1/MPEI/exame-pratico-2023-2024/ex03.m b/2ano1/MPEI/exame-pratico-2023-2024/ex03.m
new file mode 100644
index 0000000..6b191ca
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2023-2024/ex03.m
@@ -0,0 +1,15 @@
+tabela = readcell("cars3.xlsx", "NumHeaderLines", 1);
+
+S = size(tabela);
+Nl = S(1);
+
+k = 4;
+assinaturas = CalculateMinHash(tabela, Nl, k);
+
+J = zeros(Nl);
+for n1= 1:Nl
+	for n2 = n1+1:Nl
+		diff = sum(assinaturas(n1, :) ~= assinaturas(n2, :));
+		J(n1, n2) = diff / k;
+	end
+end
diff --git a/2ano1/MPEI/exame-pratico-2023-2024/hf24.m b/2ano1/MPEI/exame-pratico-2023-2024/hf24.m
new file mode 100644
index 0000000..4edd3f1
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2023-2024/hf24.m
@@ -0,0 +1,50 @@
+function hashCode = hf24(element,nhf)
+% USAGE EXAMPLE: hc=hf24('abcd',3)
+% input : element  - string 
+%         nhf      - number of the hash function to apply (1 to 5)
+% output: hashCode - from 0 to 1012 (M-1)     
+
+% AT, jan 2024
+
+%% configuration parameter. Do not chage
+l = 4;  %  length, don't change
+n = 5;  % max number of hash function
+M = 1013; % to limit hashcode to M-1
+ 
+
+%% check if nhf in the correct range
+if nhf <1 || nhf > n
+    fprintf(1,'ERROR! hf number must be between 1 and %d\n',n);
+    hashCode = -1;
+    return
+end
+
+
+%% use only l chars. Pad with spaces if  shorter than l
+if length(element) < l
+    desired_length = l;   
+    element = sprintf('%-*s', desired_length, element);   
+else
+    element = element(1:l); % keep only 1st l chars
+end
+
+
+R =[15761,14189,65576,75776;
+    97062,42177, 3571,74315;
+    95719,91576,84915,39223;
+    48539,79223,93402,65549;
+    80030,95952,67875,17119];
+
+R=R(:,1:l);
+ 
+% each line of R defines a different hash function
+r=R(nhf,:);
+
+%   (\sum r * x ) mode M
+hashCode=mod(sum (r.*  double(element)),M);
+
+% uncomment to see results during debugging 
+%fprintf("%s -> %d\n",element,hashCode)
+
+
+
diff --git a/2ano1/MPEI/exame-pratico-2023-2024/input.mat b/2ano1/MPEI/exame-pratico-2023-2024/input.mat
new file mode 100644
index 0000000000000000000000000000000000000000..c946d6fcbf2137b3b1c5126d50d78f82921d4b63
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literal 0
HcmV?d00001

diff --git a/2ano1/MPEI/exame-pratico-2023-2024/kHashValues.m b/2ano1/MPEI/exame-pratico-2023-2024/kHashValues.m
new file mode 100644
index 0000000..e91b4ba
--- /dev/null
+++ b/2ano1/MPEI/exame-pratico-2023-2024/kHashValues.m
@@ -0,0 +1,17 @@
+function out = kHashValues(key,k)
+% out = kHashValues(key,k)
+% key - row vector of characteres
+% k   - number of the hash functions
+% out - row vector with k hash values (each value between 0 and 2^32-1)   
+
+    out= zeros(1,k);
+    key=double(key);
+    hash = 5381; 
+    for i=1:length(key)
+        hash = mod(hash*33+key(i),2^32-1); 
+    end
+    for i= 1:k
+        hash = mod(hash*33+double(num2str(i)),2^32-1);
+        out(i)= hash;
+    end
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/guiao04/Hashtable/hashtable.m b/2ano1/MPEI/guiao04/Hashtable/hashtable.m
new file mode 100644
index 0000000..0cbcc2d
--- /dev/null
+++ b/2ano1/MPEI/guiao04/Hashtable/hashtable.m
@@ -0,0 +1,36 @@
+classdef hashtable < handle
+    properties (Access = private)
+        fun
+        size
+        buckets
+
+        collisions
+    end
+    
+    methods
+        function obj = hashtable(size, fun)
+            obj.fun = fun;
+            obj.size = size;
+            % Preallocate array
+            a = [hashtable_entry()];
+            a(size) = hashtable_entry();
+            obj.buckets = a;
+
+            obj.collisions = 0;
+        end
+        
+        function [] = add(obj, key, value)
+            hash = mod(obj.fun(key), obj.size - 1) + 1;
+
+            collided = obj.buckets(hash).add(key, value);
+            if collided
+                obj.collisions = obj.collisions + 1;
+            end
+        end
+
+        function collisions = get_collisions(obj)
+            collisions = obj.collisions;
+        end
+    end
+end
+
diff --git a/2ano1/MPEI/guiao04/Hashtable/hashtable_entry.m b/2ano1/MPEI/guiao04/Hashtable/hashtable_entry.m
new file mode 100644
index 0000000..b08547a
--- /dev/null
+++ b/2ano1/MPEI/guiao04/Hashtable/hashtable_entry.m
@@ -0,0 +1,30 @@
+classdef hashtable_entry < handle
+    properties (Access = private)
+        occupied
+        head
+    end
+    
+    methods
+        function obj = hashtable_entry()
+            obj.occupied = false;
+            obj.head = NaN;
+        end
+        
+        function [collided] = add(obj, key, value)
+            new_kv = hashtable_kv(key, value);
+
+            collided = obj.occupied;
+            if obj.occupied
+                obj.head.chain(new_kv);
+            else
+                obj.occupied = true;
+                obj.head = new_kv;
+            end
+        end
+
+        function occupied = is_occupied(obj)
+            occupied = obj.occupied;
+        end
+    end
+end
+
diff --git a/2ano1/MPEI/guiao04/Hashtable/hashtable_examples.m b/2ano1/MPEI/guiao04/Hashtable/hashtable_examples.m
new file mode 100644
index 0000000..a963a6c
--- /dev/null
+++ b/2ano1/MPEI/guiao04/Hashtable/hashtable_examples.m
@@ -0,0 +1,36 @@
+%% setup
+i_min = 6;
+i_max = 20;
+alphabet = ['a':'z', 'A':'Z'];
+keys = rand_keys(1e5, i_min, i_max, alphabet);
+
+%% tables
+for size=[5e5, 1e6, 2e6]
+    functions = {
+        {"string2hash (djb2)", @(key) string2hash(key, "djb2")};
+        {"string2hash (sdbm)", @(key) string2hash(key, "sdbm")};
+        {"hashstring", @(key) hashstring(key, size)};
+        {"DJB31MA", @(key) DJB31MA(key, 0)}
+        };
+
+    for f = 1:length(functions)
+        fun = functions{f}{2};
+        table = hashtable(size, fun);
+
+        for i=1:length(keys)
+            key = keys{i};
+            table.add(key, key);
+        end
+
+        fprintf("Finished for hashtable of size %d using %s\n", size, functions{f}{1});
+        fprintf("  Registered %d collisions\n", table.get_collisions());
+    end
+end
+
+
+%% test
+hashes = zeros(1, length(keys));
+for i=1:length(keys)
+    key = keys{i};
+    hashes(i) = hashstring(key, 5e5);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/guiao04/Hashtable/hashtable_kv.m b/2ano1/MPEI/guiao04/Hashtable/hashtable_kv.m
new file mode 100644
index 0000000..e97e2cb
--- /dev/null
+++ b/2ano1/MPEI/guiao04/Hashtable/hashtable_kv.m
@@ -0,0 +1,26 @@
+classdef hashtable_kv < handle
+    properties (Access = private)
+        key
+        value
+        next
+    end
+    
+    methods
+        function obj = hashtable_kv(key, value)
+            obj.key = key;
+            obj.value = value;
+            obj.next = NaN;
+        end
+        
+        function [] = chain(obj, next_kv)
+            if strcmp(obj.key, next_kv.key)
+                obj.value = next_kv.value;
+            elseif isa(obj.next, "double")
+                obj.next = next_kv;
+            else
+                obj.next.chain(next_kv);
+            end
+        end
+    end
+end
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/DJB31MA.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/DJB31MA.m"
new file mode 100644
index 0000000..82484ce
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/DJB31MA.m"	
@@ -0,0 +1,14 @@
+function h= DJB31MA( chave, seed)
+% implementação da hash function DJB31MA com base no algoritmo obtido
+% no resumo 2014(PJF) que está em C
+%
+%  chave    array de caracteres com a chave
+%  seed     semente que permite obter vários hash codes para a mesma chave
+%
+%  h        hashcode devolvido
+len= length(chave);
+chave= double(chave);
+h= seed;
+for i=1:len
+    h = mod(31 * h + chave(i), 2^32 -1) ;
+end
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/RandKeys_A.mat" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/RandKeys_A.mat"
new file mode 100644
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diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/RandKeys_B.mat" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/RandKeys_B.mat"
new file mode 100644
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diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex01.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex01.m"
new file mode 100644
index 0000000..326758f
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex01.m"	
@@ -0,0 +1,20 @@
+%% Alínea A
+i_min = 6;
+i_max = 20;
+alphabet = ['a':'z', 'A':'Z'];
+keys = rand_keys(1e5, i_min, i_max, alphabet);
+
+save RandKeys_A.mat keys
+
+%% Alínea B
+i_min = 6;
+i_max = 20;
+alphabet = 'a':'z';
+
+fileID = fopen('prob_pt.txt', 'r');
+probs = fscanf(fileID, "%f");
+fclose(fileID);
+
+keys = rand_keys(1e5, i_min, i_max, alphabet, probs);
+
+save RandKeys_B.mat keys
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex02.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex02.m"
new file mode 100644
index 0000000..130f876
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex02.m"	
@@ -0,0 +1,42 @@
+% setup
+load RandKeys_A.mat
+% For exercise 4
+% load RandKeys_B.mat
+
+% tables
+for size=[5e5, 1e6, 2e6]
+    functions = {
+        {"string2hash (djb2)", @(key) mod(string2hash(key, "djb2"), size)};
+        {"string2hash (sdbm)", @(key) mod(string2hash(key, "sdbm"), size)};
+        {"hashstring", @(key) hashstring(key, size)};
+        {"DJB31MA", @(key) mod(DJB31MA(key, 0), size)}
+        };
+    
+    for f = 1:length(functions)
+        hashes = zeros(1, length(keys));
+        
+        fprintf("Running for hashtable of size %d using %s\n", size, functions{f}{1});
+        
+        % Alínea D
+        tic
+        
+        % Alínea A
+        for i=1:length(keys)
+            key = keys{i};
+            hashes(i) = functions{f}{2}(key);
+        end
+        
+        % Alínea B
+        slots = length(unique(hashes));
+        
+        % Alínea C
+        collisions = length(keys) - slots;
+        
+        % Alínea D
+        time = toc;
+        
+        fprintf("  Used %d slots\n", slots);
+        fprintf("  Registered %d collisions\n", collisions);
+        fprintf("  Took %f seconds\n", time);
+    end
+end
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex03.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex03.m"
new file mode 100644
index 0000000..4dd7ff1
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/ex03.m"	
@@ -0,0 +1,65 @@
+% setup
+load RandKeys_A.mat
+% For exercise 4
+% load RandKeys_B.mat
+
+% Hash functions to be used
+functions = {
+    {"string2hash (djb2)", @(key, size) mod(string2hash(key, "djb2"), size)};
+    {"string2hash (sdbm)", @(key, size) mod(string2hash(key, "sdbm"), size)};
+    {"hashstring", @(key, size) hashstring(key, size)};
+    {"DJB31MA", @(key, size) mod(DJB31MA(key, 127), size)}
+    };
+
+for f = 1:length(functions)
+    % Hashtable sizes
+    sizes = [5e5, 1e6, 2e6];
+    
+    for j=1:length(sizes)
+        size = sizes(j);
+        
+        fprintf("Running for hashtable of size %d using %s\n", size, functions{f}{1});
+        
+        hashes = zeros(length(keys), 1);
+        
+        tic
+        
+        % Generate the hashes
+        for i=1:length(keys)
+            key = keys{i};
+            hashes(i) = functions{f}{2}(key, size);
+        end
+        
+        time = toc;
+        
+        % Alínea C
+        fprintf("   Took %f seconds\n", time);
+        
+        % Alínea B
+        slots = length(unique(hashes));
+        collisions = length(keys) - slots;
+        
+        fprintf("   Colisões=%d\n", collisions);
+        
+        % Calculate the maximum number of insertions
+        [GC, GR] = groupcounts(hashes);
+        [max_insert, idx] = max(GC);
+        max_insert_pos = GR(idx);
+        
+        fprintf("   Número máximo de inserções=%d (Posição %d)\n", max_insert, max_insert_pos);
+        
+        % Alínea A.i: plot the histogram
+        index = (j - 1) * length(functions) + f;
+        subplot(length(sizes), length(functions), index);
+        histogram(hashes, 100);
+        title(sprintf("%s with %d", functions{f}{1}, size));
+        
+        % Alínea A.ii: Determine the moments
+        for momento=[2, 5, 10]
+            teorico = 1/(momento + 1);
+            Hnorm = mean((hashes/size) .^ momento);
+            
+            fprintf("   Momento %d: teorico=%f; momento=%f\n", momento, teorico, Hnorm);
+        end
+    end
+end
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/hashstring.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/hashstring.m"
new file mode 100644
index 0000000..f11b01c
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/hashstring.m"	
@@ -0,0 +1,15 @@
+function code =  hashstring(chave, tablesize)
+%  baseado em hashstring the Programação II
+
+len=length(chave);
+chave= double(chave);
+hash=0;
+
+for i=1:len  
+
+    c = chave(i)+33;
+    %hash = ((hash<<3) + (hash>>28) + c);
+    hash= (bitshift(hash,3)+ bitshift(hash,-28))+c;
+end
+code=mod(hash,tablesize);
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/prob_pt.txt" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/prob_pt.txt"
new file mode 100644
index 0000000..db144c0
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/prob_pt.txt"	
@@ -0,0 +1,26 @@
+   1.4620000e-01
+   1.0400000e-02
+   3.8800000e-02
+   4.9900000e-02
+   1.2570000e-01
+   1.0200000e-02
+   1.3000000e-02
+   1.2800000e-02
+   6.1800000e-02
+   4.0000000e-03
+   2.0000000e-04
+   2.7800000e-02
+   4.7400000e-02
+   5.0500000e-02
+   1.0730000e-01
+   2.5200000e-02
+   1.2000000e-02
+   6.5300000e-02
+   7.8100000e-02
+   4.3400000e-02
+   4.6300000e-02
+   1.6700000e-02
+   1.0000000e-04
+   2.1000000e-03
+   1.0000000e-04
+   4.7000000e-03
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/rand_keys.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/rand_keys.m"
new file mode 100644
index 0000000..26e7017
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/rand_keys.m"	
@@ -0,0 +1,42 @@
+function [keys] = rand_keys(N, i_min, i_max, alphabet, probs)
+arguments
+    N {mustBeInteger, mustBeNonnegative}
+    i_min {mustBeInteger, mustBeNonnegative}
+    i_max {mustBeInteger, mustBeNonnegative, mustBeGreaterThan(i_max, i_min)}
+    alphabet (1, :)
+    % If the probabilities aren't passed to the function assume a uniform distribution
+    probs (:, 1) = ones(length(alphabet), 1) / length(alphabet)
+end
+
+% Pre allocate the result cell array
+keys = cell(1, N);
+
+% Do a first pass generating the N keys
+for i=1:N
+    keys{i} = generate_one_key(i_min, i_max, alphabet, probs);
+end
+
+% Filter out duplicate keys
+keys = unique(keys);
+
+% Generate unique keys until the size of the cell array equals N
+while length(keys) ~= N
+    key = generate_one_key(i_min, i_max, alphabet, probs);
+    if ~ismember(key, keys)
+        keys{length(keys) + 1} = key;
+    end
+end
+end
+
+function [key] = generate_one_key(i_min, i_max, alphabet, probs)
+% Helper function to generate a random key
+
+% Randomize the key size within the limits
+tamanho = randi(i_max - i_min) + i_min;
+
+% Generate random indices for the alphabet array based on the probabilities
+U = rand(1, tamanho);
+positions = 1 + sum(U > cumsum(probs));
+
+key = alphabet(positions);
+end
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/string2hash.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/string2hash.m"
new file mode 100644
index 0000000..efc8f0a
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 1/string2hash.m"	
@@ -0,0 +1,48 @@
+function hash=string2hash(str,type)
+% This function generates a hash value from a text string
+%
+% hash=string2hash(str,type);
+%
+% inputs,
+%   str : The text string, or array with text strings.
+% outputs,
+%   hash : The hash value, integer value between 0 and 2^32-1
+%   type : Type of has 'djb2' (default) or 'sdbm'
+%
+% From c-code on : http://www.cse.yorku.ca/~oz/hash.html 
+%
+% djb2
+%  this algorithm was first reported by dan bernstein many years ago 
+%  in comp.lang.c
+%
+% sdbm
+%  this algorithm was created for sdbm (a public-domain reimplementation of
+%  ndbm) database library. it was found to do well in scrambling bits, 
+%  causing better distribution of the keys and fewer splits. it also happens
+%  to be a good general hashing function with good distribution.
+%
+% example,
+%
+%  hash=string2hash('hello world');
+%  disp(hash);
+%
+% Function is written by D.Kroon University of Twente (June 2010)
+
+
+% From string to double array
+str=double(str);
+if(nargin<2), type='djb2'; end
+switch(type)
+    case 'djb2'
+        hash = 5381*ones(size(str,1),1); 
+        for i=1:size(str,2), 
+            hash = mod(hash * 33 + str(:,i), 2^32-1); 
+        end
+    case 'sdbm'
+        hash = zeros(size(str,1),1);
+        for i=1:size(str,2), 
+            hash = mod(hash * 65599 + str(:,i), 2^32-1);
+        end
+    otherwise
+        error('string_hash:inputs','unknown type');
+end
\ No newline at end of file
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/BloomFilter.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/BloomFilter.m"
new file mode 100644
index 0000000..90a459b
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/BloomFilter.m"	
@@ -0,0 +1,51 @@
+classdef BloomFilter < handle
+    properties (Access = private)
+        members,
+        filter_array,
+        number_of_hashes,
+        hash_function
+    end
+    
+    methods
+        function obj = BloomFilter(n, k, hash)
+            obj.members = 0;
+            obj.filter_array = false(1, n);
+            obj.number_of_hashes = k;
+            obj.hash_function = hash;
+        end
+        
+        function [] = insert(obj, key)
+            key = convertStringsToChars(key);
+            n = length(obj.filter_array);
+            
+            for i=1:obj.number_of_hashes
+                key = [key num2str(i)];
+                h = obj.hash_function(key, n) + 1;
+                obj.filter_array(h) = true;
+            end
+            
+            obj.members = obj.members + 1;
+        end
+        
+        function [contained] = contains(obj, key)
+            key = convertStringsToChars(key);
+            n = length(obj.filter_array);
+            
+            for i=1:obj.number_of_hashes
+                key = [key num2str(i)];
+                h = obj.hash_function(key, n) + 1;
+                if ~obj.filter_array(h)
+                    contained = false;
+                    return
+                end
+            end
+            
+            contained = true;
+        end
+        
+        function [members] = get_members(obj)
+            members = obj.members;
+        end
+    end
+end
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/DJB31MA.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/DJB31MA.m"
new file mode 100644
index 0000000..82484ce
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/DJB31MA.m"	
@@ -0,0 +1,14 @@
+function h= DJB31MA( chave, seed)
+% implementação da hash function DJB31MA com base no algoritmo obtido
+% no resumo 2014(PJF) que está em C
+%
+%  chave    array de caracteres com a chave
+%  seed     semente que permite obter vários hash codes para a mesma chave
+%
+%  h        hashcode devolvido
+len= length(chave);
+chave= double(chave);
+h= seed;
+for i=1:len
+    h = mod(31 * h + chave(i), 2^32 -1) ;
+end
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/ex05.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/ex05.m"
new file mode 100644
index 0000000..479ad28
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/ex05.m"	
@@ -0,0 +1,51 @@
+words = readlines('wordlist-preao-20201103.txt', 'EmptyLineRule', 'skip')';
+
+% k values from exercise 1 and 5
+hashes = 3:10;
+
+teoricos = zeros(1, length(hashes));
+praticos = zeros(1, length(hashes));
+
+for k_idx=1:length(hashes)
+    k = hashes(k_idx);
+    n = 8000;
+    
+    % Exercise 1: Create the bloom filter
+    filter = BloomFilter(n, k, @(key, size) mod(DJB31MA(key, 127), size));
+    
+    for word=words(1:1000)
+        filter.insert(word);
+    end
+    
+    % Exercise 2
+    for i=1:1000
+        % Verify that there are no false negatives
+        assert(filter.contains(words(i)));
+    end
+    
+    % Exercise 3: caculate false postives
+    false_positives = 0;
+    test_words = words(1001:11000);
+    for word=test_words
+        if filter.contains(word)
+            false_positives = false_positives + 1;
+        end
+    end
+    
+    false_positive_rate = false_positives / length(test_words);
+    m = filter.get_members();
+    % Exercise 4
+    teorico = (1 - (1 - 1/n)^(k * m))^k;
+    
+    praticos(k_idx) = false_positive_rate;
+    teoricos(k_idx) = teorico;
+end
+
+%%
+plot(hashes, praticos, 'b', 'DisplayName', 'Simulação');
+title("False positives rate");
+xlabel("k-values");
+hold on
+plot(hashes, teoricos, 'r', 'DisplayName', 'Teóricos');
+legend('location', 'best');
+hold off
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/wordlist-preao-20201103.txt" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/wordlist-preao-20201103.txt"
new file mode 100644
index 0000000..7e79db4
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 2/wordlist-preao-20201103.txt"	
@@ -0,0 +1,994898 @@
+AAC
+ABC
+ACP
+AD
+ADN
+ADSL
+AFP
+AML
+AMP
+ANACOM
+ANC
+ANMP
+APEL
+API
+APL
+APPACDM
+ARS
+ASAE
+ASCII
+AVC
+Aachen
+Aalborg
+Aarhus
+Abecassis
+Abel
+Abissínia
+Aboim
+Abraham
+Abrams
+Abrantes
+Abraão
+Abreu
+Abril
+Abu
+Abílio
+Acre
+Acácio
+Adalberto
+Adamastor
+Adams
+Adelaide
+Adelina
+Adelino
+Adelson
+Adolfo
+Adriana
+Adriano
+Adriático
+Adão
+Adélia
+Adérito
+Adónis
+Afeganistão
+Afonso
+Afrodite
+Agostinho
+Agostinhos
+Agosto
+Agra
+Agraço
+Aguiar
+Aida
+Aires
+Aix-en-Provence
+Aix-la-Chapelle
+Alandroal
+Alarico
+Alasca
+Alba
+Albano
+Albergaria-a-Nova
+Albergaria-a-Velha
+Albert
+Albertina
+Albertino
+Alberto
+Albino
+Albufeira
+Albuquerque
+Albânia
+Alcanena
+Alcino
+Alcinos
+Alcobaça
+Alcochete
+Alcoforado
+Alcorão
+Alcoutim
+Alcácer
+Alcântara
+Aldora
+Aleixo
+Alemanha
+Alencar
+Alenquer
+Alentejo
+Alexandra
+Alexandre
+Alexandria
+Alfragide
+Alfredo
+Algarve
+Algarves
+Algodres
+Algés
+Alhambra
+Alhandra
+Alicante
+Alice
+Alijó
+Aljezur
+Aljubarrota
+Aljustrel
+Allen
+Almada
+Almançor
+Almeida
+Almeirim
+Almodôvar
+Almortão
+Alpes
+Alpiarça
+Alportel
+Alqueva
+Alsácia
+Aluísio
+Alvaiázere
+Alvalade
+Alverca
+Alves
+Alvim
+Alvito
+Alzira
+Alá
+Alípio
+Amadeu
+Amadeus
+Amado
+Amadora
+Amapá
+Amaral
+Amarante
+Amares
+Amaro
+Amato
+Amazonas
+Amazónia
+Ambrósio
+Amesterdão
+Amorim
+Amália
+Amâncio
+Amândio
+Amã
+Amélia
+América
+Américas
+Américo
+Amílcar
+Ana
+Anabela
+Anadia
+Anastácio
+Anatólia
+Anaximandro
+Anaxímenes
+Ancara
+Andaluzia
+Andersen
+Andorra
+Andrade
+Andreia
+Andrews
+André
+Andrómeda
+Andy
+Angeiras
+Angeles
+Angkor
+Angola
+Angra
+Anguilha
+Angélica
+Aniceto
+Anita
+Anselmo
+Ansiães
+Ansião
+Antas
+Antero
+Antilhas
+Antioquia
+Antoine
+Antonieta
+Antunes
+Antuérpia
+Antárctida
+Antão
+Antónia
+António
+Aníbal
+Apalaches
+Aparício
+Apocalipse
+Apolinário
+Apolo
+Apolónia
+Apolónio
+Apple
+Apúlia
+Aquiles
+Aquilino
+Aquino
+Aquisgrana
+Aquitânia
+Arafat
+Aragão
+Aranjuez
+Araão
+Araújo
+Arcádia
+Ardenas
+Ardila
+Arganil
+Argel
+Argentina
+Argélia
+Argóvia
+Aristides
+Aristófanes
+Aristóteles
+Arizona
+Arkansas
+Arles
+Arlindo
+Armamar
+Armando
+Arminda
+Armindo
+Arménia
+Arménio
+Arnaldo
+Arno
+Arnold
+Arnoldo
+Arouca
+Arquimedes
+Arrabal
+Arraiolos
+Arronches
+Arruda
+Arrábida
+Artur
+Aruba
+Arábia
+Aspásia
+Assembler
+Assis
+Assunção
+Assíria
+Astérix
+Astúrias
+Atenas
+Atlanta
+Atlântico
+Atlântida
+Auckland
+Augusta
+Augustini
+Augusto
+Aurélia
+Aurélio
+Auschwitz
+Austrália
+Aveiro
+Avelar
+Aveleda
+Avelino
+Avicena
+Avilez
+Avinhão
+Avintes
+Avis
+Azambuja
+Azeitão
+Azeméis
+Azerbaijão
+Azevedo
+Açores
+BASIC
+BBC
+BCE
+BCI
+BCM
+BCP
+BD
+BE
+BESCL
+BFE
+BMW
+BNU
+BP
+BPA
+BPI
+BPSM
+BSE
+BT
+BVL
+Baamas
+Babilónia
+Bacelar
+Bach
+Baco
+Bacon
+Badajoz
+Bagdade
+Baiona
+Bairrada
+Baião
+Baker
+Balcãs
+Balsemão
+Baltasar
+Baltazar
+Baltimore
+Balzac
+Bangladeche
+Baptista
+Baptiste
+Barahona
+Barbosa
+Barcelona
+Barcelos
+Barnabé
+Barquinha
+Barrabás
+Barrancos
+Barreiro
+Barreiros
+Barreto
+Barroso
+Bartok
+Bartolomeu
+Basileia
+Basilicata
+Basilienses
+Bassorá
+Basto
+Bastos
+Basílio
+Baudelaire
+Baviera
+Baía
+Beatles
+Beatriz
+Beaumont
+Becket
+Beethoven
+Beijing
+Beirute
+Beja
+Belarmino
+Belchior
+Belfast
+Belgrado
+Belinda
+Belize
+Belmiro
+Belmonte
+Beltrão
+Belzebu
+Belém
+Benavente
+Benedito
+Benelux
+Benfica
+Bengala
+Benguela
+Benilde
+Benim
+Benjamin
+Bento
+Berengário
+Bergen
+Berger
+Bergman
+Bergson
+Berkeley
+Berlenga
+Berlim
+Berlioz
+Berna
+Bernard
+Bernardes
+Bernardino
+Bernardo
+Bernoulli
+Bernstein
+Berta
+Berto
+Bertrand
+Bessa
+Bettencourt
+Betânia
+Bielorrússia
+Bilbau
+Bill
+Birmânia
+Biscaia
+Bismarck
+Bissau
+Bizet
+Bié
+Bluetooth
+Boaventura
+Boavista
+Bocage
+Bogotá
+Bohr
+Bolena
+Bolonha
+Boltzmann
+Bolívia
+Bombaim
+Bombarda
+Bombarral
+Bona
+Bonaparte
+Bonapartismo
+Bonapartismos
+Bonapartista
+Bonapartistas
+Bonfim
+Bonifácio
+Bonjardim
+Boole
+Borba
+Bordalo
+Borges
+Borgonha
+Borguinhões
+Boris
+Bornéu
+Boston
+Botelho
+Botsuana
+Boulevard
+Bouro
+Bouvet
+Boximanes
+Boyle
+Brabante
+Bracara
+Bradenburgo
+Braga
+Bragança
+Brahms
+Brama
+Branca
+Brandeburgo
+Brandt
+Brandão
+Brasil
+Brasília
+Bratislava
+Braun
+Bremen
+Bretanha
+Breyner
+Brighton
+Briolanja
+Bristol
+Briteiros
+British
+Brito
+Britânia
+Brno
+Broadway
+Brooklyn
+Brown
+Bruce
+Bruges
+Bruno
+Brutus
+Bruxelas
+Brás
+Buarque
+Bucareste
+Buda
+Budapeste
+Buenos
+Bulgária
+Burgenland
+Burgos
+Burquina
+Burúndi
+Bush
+Buçaco
+Byron
+Báltico
+Bárbara
+Bélgica
+Bética
+Bíblia
+Bósnia
+Bósnia-Herzegovina
+CAD
+CAM
+CAP
+CCB
+CCRN
+CD
+CD-ROM
+CDS
+CDU
+CE
+CEI
+CES
+CGD
+CGTP
+CIG
+CIP
+CML
+CMP
+CMVM
+CNE
+CNN
+COI
+COP
+CP
+CPLP
+CREL
+CRIL
+CSCE
+CTT
+CV
+CVS
+Cabanelas
+Cabral
+Cabralismo
+Cabralismos
+Cabralista
+Cabralistas
+Cabul
+Cacilhas
+Cacém
+Cadaval
+Caeiro
+Caetano
+Caicos
+Caim
+Caio
+Cairo
+Calcedónia
+Calcutá
+Caldelas
+Caledónia
+Calheiro
+Calheiros
+Calheta
+Califórnia
+Calisto
+Calvin
+Calvinismo
+Calvinismos
+Calvinista
+Calvinistas
+Calvino
+Calábria
+Calígula
+Camacho
+Cambodja
+Cambra
+Cambridge
+Camelot
+Camilista
+Camilistas
+Camilo
+Campanhã
+Campus
+Campânia
+Camões
+Canadá
+Canaveses
+Canaã
+Caneças
+Cannes
+Cansas
+Cantanhede
+Cantuária
+Cantábria
+Cantão
+Canárias
+Capadócia
+Caparica
+Capricórnio
+Carachi
+Caraíbas
+Carcavelos
+Cardan
+Cardoso
+Carl
+Carla
+Carlos
+Carlota
+Carmelo
+Carminda
+Carmo
+Carmona
+Carnaxide
+Carnegie
+Carol
+Carolina
+Carrazeda
+Carregal
+Carrilho
+Carrol
+Cartago
+Cartaxo
+Cartuxa
+Carvalhas
+Carvalhos
+Carélia
+Caríntia
+Casablanca
+Casanova
+Cascais
+Casimiro
+Cassiano
+Cassinga
+Cassiopeia
+Castela
+Castilho
+Castro
+Catalunha
+Catar
+Catarina
+Catherine
+Catulo
+Catânia
+Cavaco
+Cavaquismo
+Cavaquismos
+Cavaquista
+Cavaquistas
+Caxias
+Cazaquistão
+Ceará
+Cecília
+Cedofeita
+Ceilão
+Celeste
+Celorico
+Celso
+Cenáculo
+Cerqueira
+Cervantes
+Cerveira
+Cesareia
+Cesário
+Ceuta
+Chade
+Chang
+Chaplin
+Charles
+Charlot
+Charlotte
+Chaves
+Checoslováquia
+Chen
+Cher
+Chevalier
+Chicago
+Chico
+Chile
+China
+Chipre
+Chomsky
+Chopin
+Christian
+Christopher
+Cid
+Cidália
+Cinderela
+Cinfães
+Cintra
+Cipião
+Cipriano
+Circe
+Cirilo
+Cisjordânia
+City
+Citânia
+Claire
+Clark
+Claude
+Claudel
+Clemente
+Clementina
+Cleópatra
+Clinton
+Clotilde
+Cluj
+Cláudia
+Cláudio
+Cobol
+Cohen
+Coimbra
+Colegiada
+College
+Collins
+Colombo
+Colonato
+Colorado
+Columbano
+Colômbia
+Colúmbia
+Comba
+Comores
+Compostela
+Conceição
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diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistance.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistance.m"
new file mode 100644
index 0000000..e639603
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistance.m"	
@@ -0,0 +1,15 @@
+function [J] = CalculateJaccardDistance(Set, users)
+    Nu = length(users);
+    J = zeros(Nu);
+    h = waitbar(0,"Calculating");
+    for n1= 1:Nu
+        waitbar(n1/Nu,h);
+        for n2 = n1+1:Nu
+            lI = length(intersect(Set{n1}, Set{n2}));
+            lU = length(union(Set{n1}, Set{n2}));
+            J(n1, n2) = 1 - lI / lU;
+        end
+    end
+    delete (h)
+end
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistanceMinHash.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistanceMinHash.m"
new file mode 100644
index 0000000..3f8254f
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateJaccardDistanceMinHash.m"	
@@ -0,0 +1,17 @@
+function [J] = CalculateJaccardDistanceMinHash(Set, users, k)
+    Nu = length(users);
+
+    assinaturas = CalculateMinHash(Set, Nu, k);
+
+    J = zeros(Nu);
+    h = waitbar(0,"Calculating distances");
+    for n1= 1:Nu
+        waitbar(n1/Nu,h);
+        for n2 = n1+1:Nu
+            diff = sum(assinaturas(n1, :) ~= assinaturas(n2, :));
+            J(n1, n2) = diff / k;
+        end
+    end
+    delete (h)
+end
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateMinHash.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateMinHash.m"
new file mode 100644
index 0000000..6167d4f
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CalculateMinHash.m"	
@@ -0,0 +1,21 @@
+function [assinaturas] = CalculateMinHash(Set, Nu, k)
+assinaturas = inf(Nu, k);
+
+h = waitbar(0,"Calculating signatures");
+
+for u=1:Nu
+    waitbar(u/Nu,h);
+    
+    items = Set{u};
+    
+    for item_idx=1:length(items)
+        item = items(item_idx);
+        hash = muxDJB31MA(item, 127, k);
+        
+        assinaturas(u, :) = min(hash, assinaturas(u, :));
+    end
+end
+
+delete (h)
+end
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CreateMoviesSet.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CreateMoviesSet.m"
new file mode 100644
index 0000000..00accd3
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/CreateMoviesSet.m"	
@@ -0,0 +1,10 @@
+function [Set] = CreateMoviesSet(data, users)
+    Nu = length(users);
+    Set = cell(Nu,1);
+    for n = 1:Nu
+        % Stores in position ’n’ of the cell array the movies of user ’users(n)’:
+        ind = data(:,1) == users(n);
+        Set{n} = [Set{n} data(ind, 2)];
+    end
+end
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex01UserPairsDistance.mat" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex01UserPairsDistance.mat"
new file mode 100644
index 0000000000000000000000000000000000000000..518ff0953c24150af5e5a794b35189a196d2c1d0
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diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex02UserPairsDistance.mat" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex02UserPairsDistance.mat"
new file mode 100644
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diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex04UserPairsDistance.mat" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/Ex04UserPairsDistance.mat"
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diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/SimilarPairs.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/SimilarPairs.m"
new file mode 100644
index 0000000..613d51d
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/SimilarPairs.m"	
@@ -0,0 +1,14 @@
+function [SimilarUsers] = SimilarPairs(J, users, threshold)
+    Nu = length(users);
+    SimilarUsers= zeros(1,3);       % Array to store: user1, user2, distance
+    k= 1;
+    for n1= 1:Nu
+        for n2= n1+1:Nu
+            if J(n1, n2) < threshold
+                SimilarUsers(k,:) = [users(n1) users(n2) J(n1,n2)];
+                k= k+1;
+            end
+        end
+    end
+end
+
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex01.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex01.m"
new file mode 100644
index 0000000..d606a21
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex01.m"	
@@ -0,0 +1,56 @@
+% Base code for finding similar sets
+% Loads the data file:
+udata = load('u.data');
+% Keeps only the two first columns:
+u = udata(1:end,1:2);
+clear udata;
+% Determines the list of users:
+users = unique(u(:,1));         % Extracts the unique user IDs
+Nu = length(users);             % Computes the total number of users
+
+% Creates the data structure with the set of movies of each user
+% (uses a cell array since each user has a different number of movies):
+Set = cell(Nu,1);
+for n = 1:Nu
+    % Stores in position ’n’ of the cell array the movies of user ’users(n)’:
+    ind = find(u(:,1) == users(n));
+    Set{n} = [Set{n} u(ind,2)];
+end
+
+% Calculates the Jaccard distance between the movie sets of all user pairs:
+J = zeros(Nu);                 % initialize the matrix of the distances
+h = waitbar(0,"Calculating");
+tic
+for n1= 1:Nu
+    waitbar(n1/Nu,h);
+    for n2 = n1+1:Nu
+        lI = length(intersect(Set{n1}, Set{n2}));
+        lU = length(union(Set{n1}, Set{n2}));
+        J(n1, n2) = 1 - lI / lU;
+    end
+end
+calcTime = toc;
+delete (h)
+
+% Determines the most similar pairs of users, in terms of their movie sets:
+threshold = 0.4                 % similarity threshold
+SimilarUsers= zeros(1,3);       % Array to store: user1, user2, distance
+k= 1;
+tic
+for n1= 1:Nu
+    for n2= n1+1:Nu
+        if J(n1, n2) < threshold
+            SimilarUsers(k,:) = [users(n1) users(n2) J(n1,n2)];
+            k= k+1;
+        end
+    end
+end
+checkTime = toc;
+
+fprintf("Took %f seconds to calculate the distante\n", calcTime);
+fprintf("Took %f seconds to check the distance threshold\n", checkTime);
+fprintf("Got %d similar users\n", length(SimilarUsers));
+
+SimilarUsers
+
+save Ex01UserPairsDistance.mat J
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex02.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex02.m"
new file mode 100644
index 0000000..c4e2f6e
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex02.m"	
@@ -0,0 +1,32 @@
+% Base code for finding similar sets
+% Loads the data file:
+udata = load('u.data');
+% Keeps only the two first columns:
+u = udata(1:end,1:2);
+clear udata;
+% Determines the list of users:
+users = unique(u(:,1));         % Extracts the unique user IDs
+Nu = length(users);             % Computes the total number of users
+
+% Creates the data structure with the set of movies of each user
+% (uses a cell array since each user has a different number of movies):
+Set = CreateMoviesSet(u, users);
+
+% Calculates the Jaccard distance between the movie sets of all user pairs:
+tic
+J = CalculateJaccardDistance(Set, users); % initialize the matrix of the distances
+calcTime = toc;
+
+% Determines the most similar pairs of users, in terms of their movie sets:
+threshold = 0.4;
+tic
+SimilarUsers= SimilarPairs(J, users, threshold);
+checkTime = toc;
+
+fprintf("Took %f seconds to calculate the distante\n", calcTime);
+fprintf("Took %f seconds to check the distance threshold\n", checkTime);
+fprintf("Got %d similar users\n", length(SimilarUsers));
+
+SimilarUsers
+
+save Ex02UserPairsDistance.mat J
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex04.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex04.m"
new file mode 100644
index 0000000..c1be909
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/ex04.m"	
@@ -0,0 +1,33 @@
+% Base code for finding similar sets
+% Loads the data file:
+udata = load('u.data');
+% Keeps only the two first columns:
+u = udata(1:end,1:2);
+clear udata;
+% Determines the list of users:
+users = unique(u(:,1));         % Extracts the unique user IDs
+Nu = length(users);             % Computes the total number of users
+
+% Creates the data structure with the set of movies of each user
+% (uses a cell array since each user has a different number of movies):
+Set = CreateMoviesSet(u, users);
+
+% Calculates the Jaccard distance between the movie sets of all user pairs:
+tic
+J = CalculateJaccardDistanceMinHash(Set, users, 200); % initialize the matrix of the distances
+calcTime = toc;
+
+
+% Determines the most similar pairs of users, in terms of their movie sets:
+threshold = 0.4;
+tic
+SimilarUsers= SimilarPairs(J, users, threshold);
+checkTime = toc;
+
+fprintf("Took %f seconds to calculate the distante\n", calcTime);
+fprintf("Took %f seconds to check the distance threshold\n", checkTime);
+fprintf("Got %d similar users\n", length(SimilarUsers));
+
+SimilarUsers
+
+save Ex04UserPairsDistance.mat J
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/muxDJB31MA.m" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/muxDJB31MA.m"
new file mode 100644
index 0000000..0e7cb2e
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/muxDJB31MA.m"	
@@ -0,0 +1,12 @@
+function h_out= muxDJB31MA( chave, seed, k)
+len= length(chave);
+chave= double(chave);
+h= seed;
+for i=1:len
+    h = mod(31 * h + chave(i), 2^32 -1);
+end
+h_out = zeros(1,k);
+for i = 1:k
+    h = mod(31 * h + i, 2^32 -1);
+    h_out(i) = h;
+end
\ No newline at end of file
diff --git "a/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/u.data" "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/u.data"
new file mode 100644
index 0000000..16ef21e
--- /dev/null
+++ "b/2ano1/MPEI/guiao04/Sec\303\247\303\243o 3/u.data"	
@@ -0,0 +1,100000 @@
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diff --git a/2ano1/MPEI/trabalho-pratico-1-2022-2023/L.mat b/2ano1/MPEI/trabalho-pratico-1-2022-2023/L.mat
new file mode 100644
index 0000000000000000000000000000000000000000..e67ae695c227cd26cc0e272b111004c57636b7de
GIT binary patch
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diff --git a/2ano1/MPEI/trabalho-pratico-1-2022-2023/crawl.m b/2ano1/MPEI/trabalho-pratico-1-2022-2023/crawl.m
new file mode 100644
index 0000000..d8f80fe
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2022-2023/crawl.m
@@ -0,0 +1,34 @@
+function [state] = crawl(H, first, last)
+    % the sequence of states will be saved in the vector "state"
+    % initially, the vector contains only the initial state:
+    state = [first];
+    % keep moving from state to state until state "last" is reached:
+    while (1)
+        state(end+1) = nextState(H, state(end));
+        if ismember(state(end), last) % verifies if state(end) is absorbing
+            break;
+        end
+    end
+end
+
+% Returning the next state
+% Inputs:
+% H - state transition matrix
+% currentState - current state
+function state = nextState(H, currentState)
+    % find the probabilities of reaching all states starting at the current one:
+    probVector = H(:,currentState)'; % probVector is a row vector
+    n = length(probVector); %n is the number of states
+    % generate the next state randomly according to probabilities probVector:
+    state = discrete_rnd(1:n, probVector);
+end
+
+% Generate randomly the next state.
+% Inputs:
+% states = vector with state values
+% probVector = probability vector
+function state = discrete_rnd(states, probVector)
+    U=rand();
+    i = 1 + sum(U > cumsum(probVector));
+    state= states(i);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex1.m b/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex1.m
new file mode 100644
index 0000000..3bac0fb
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex1.m
@@ -0,0 +1,40 @@
+%
+%                       | Oceano | Floresta | Deserto | Urbano |
+%                       |        |          |         |        |
+%   P(passar Oceano)    |   0.1  |   0.25   |   0.2   |  0.25  |
+%                       |        |          |         |        |
+%   P(passar Floresta)  |   0.3  |   0.25   |   0.2   |  0.25  |
+%                       |        |          |         |        |
+%   P(passar Deserto)   |   0.3  |   0.25   |   0.4   |  0.25  |
+%                       |        |          |         |        |
+%   P(passar Urbano)    |   0.3  |   0.25   |   0.2   |  0.25  |
+%                       |        |          |         |        |
+
+M = [0.1 0.25 0.2 0.25; 0.3 0.25 0.2 0.25; 0.3 0.25 0.4 0.25; 0.3 0.25 0.2 0.25];
+fprintf("Matriz de Markov:\n");
+disp(M);
+estado_inicial = [0.25 0.25 0.25 0.25]';
+
+%% c)
+
+setima_sessao = M^6 * estado_inicial;
+fprintf("c) Na setima sessao, a probabilidade do jogo ser no estado Floresta e %f\n", setima_sessao(2));
+
+%% d)
+
+% Calculo do steady-state vector:
+
+T = [M - eye(4); ones(1,4)];
+u = T\[0 0 0 0 1]';
+
+fprintf("d) A probabilidade limite de do cenario escolhido ser floresta e %f\n", u(2));
+
+%% e)
+
+estado_1 = estado_inicial;
+estado_2 = M * [0 0 1 0]'; % Sabemos que o estado anterior foi Deserto;
+estado_4 = M * estado_2;    % As probabilidades do estado 3 sao iguais as do estado 2;
+estado_5 = M * [0 0 0 1]';  % Sabemos que o estado anterior foi Urbano;
+
+prob_final = estado_1(3) * estado_2(3) * estado_4(4) * estado_5(4);
+fprintf("A probabilidade das sessoes serem Deserto - Deserto - X - Urbano - Urbano e %f.\n", prob_final);
\ No newline at end of file
diff --git a/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex2.m b/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex2.m
new file mode 100644
index 0000000..ce5ac5c
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex2.m
@@ -0,0 +1,52 @@
+close all;
+clear all;
+load("L.mat");
+N = size(L);
+S = sum(L);
+
+%% a)
+
+fprintf("N = %d\n", N(1));
+fprintf("Dead ends:\n");
+dead_ends = find(S == 0);
+disp(dead_ends);
+
+%% b)
+
+H = zeros(N);
+
+for i = 1:N(2)
+    n = sum(L(:, i));
+    H(:, i) = L(:,i) / n;
+end
+fprintf("A matriz H e");
+disp(H)
+
+%% c)
+
+for i = dead_ends
+    H(:, i) = ones(1, N(1)) / N(1);
+end
+
+random = ones(N) / N(1);
+
+google = (H * 0.85) + (random * 0.15);
+
+%% d)
+
+% Para calcular o valor final do pagerank podemos aplicar o "power method"
+
+M=[google - eye(N(1)); ones(1, N(1))];
+x = [zeros(N(1), 1); 1];
+state = M\x;
+fprintf("O pagerank final e:\n");
+for p = 1:N(1)
+    fprintf(1,'Pagina %d: %.3f \n', p, state(p));
+end
+
+%% e)
+
+sorted_state = sort(state, 'descend');
+fprintf("1º : Pagina %d -> Pagerank: %.5f\n", find(state == sorted_state(1)), sorted_state(1));
+fprintf("2º : Pagina %d -> Pagerank: %.5f\n", find(state == sorted_state(2)), sorted_state(2));
+fprintf("3º : Pagina %d -> Pagerank: %.5f\n", find(state == sorted_state(3)), sorted_state(3));
diff --git a/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex3.m b/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex3.m
new file mode 100644
index 0000000..a94285e
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2022-2023/ex3.m
@@ -0,0 +1,108 @@
+%
+%               |   T   |   A   |   C   |   O   |   R   |   FIM   |
+%               |       |       |       |       |       |         |
+%   P(passar T) |   0   |  7/30 |   0   |  7/30 |  7/30 |    0    |
+%               |       |       |       |       |       |         |
+%   P(passar A) |  0.5  |   0   |  0.5  |   0   |  7/30 |    0    |
+%               |       |       |       |       |       |         |
+%   P(passar C) |   0   |  7/30 |   0   |  7/30 |   0   |    0    |
+%               |       |       |       |       |       |         |
+%   P(passar O) |  0.5  |   0   |  0.5  |   0   |  7/30 |    0    |
+%               |       |       |       |       |       |         |
+%   P(passar R) |   0   |  7/30 |   0   |  7/30 |   0   |    0    |
+%               |       |       |       |       |       |         |
+%   P(FIM)      |   0   |  0.3  |   0   |  0.3  |  0.3  |    1    |
+%               |       |       |       |       |       |         |
+%
+
+%% b)
+
+T = [0    7/30 0    7/30 7/30 0;
+     0.5  0    0.5  0    7/30 0;
+     0    7/30 0    7/30 0    0;
+     0.5  0    0.5  0    7/30 0;
+     0    7/30 0    7/30 0    0;
+     0    0.3  0    0.3  0.3  1
+    ];
+
+%% c)
+letters = ['T', 'A', 'C', 'O', 'R', 'F'];
+
+final_word = crawl(T, 2, 6);
+fprintf("A palavra gerada foi: ")
+for i = final_word
+    if i == 6
+        break;
+    end
+    fprintf("%s", letters(i));
+end
+fprintf("\n");
+
+%% d)
+
+
+N = 1e6;
+simulations = cell(1,N);
+for i = 1:N
+    start_letter = randi(5);
+    simulations{i} = crawl(T, start_letter, 6);
+end
+
+%% e)
+
+counter = 0;
+for i = 1:N
+    word = simulations{i};
+    if length(word) == 5 & word == [1 2 3 4 6]
+        counter = counter + 1;
+    end
+end
+
+prob_taco_simulada = counter / N;
+fprintf("A probabilidade de gerar a palavra TACO e %.5f\n", prob_taco_simulada)
+
+%% f)
+
+% Probabilidade de 1a letra ser T = 0.20
+p_1a_letra = 1/5;
+
+% Probabilidade de 2a letra ser A sendo que 1a foi T
+p_2a_letra = T * [1 0 0 0 0 0]';
+
+% Probabilidade de 3a letra ser C sendo que 2a foi A
+p_3a_letra = T * [0 1 0 0 0 0]';
+
+% Probabilidade de 4a letra ser O sendo que 3a foi C
+p_4a_letra = T * [0 0 1 0 0 0]';
+
+% Probabilidade de 5a letra ser FIM sendo que 4a foi O
+p_5a_letra = T * [0 0 0 1 0 0]';
+
+prob_taco_algebrica = p_1a_letra * p_2a_letra(2) * p_3a_letra(3) * p_4a_letra(4) * p_5a_letra(6);
+fprintf("A probabilidade de gerar a palavra TACO e %.5f\n", prob_taco_algebrica)
+
+%% g)
+
+N_estados_absorventes = 1;
+Q = T(1:end-N_estados_absorventes, 1:end-N_estados_absorventes);
+
+F = (eye(length(Q)) - Q)^-1;
+t = F' * ones(length(F), 1);
+
+fprintf("O tamanho medio de uma palavra e %f\n", t(1, 1));
+
+R = T(end-N_estados_absorventes+1:end, 1:end - N_estados_absorventes);
+B = R * F;
+
+fprintf("Probabilidade de absorcao e %f\n", B(1, 1));
+
+countT = 0;
+lengthT = 0;
+for i=1:length(simulations)
+    if simulations{i}(1) == 1
+        countT = countT + 1;
+        lengthT = lengthT + length(simulations{i}) - 1;
+    end
+end
+
+lengthT/countT
\ No newline at end of file
diff --git a/2ano1/MPEI/trabalho-pratico-1-2023-2024/Exemplo_cod_Cadeia_Markov.m b/2ano1/MPEI/trabalho-pratico-1-2023-2024/Exemplo_cod_Cadeia_Markov.m
new file mode 100644
index 0000000..553597f
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2023-2024/Exemplo_cod_Cadeia_Markov.m
@@ -0,0 +1,50 @@
+% a state transition matrix example
+H = [0.5 0.5 0;
+        0.5 0.4 0;
+        0     0.1 1];
+
+ % how to use crawl()
+state = crawl(H, 1, 3)
+% if the Markov chain has more than 1 absorving state the third argument
+% must be a vector with the absorving states
+% for example in a chain with 5 states,and considering that states 4 and 5 are absorbing states:
+% state = crawl(H5, 1,  [4 5])  
+% Random walk on the Markov chain
+% Inputs:
+% H - state transition matrix
+% first - initial state
+% last - terminal or absorving state
+function [state] = crawl(H, first, last)
+     % the sequence of states will be saved in the vector "state"
+     % initially, the vector contains only the initial state:
+     state = [first];
+     % keep moving from state to state until state "last" is reached:
+     while (1)
+          state(end+1) = nextState(H, state(end));
+          if ismember(state(end), last) % verifies if state(end) is absorving
+              break;
+          end
+     end
+end
+
+% Returning the next state
+% Inputs:
+% H - state transition matrix
+% currentState - current state
+function state = nextState(H, currentState)
+     % find the probabilities of reaching all states starting at the current one:
+     probVector = H(:,currentState)';  % probVector is a row vector 
+     n = length(probVector);  %n is the number of states
+     % generate the next state randomly according to probabilities probVector:
+     state = discrete_rnd(1:n, probVector);
+end
+
+% Generate randomly the next state.
+% Inputs:
+% states = vector with state values
+% probVector = probability vector 
+function state = discrete_rnd(states, probVector)
+     U=rand();
+     i = 1 + sum(U > cumsum(probVector));
+     state= states(i);
+end
\ No newline at end of file
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new file mode 100644
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diff --git a/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex01.m b/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex01.m
new file mode 100644
index 0000000..013c6cc
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex01.m
@@ -0,0 +1,32 @@
+% Estados: A B C D
+T = [0.1 0.3 0.25 0.5;
+     0.3 0.1 0.25 0.3;
+     0.3 0.3 0.1  0.1;
+     0.3 0.3 0.4  0.1];
+
+estocastica = all(abs(1 - sum(T)) < 1e-15);
+fprintf("Estocastica? = %s\n", string(estocastica));
+
+% c)
+I = [0.25 0.25 0.25 0.25]';
+P = T^5 * I;
+
+empresa_B = P(2);
+
+fprintf("Probabilidade 7:10 ser a empresa B %f\n", P(2))
+
+% d)
+N = length(T);
+M=[T - eye(N); ones(1, N)];
+x = [zeros(N, 1); 1];
+u = M\x;
+
+tempo_medio = u(2) * 60
+
+% e)
+p_estado_1 = [0.25 0.25 0.25 0.25]';
+p_estado_2 = T * [1 0 0 0]';
+p_estado_6 = T^4 * [0 1 0 0]';
+p_estado_7 = T * [0 1 0 0]';
+
+p = p_estado_1(1) * p_estado_2(2) * p_estado_6(2) * p_estado_7(1)
\ No newline at end of file
diff --git a/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex02.m b/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex02.m
new file mode 100644
index 0000000..cbf2751
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex02.m
@@ -0,0 +1,37 @@
+load L.mat;
+
+% a)
+N = length(L);
+dead_ends = find(sum(L) == 0);
+
+% b)
+links_saida = sum(L);
+H = L./links_saida;
+H(:, dead_ends) = 0;
+
+% c)
+H_no_dead_end = H;
+H_no_dead_end(:, dead_ends) = ones(N, length(dead_ends))/N;
+
+beta = 0.8;
+A = beta*H_no_dead_end + (1-beta)*(ones(N)/N);
+
+% d)
+I = ones(N, 1);
+I = I/sum(I);
+
+passos = 1;
+prev_P = I;
+ranking = A*prev_P;
+
+while any(abs(ranking - prev_P) > 1e-4)
+    prev_P = ranking;
+    ranking = A*prev_P;
+
+    passos = passos + 1;
+end
+
+% e)
+for i=dead_ends
+    fprintf("pagerank pagina %d = %f\n", i, ranking(i));
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex03.m b/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex03.m
new file mode 100644
index 0000000..36f5cfe
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-1-2023-2024/ex03.m
@@ -0,0 +1,105 @@
+% Estados: 1 3 5 7 9 FIM
+T = [0   0.3 0   0.3 0    0;
+     1/3 0   0.5 0   0.45 0;
+     1/3 0.3 0   0.3 0    0;
+     1/3 0   0.5 0   0.45 0;
+     0   0.3 0   0.3 0    0;
+     0   0.1 0   0.1 0.1  1];
+
+%% c)
+digits = ['1', '3', '5', '7', '9', 'F'];
+
+prob_first = [1/4 1/8 1/4 1/4 1/8 0];
+states = length(T);
+
+start_digit = discrete_rnd(1:states, prob_first);
+gen_states = crawl(T, start_digit, states);
+sequence = convertCharsToStrings(digits(gen_states(1:end -1)))
+
+%% d)
+N = 1e6;
+sequences = cell(1,N);
+for i = 1:N
+    start_digit = discrete_rnd(1:states, prob_first);
+    gen_states = crawl(T, start_digit, states);
+    sequences{i} = convertCharsToStrings(digits(gen_states(1:end -1)));
+end
+
+%% e)
+occurences = 0;
+
+for i=1:length(sequences)
+    if sequences{i} == "97153"
+        occurences = occurences + 1;
+    end
+end
+
+fprintf("Probabilidade: %f\n", occurences/length(sequences))
+
+%% f)
+estado_1 = [1/4 1/8 1/4 1/4 1/8 0]';
+estado_2 = T * [0 0 0 0 1 0]';
+estado_3 = T * [0 0 0 1 0 0]';
+estado_4 = T * [1 0 0 0 0 0]';
+estado_5 = T * [0 0 1 0 0 0]';
+estado_final = T * [0 1 0 0 0 0]';
+
+prob = estado_1(5) * estado_2(4) * estado_3(1) * estado_4(3) * estado_5(2) * estado_final(6);
+
+fprintf("Probabilidade (algebrica): %f\n", prob)
+
+%% g)
+N_estados_absorventes = 1;
+Q = T(1:end-N_estados_absorventes, 1:end-N_estados_absorventes);
+
+F = (eye(length(Q)) - Q)^-1;
+t = F' * ones(length(F), 1);
+
+medio_7 = t(4);
+
+fprintf("O tamanho medio de uma sequencia comecada em 7 e %f\n", medio_7);
+
+
+% if the Markov chain has more than 1 absorving state the third argument
+% must be a vector with the absorving states
+% for example in a chain with 5 states,and considering that states 4 and 5 are absorbing states:
+% state = crawl(H5, 1,  [4 5])  
+% Random walk on the Markov chain
+% Inputs:
+% H - state transition matrix
+% first - initial state
+% last - terminal or absorving state
+function [state] = crawl(H, first, last)
+     % the sequence of states will be saved in the vector "state"
+     % initially, the vector contains only the initial state:
+     state = [first];
+     % keep moving from state to state until state "last" is reached:
+     while (1)
+          state(end+1) = nextState(H, state(end));
+          if ismember(state(end), last) % verifies if state(end) is absorving
+              break;
+          end
+     end
+end
+
+% Returning the next state
+% Inputs:
+% H - state transition matrix
+% currentState - current state
+function state = nextState(H, currentState)
+     % find the probabilities of reaching all states starting at the current one:
+     probVector = H(:,currentState)';  % probVector is a row vector 
+     n = length(probVector);  %n is the number of states
+     % generate the next state randomly according to probabilities probVector:
+     state = discrete_rnd(1:n, probVector);
+end
+
+% Generate randomly the next state.
+% Inputs:
+% states = vector with state values
+% probVector = probability vector 
+function state = discrete_rnd(states, probVector)
+     U=rand();
+     i = 1 + sum(U > cumsum(probVector));
+     state= states(i);
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignatures.m b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignatures.m
new file mode 100644
index 0000000..6770002
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignatures.m
@@ -0,0 +1,23 @@
+function [assinaturas] = CalculateSignatures(Set, k)
+N = length(Set);
+
+assinaturas = inf(N, k);
+
+h = waitbar(0,"Calculating signatures");
+
+for i=1:N
+    waitbar(i/N,h);
+    
+    items = Set{i};
+    
+    for item_idx=1:length(items)
+        item = num2str(items(item_idx));
+        hash = muxDJB31MA(item, 127, k);
+        
+        assinaturas(i, :) = min(hash, assinaturas(i, :));
+    end
+end
+
+delete (h)
+end
+
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignaturesWithShingles.m b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignaturesWithShingles.m
new file mode 100644
index 0000000..70df13f
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CalculateSignaturesWithShingles.m
@@ -0,0 +1,34 @@
+function [assinaturas] = CalculateSignaturesWithShingles(Corpus, k_hashes, k_grams)
+N = length(Corpus);
+
+assinaturas = inf(N, k_hashes);
+
+h = waitbar(0,"Calculating signatures (with shingles)");
+
+for i=1:N
+    waitbar(i/N,h);
+    
+    % Make the string lower cased
+    text = lower(Corpus{i});
+    % Remove punctuation from the string
+    text(isstrprop(text, 'punct')) = '';
+    % Fold space in string
+    text = regexprep(text, '\s+', ' ');
+    % Trim spaces at the beginning and end
+    text = strtrim(text);
+    
+    text_length = length(text);
+    
+    for shingle_start=1:(text_length - k_grams + 1)
+        shingle_end = shingle_start + k_grams - 1;
+        shingle = text(shingle_start:shingle_end);
+        
+        hash = muxDJB31MA(shingle, 127, k_hashes);
+        
+        assinaturas(i, :) = min(hash, assinaturas(i, :));
+    end
+end
+
+delete (h)
+end
+
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CountingBloomFilter.m b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CountingBloomFilter.m
new file mode 100644
index 0000000..2e4ebc0
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/CountingBloomFilter.m
@@ -0,0 +1,34 @@
+classdef CountingBloomFilter < handle
+    properties (Access = private)
+        filter_array,
+        number_of_hashes,
+    end
+    
+    methods
+        function obj = CountingBloomFilter(n, k)
+            obj.filter_array = zeros(1, n);
+            obj.number_of_hashes = k;
+        end
+        
+        function [] = insert(obj, key)
+            n = length(obj.filter_array);
+            
+            hashes = muxDJB31MA(key, 127, obj.number_of_hashes);
+            positions = mod(hashes, n) + 1;
+            
+            for pos=positions
+                obj.filter_array(pos) = obj.filter_array(pos) + 1;
+            end
+        end
+        
+        function res = getInsertedAssured(obj, key)
+            n = length(obj.filter_array);
+            
+            hashes = muxDJB31MA(key, 127, obj.number_of_hashes);
+            positions = mod(hashes, n) + 1;
+            
+            res = min(obj.filter_array(positions));
+        end
+    end
+end
+
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/folha 1.jpg b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/folha 1.jpg
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HcmV?d00001

diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/muxDJB31MA.m b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/muxDJB31MA.m
new file mode 100644
index 0000000..0e7cb2e
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/muxDJB31MA.m
@@ -0,0 +1,12 @@
+function h_out= muxDJB31MA( chave, seed, k)
+len= length(chave);
+chave= double(chave);
+h= seed;
+for i=1:len
+    h = mod(31 * h + chave(i), 2^32 -1);
+end
+h_out = zeros(1,k);
+for i = 1:k
+    h = mod(31 * h + i, 2^32 -1);
+    h_out(i) = h;
+end
\ No newline at end of file
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte1.m b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte1.m
new file mode 100644
index 0000000..682fadc
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte1.m
@@ -0,0 +1,37 @@
+rest = readcell('restaurantes.txt', 'Delimiter', '\t');
+evals = load('turistas1.data');
+
+users = unique(evals(:,1));     % Extracts the unique user IDs
+Nu = length(users);             % Computes the total number of users
+
+RestaurantsRated = cell(Nu,1);
+for n = 1:Nu
+	ind = find(evals(:,1) == users(n));
+	RestaurantsRated{n} = [RestaurantsRated{n} evals(ind, 2)];
+end
+
+% TODO: Find a good `k`
+EvalSignatures = CalculateSignatures(RestaurantsRated, 200);
+% TODO: Find a good `k_hashes` and `k_shingles`
+TitleSignatures = CalculateSignaturesWithShingles(rest(:, 2), 200, 2);
+
+mask = cellfun(@anymissing, rest);
+rest(mask) = {''};
+concat_fields = join(rest(:, 3:end));
+% TODO: Find a good `k_hashes` and `k_shingles`
+FieldSignatures = CalculateSignaturesWithShingles(concat_fields, 200, 3);
+
+% TODO: Find a good `m` and `k`
+NumRatingsBloom = CountingBloomFilter(1000, 3);
+
+for n = 1:length(evals)
+	NumRatingsBloom.insert(evals(n, 2));
+end
+
+rIDs = [rest{:, 1}];
+AverageRating = zeros(length(rIDs), 1);
+for id = rIDs
+	AverageRating(id) = mean(evals(evals(:, 2) == id, 4));
+end
+
+save 'processed.mat' rest RestaurantsRated EvalSignatures TitleSignatures FieldSignatures NumRatingsBloom AverageRating;
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte2.m b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte2.m
new file mode 100644
index 0000000..51c30b9
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/parte2.m
@@ -0,0 +1,37 @@
+load 'processed.mat';
+
+user_id = input('Insert User ID (1 to ??): ');
+
+while true
+	fprintf("1 - Restaurants evaluated by you\n");
+	fprintf("2 - Set of restaurants evaluated by the most similar user\n");
+	fprintf("3 - Search Restaurant\n");
+	fprintf("4 - Find most similar restaurants\n");
+	fprintf("5 - Estimate the number of evaluations for each restaurant\n");
+	fprintf("6 - Exit\n");
+	choice = input("Select choice: ");
+	
+	fprintf("\n");
+	
+	switch choice
+		case 1
+			printRestaurants(rest, [RestaurantsRated{user_id}]');
+		case 6
+			break
+		otherwise
+			fprintf("Unknown option\n");
+	end
+	
+	fprintf("\n");
+end
+
+function printRestaurants(rest, rIDs)
+% fprintf("Nome\tLocalidade\tConcelho\tTipo de Cozinha\tPrato(s) recomendado(s)\tDia(s) encerrado\n");
+% for id = rIDs
+% 	fprintf("%s\t%s\t%s\t%s\t%s\t%s\n", rest{id, 2:end});
+% end
+
+header = {'Nome', 'Localidade', 'Concelho', 'Tipo de Cozinha', 'Prato(s) recomendado(s)', 'Dia(s) encerrado'};
+T = cell2table(rest(rIDs, 2:end), 'VariableNames', header);
+disp(T)
+end
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/processed.mat b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/processed.mat
new file mode 100644
index 0000000000000000000000000000000000000000..ce52133caf6a6bd35b199be1c1b64455984470e9
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diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/restaurantes.txt b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/restaurantes.txt
new file mode 100644
index 0000000..af5086e
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/restaurantes.txt
@@ -0,0 +1,215 @@
+1	Campo de Golfe	Amarante	Amarante	Tradicional portuguesa	Bacalhau com broa e outros	Domingo à noite
+2	Casa da Calçada	Amarante	Amarante	1 * Michelin		
+3	Quinta da Lama	Real - Vila - Meã	Amarante	Tradicional portuguesa	Bacalhau	
+4	Zé da Calçada	Amarante	Amarante	Tradicional portuguesa	Cabrito Assado, arroz de pato e outros	
+5	Churrasqueira Caldelas	Caldelas	Amares	Tradicional portuguesa	Bacalhau à casa/peixe a pedido	
+6	Cruzeiro	Amares	Amares	Tradicional portuguesa	Vários	Não encerra
+7	Espalha Brasas	Braga	Amares	Tradicional portuguesa	Açorda de Marisco/Bacalhau	3ª feira
+8	Pousada Santa Maria do Bouro	Amares	Amares	Variada		Não encerra
+9	Quinta do Esquilo	Amares	Amares	Regional		Não encerra
+10	O Caneiro	Arco de Baúlhe	Arco de Baúlhe	Regional	Arroz de Tamboril, Lombinhos	2ª feira
+11	Alto da Prova	Arcos de Valdevez	Arcos de Valdevez	Variada	Bacalhau com broa	Não encerra
+12	Grill/Costa do Vez	Silvares	Arcos de Valdevez	Tradicional portuguesa		2ª feira
+13	O Lagar	Arcos de Valdevez	Arcos de Valdevez	Tradicional portuguesa		Não encerra
+14	Videira	Arcos de Valdevez	Arcos de Valdevez	Tradicional portuguesa		3ª e 4ª feira
+15	DOC	Folgosa	Armamar	Gourmet	Tudo Bom	Domingo à noite e 2ª feira
+16	Pensão Borges	Baião	Baião	Tradicional portuguesa	Arroz do forno e anho assado e cozido à portuguesa	Não encerra
+17	Bagoeira	Barcelos	Barcelos	Regional	Vários	Não encerra
+18	Outerinho	Barcelos	Barcelos	Tradicional portuguesa	Bacalhau com Broa	Domingo à noite e 2ª feira
+19	Pedra Furada	Barcelos	Barcelos	Regional		Não encerra
+20	Viúva de Medros	Barcelinhos	Barcelos	Caseira	Estufados	
+21	Casa de Carvalhelhos (Taberna)	Boticas	Boticas	Regional		Não encerra (por marcação)
+22	Casa de Vilar (Taberna)	Boticas	Boticas	Regional	Vitela Barrosã	Não encerra
+23	5 Hoteis Bom Jesus 	Braga	Braga	Tradicional portuguesa	Variados	Não encerra
+24	Abade de Priscos	Braga	Braga	Variada		Domingo e 2ª feira ao almoço
+25	Arcoense	Braga	Braga	Tradicional portuguesa	Rojões c/papas, cabrito, cozido, etc.	Domingo
+26	Brito´s	Braga	Braga	Tradicional portuguesa	Rojões c/papas, cabrito, bacalhau, etc.	4ª feira
+27	Casa da Pedra Cavalgada	Braga	Braga	Regional		Domingo à noite e 2ª feira
+28	D. Júlia	Braga	Braga	Regional	Cabrito, Bacalhau/ peixe grelhado	2ª feira
+29	D.Elvira	Braga	Braga	Tradicional portuguesa	Filetes de Polvo c/ arroz de grelos, Bacalhau na Braga e Medalhões de Vitela	Não encerra
+30	Inácio	Braga	Braga	Variada		3ª feira
+31	Maia	Braga	Braga	Regional	Bacalhau à Sameiro e Papas à moda de Braga c/ rojões	Não encerra
+32	Expositor do Migaitas	Braga	Braga	Variada	"Peixe fresco; costelinha barrosã no forno; cabrito no forno; moamba"	Domingo à noite e 3ª feira
+33	O Fausto	Braga	Braga	Caseira	Cabrito e pica no chão	
+34	São Frutuoso	Braga	Braga	Tradicional portuguesa	Papas sarrabulho, Arroz pica no chão.	2ª feira
+35	Solar do Paço 	Braga	Braga	Tradicional portuguesa	Costeletão Grelhado	Não encerra
+36	Chefe Ruca	Bragança	Bragança	Tradicional portuguesa	Posta/Cabrito Assado na Brasa	3ª feira
+37	O Abel             (Rest. Típico)	Bragança	Bragança	Tradicional portuguesa	Posta/Cabrito Assado na Brasa	2ª feira
+38	O Geadas	Bragança	Bragança	Tradicional portuguesa	Cherne/Linguado grelhado	Não encerra
+39	O Javali	Bragança	Bragança	Tradicional portuguesa	Javali c/ Castanhas	2ª feira
+40	O Rochedo	Bragança	Bragança	Regional	"Bacalhau com gambas; Bacalhau com Natas
+"	Não encerra
+41	Pousada S. Bartolomeu	Bragança	Bragança	Tradicional portuguesa	Filetes Polvo	Não encerra
+42	Real Feitoria	Bragança	Bragança	Regional		Não encerra
+43	Solar Bragançano	Bragança	Bragança	Regional		2ª. feira (Inverno)
+44	Churraqueira o Paço	Arco de Baúlhe	Cabeceiras de Basto	Tradicional portuguesa	Lombinho, costelinhas. Churrasco de boi, frango de churrasco	3ª feira
+45	Luis do Outeirinho	Outeirinho	Cabeceiras de Basto	Tradicional portuguesa	Bacalhau c/ batatas a murro	4ª feira noite
+46	Nariz do Mundo	Cabeceiras de Basto	Cabeceiras de Basto	Regional		2ª e 3ª feira
+47	A Gaivota	Moledo	Caminha	Regional		Domingo (jantar)
+48	Ancoradouro	Caminha	Caminha	Regional		2ª feira
+49	Casa Tornedó	Moledo	Caminha	Tradicional portuguesa		
+50	Foz do Minho	Caminha	Caminha	Tradicional portuguesa	Mariscos e cabrito	4ª à noite e 5ª feira
+51	Mar de Moledo	Caminha	Caminha	Tradicional portuguesa	"Peixe grelhado; polvo assado no forno e cabrito da serra d'Arga no forno"	2ª feira
+52	Solar do Pescado	Caminha	Caminha	Tradicional portuguesa	Peixe	Domingo à noite e 2ª feira
+53	Calça Curta  ( Rest. Típico )	Foz -Tua 	Carrazeda de Ansiães	Tradicional portuguesa	Javali-Veado-Polvo Para petiscos- peixes do rio e enguias	Não encerra
+54	Churrascaria Veiga	Carrazeda de Ansiães	Carrazeda de Ansiães	Tradicional portuguesa	Posta à Mirandesa, Carnes grelhadas ( na brasa)                   Cozido à Portuguesa	Sábado
+55	Quintinha do Manel	Carrazeda de Ansiães	Carrazeda de Ansiães	Tradicional portuguesa	Bacalhau à quintinha. Vitela assada	Não encerra
+56	Sabores da Quinta	Fermil	Celorico de Basto	Tradicional portuguesa	Vitela assada, cabrito assado no forno	2ª,3ª e 4ª feira
+57	A Talha	Chaves	Chaves	Regional	Palhada Transmontana, Lombelos c/ presunto, Filetes de polvo e Arroz de grão de bico.	Sábado
+58	Adega Faustino	Chaves	Chaves	Regional	Orelha de porco, moelas, alheira, pica-pau, linguiça assada.	Domingo
+59	Albergaria Borges ( Rest.Típico )	Outeiro Jusão	Chaves	Regional	Cabrito assado, Bacalhau e Ossos da Suã	2ª feira
+60	Aprígio	Chaves	Chaves	Regional	Milhos, Cozido à Portuguesa e Vitela	Não encerra
+61	Carvalho	Chaves	Chaves	Regional	"Cabrito, Naco ""grelhado"" de vitela, Arroz de Fumeiro, Cozido à Portuguesa"	2ª feira
+62	Casa Os Três Lagares (Taberna)	Chaves	Chaves	Regional		Abre de 5ª a domingo (por marcação)
+63	Lavrador	Chaves	Chaves	Regional	"Pernil de Porco, Bacalhau;               Peixe."	5ª feira
+64	Quinta de Samaiões	Chaves	Chaves	Regional	Açorda de marisco, bacalhau e cabrito assado.	Não encerra
+65	O Recanto das Carvalhas	Gralheira	Cinfães	Regional	Cabrito, borrego….	2ª feira
+66	Azeite e Alho	Apúlia	Esposende	Tradicional portuguesa	Bacalhau com Broa	
+67	Casa da Fonte	Forjães	Esposende	Tradicional portuguesa	Açorda de Marisco e Açorda de Bacalhau, Bacalhau com Broa Polvo Grelhado,…	2ª feira
+68	Foz do Cávado	Esposende	Esposende	Tradicional portuguesa	Rojões à Minhota	2ª feira
+69	Hotel Suave Mar	Esposende	Esposende	Tradicional portuguesa		
+70	Mira Rio	Esposende	Esposende	Tradicional portuguesa	Filetes Pescada	
+71	O Apúliense	Apúlia	Esposende	Tradicional portuguesa	Sapateira Recheada	
+72	O Camelo	Apúlia	Esposende	Tradicional portuguesa	Rojões	
+73	O Forno	Apúlia	Esposende	Tradicional portuguesa	Peixe Grelhado	
+74	Salgueira	Apúlia	Esposende	Tradicional portuguesa	Arroz Gambas c/ Lagosta	
+75	Adega Popular	Fafe	Fafe	Regional	Vitela assada (lista de bons pratos)	Domingo
+76	Pinto da Costa	Fafe	Fafe	Regional	Vitela assada (lista de bons pratos)	Domingo à noite e 2ª feira
+77	Tasca do Ademar	S.Clemente de Silvares - Fafe	Fafe	Regional	Churrasco de Boi c/arroz malandro e Bacalhau na brasa.	Domingo
+78	Casa Outeirinho 	Famalicão	Famalicão	Tradicional portuguesa	Cabrito assado no forno 	Domingo à noite e 2ª feira
+79	Moutados de Baixo	Famalicão	Famalicão	Regional	Bacalhau à Devesa	Não encerra
+80	O Benfica 	Famalicão	Famalicão	Tradicional portuguesa	Cabrito assado no forno 	Domingo à noite e 2ª feira
+81	O Ferrugem	Famalicão	Famalicão	Variada	Menu degustação 	2ª feira
+82	O Serenata 	Joane	Famalicão	Cozinha inspiração Italiana 	Pastas 	Domingo
+83	O Tanoeiro 	Famalicão	Famalicão	Tradicional portuguesa	Rojões e Papas de Sarrabulho 	Domingo ao jantar
+84	Santa Quitéria	Felgueiras	Felgueiras	Tradicional portuguesa	Vitela/cabrito assados e grelhados diversos…	2ª feira
+85	Petisqueira Preguiça	Mós do DOURO	Foz Côa	Regional		Não encerra
+86	Clube Paraiso 	Pevidém	Guimarães	Tradicional portuguesa	Assados vários.	2ª feira
+87	ComRequinte	Guimarães	Guimarães	Peixe Fresco	Rodovalho Fresco / Marisco Fresco	
+88	Papa Boa	Guimarães	Guimarães	Moderna	Coxa de Porco Preto c/Gambas / Tamboril c/Ameijoas e molho de salsa	Domingo
+89	Picadeiro	Guimarães	Guimarães	Moderna	Pernil Assado no Forno / Folhado de Pato c/castanhas	Domingo à noite e 2ª feira
+90	S. Gião 	Moreira Conegos 	Guimarães	Regional	Polvo, Especialidades Caça , Entradas várias	2ª feira
+91	Templo da Gula	Guimarães	Guimarães	Cozinha Moderna	Espetada de Pescada c/Arroz de Gambas	2ª feira
+92	Aquapura Douro Valley	Lamego	Lamego	Tradicional portuguesa	Cabrito assado	3ª feira
+93	Quinta Ferra Bordão	Lamego	Lamego	Tradicional portuguesa	Cabrito assado	3ª feira
+94	Caçador	Lousada	Lousada	Tradicional portuguesa	Naco de vitela assado na brasa	2ª feira
+95	Pitarisca	Lousada	Lousada	Tradicional portuguesa	Cabrito assado no forno	Domingo
+96	Visconde	Lousada	Lousada	Tradicional portuguesa		Domingo à noite
+97	Choupada 5 Coroas  ( Rest.Típico)	Macedo Cavaleiros	Macedo Cavaleiros	Tradicional portuguesa	Posta e Rodeao assados na brasa	Não encerra
+98	O Montanhês	Macedo Cavaleiros	Macedo Cavaleiros	Tradicional portuguesa	Cabrito assado na brasa                           Sortido de carnes assadas c/ fumeiro	Não encerra
+99	Saldanha	Macedo Cavaleiros	Macedo Cavaleiros	Regional		Não encerra
+100	Pensão Magalhães	Marco Canaveses	Marco Canaveses	Tradicional portuguesa	Arroz de Forno lenha e Anho	
+101	Plátano	Marco Canaveses	Marco Canaveses	Tradicional portuguesa	Carne Arouquesa+ Anho	2ª feira
+102	Ponte de Pedra	Marco Canaveses	Marco Canaveses	Tradicional portuguesa	"Bacalhau c/ broa; Picanha ; Cabrito, Menu ( diversos pratos s/ limite)"	Não encerra
+103	Quinta da Lama	Vila Meã	Marco Canaveses	Regional	"Anho assado com chouriço; bife com castanhas; lombo à lagar; por encomenda: picanha"	Domingo e feriados
+104	Quinta do Mosteirô	Marco Canaveses	Marco Canaveses	Regional	Anho no forno	
+105	Solar do Muro	Marco Canaveses	Marco Canaveses	Tradicional portuguesa	"Bacalhau à Solar; Anho assado"	2ª feira
+106	Adega do Sossego	Melgaço	Melgaço	Regional	Naco grelhado ,Cozido á portuguesa com carnes caseiras, lampreia	2ª feira
+107	Panorama	Melgaço	Melgaço	Regional	Entradas variadas, lampreia , sável do rio Minho e naco grelhado	2ª feira
+108	O Mirandês	Miranda do Douro	Miranda do Douro	Regional		Domingo ao jantar
+109	A Adega Regional	Mirandela	Mirandela	Regional		Domingo ao jantar
+110	Flor de Sal	Mirandela	Mirandela	Regional	"Trio de porco bísaro; Peixe no Sal"	2ª feira
+111	Maria Rita	Romeu	Mirandela	Tradicional portuguesa	Açorda de espargos e bacalhau à Maria Rita	2ª feira
+112	O Grés	Mirandela	Mirandela	Tradicional portuguesa	"Bacalhau à Grés; posta Mirandesa"	
+113	A Lareira	Mogadouro	Mogadouro	Regional		2ª feira
+114	Lagar	Moncorvo	Moncorvo	Regional	Posta Mirandesa	Não encerra
+115	O Artur	Carviçais	Moncorvo	Regional	Posta Mirandesa -Cabrito Assado	2ª feira
+116	Adega Regional - Os Setes Condes	Mondim de Basto	Mondim de Basto	Regional	O cozido. O cabrito. A vitela assada/forno. A cabidela. 	Não encerra
+117	O Transmontano	Mondim de Basto	Mondim de Basto	Regional	Javali, As couves, Os milhos, O cozido, O cabrito/forno. Vitela assada/Forno,  A cabidela, A feijoada à transmontana.	Não encerra
+118	Tasca da Tia Alice	Mondim de Basto	Mondim de Basto	Tradicional portuguesa	Enchidos e Petiscos	Não encerra
+119	Casa de Padornelos (Taberna)	Montalegre	Montalegre	Regional	Vários - sobremesa rabanadas	Não encerra (por marcação)
+120	Nevada	Montalegre	Montalegre	Regional		4ª feira
+121	Sol e Chuva	Montalegre	Montalegre	Tradicional portuguesa		Não encerra
+122	A Casa do Baixinho	Paredes	Paredes	Tradicional portuguesa	Bacalhau folhado com creme 	Domingo
+123	A Cozinha da Terra	Paredes	Paredes	Tradicional portuguesa	"Bacalhau com Broa; Cabrito assado no formo"	2ª feira
+124	Conselheiro	Paredes de Coura	Paredes de Coura	Regional	"Bacalhau à Cons; Cozido à Cons.; Arroz de lampreia; Trutas de escabeche; Pica no chão; cabrito"	Domingo à noite e 2ª feira
+125	O Conde	Pedras Salgadas	Pedras Salgadas	Tradicional portuguesa	Cozinha típica Portuguesa, com cabrito assado.	Não encerra
+126	Miradouro	Penafiel	Penafiel	Tradicional portuguesa	Lampreia, Cabrito e Bacalhau	
+127	O Moinho do Moleiro	Paço Sousa	Penafiel	Tradicional portuguesa	Presunto/broa e vinho.Cozido Portuguesa	4ª feira 
+128	O Ramirinho	Penafiel	Penafiel	Tradicional portuguesa	Assados	2ª feira a partir das 19h
+129	O Moinho	Campo do Corrô	Ponte da Barca	Regional	Panados de polvo com arroz de legumes e feijão	3ª feira
+130	A Carvalheira	Ponte de Lima	Ponte de Lima	Regional	"Cabrito assado; Bacalhau c/ broa"	2ª feira (Férias de 11 a 31 Out.)
+131	Beco das Selas 	Ponte de Lima	Ponte de Lima	Regional		Sábado
+132	Bocados	Ponte de Lima	Ponte de Lima	Regional	"Lampreia e sável; Bacalhau espiritual; Arroz de sarrabulho"	Domingo
+133	Cozinha Velha	Ponte de Lima	Ponte de Lima	Tradicional portuguesa	Cabrito e Leitão assado	3ª feira
+134	Encanada	Ponte de Lima	Ponte de Lima	Tradicional portuguesa		Não encerra
+135	O Açude	Arcozelo	Ponte de Lima	Regional		Domingo à noite e 2ª feira
+136	O Bodegão	Póvoa de Varzim	Póvoa de Varzim	Tradicional portuguesa	Arroz Cabidela, Sardinhas, Peixe Grelhado	2ª feira
+137	O Costa	Póvoa de Varzim	Póvoa de Varzim	Tradicional portuguesa	Arroz de tamboril e açorda de marisco	3ª feira
+138	O Dhalia	Póvoa de Varzim	Póvoa de Varzim	gourmet	Bife de veado	Não encerra
+139	O Farol	Póvoa de Varzim	Póvoa de Varzim	Peixes e Mar	Mariscos e Snacks diversos	
+140	O Firmino	Póvoa de Varzim	Póvoa de Varzim	Tradicional portuguesa	Sardinha, Peixe Grelhado, Bacalhau	3ª feira
+141	O Marinheiro	Póvoa de Varzim	Póvoa de Varzim	Peixes e Mar	Mariscos e Peixe Grelhado/Assado	
+142	O Patio	Póvoa de Varzim	Póvoa de Varzim	Tradicional portuguesa	Peixe, Arroz Cabidela	
+143	O Zé das letras	Povoa de Varzim	Póvoa de Varzim	Tradicional portuguesa	Pá de Cabrito e de Porto e Bacalhau à Zé	Domingo
+144	Quebra-Mar	Póvoa de Varzim	Póvoa de Varzim	Peixes e Mar	Peixes e Mariscos	2ª feira
+145	Castas e Pratos	Régua	Régua	Cozinha Moderna		Não encerra
+146	Cêpa Torta	Alijó	Régua	Regional	Cacho de Porco Bizaro	3ª feira
+147	Douro In	Régua	Régua	Cozinha requintada	Bacalhau à Douro In	
+148	Qta. da Romaneira dos Sonhos	Alijó	Alijó	Tradicional portuguesa		Domingo à noite e 2ª feira
+149	Pelourinho	Alijó	Régua	Variada		Não encerra
+150	Quinta de São Domingos	Régua	Régua	Variada		Não encerra
+151	Rabelo - Vintage House	Pinhão	Régua	Cozinha requintada	Posta à mirandeza	Não encerra
+152	Repentina (Típico)	Vila Seca de Poiares	Régua	Tradicional portuguesa	Cabrito Assado	2ª feira
+153	Varanda da Régua	Régua	Régua	Regional		Não encerra
+154	Alice da Barraca	Resende	Resende	Tradicional portuguesa	Peixe do Rio, Arroz de Cabidela 	Não encerra
+155	Douro à Vista	Resende	Resende	Tradicional portuguesa	Cabrito Assado no Forno, Cozido á Portuguesa	2ª feira
+156	Douro Park Hotel	Resende	Resende	Tradicional portuguesa	Cabrito Assado no Forno, Cozido á Portuguesa	Não encerra
+157	O Forno ( Casa Regional )	S. João da Pesqueira	S. João da Pesqueira	Tradicional portuguesa		Não encerra
+158	Cá Te Espero	Rebordões	Santo Tirso	"Petiscos
+Tipica Portuguesa"	Cabrito assado no Forno a lenha/ Rojões á moda do Minho	2ª feira
+159	Solar do Burguês	Santo Tirso	Santo Tirso	Tradicional portuguesa	Especialidade Assados no Forno e petiscos variados	Não encerra
+160	O Abocanhado	Brufe	Terras de Bouro	Regional	Bacalhau com migas, Cabrito e vitela Barrosã	
+161	Flor do Ave	Trofa	Trofa	Tradicional portuguesa	Leitão	3ª feira
+162	O Beco 	Trofa	Trofa	Tradicional portuguesa	Bacalhau no Forno e Sarrabulho	2ª feira
+163	Tourigalo	Trofa	Trofa	Tradicional portuguesa	Especialidade de Grelhados (Carne e Peixe) 	Não encerra
+164	Ancoramar	V. Praia Âncora	V. Praia Âncora	Tradicional portuguesa	Peixe	5ª feira Inverno
+165	Portobello	V. Praia Âncora	V. Praia Âncora	Tradicional portuguesa		Não encerra
+166	Tasquinha do Ibraim	V. Praia Âncora	V. Praia Âncora	Tradicional portuguesa	Peixe	Não encerra
+167	Verdes Lírios	V. Praia Âncora	V. Praia Âncora	Tradicional portuguesa	Peixe	Não encerra
+168	Casa Álvaro	Valença	Valença	Tradicional portuguesa		2ª feira
+169	Pousada S. Teotonico	Valença	Valença	Tradicional portuguesa		2ª feira
+170	Restaurante Quinta do Prazo	Valença	Valença	Variada		Domingo à noite e 2ª feira
+171	Casa da Amoreira (Taberna)	Valpaços	Valpaços	Regional		Não encerra
+172	Casa do Ermeiro (Taberna)	Valpaços	Valpaços	Regional		Não encerra 
+173	Casa Mariana	Viana Castelo	Viana Castelo	Tradicional portuguesa		3ª feira
+174	O Camelo	Sta. Marta Portuzelo	Viana Castelo	Regional	"Arroz de cabidela; sarrabulho; bacalhau"	2ª feira 
+175	Darque Vila 	Darque	Viana Castelo	Internacional		2ª feira 
+176	O Espigueiro de Santoínho	Darque	Viana Castelo	Tradicional portuguesa		3ª feira
+177	Aquafalls Spa Hotel Rural	Vieira do Minho	Vieira do Minho	Requintada		Não encerra
+178	Taberna Valentim	Viana Castelo	Viana Castelo	Pratos Peixe	Peixe	Domingo
+179	Hotel Forte S. João Baptista	Vila do Conde	Vila do Conde	Requintada		-
+180	Le Fruit des Fondues	Vila do Conde	Vila do Conde	Fondues 	Fondues (sobremesa fondue chocolate) 	Só abre ao jantar e Domingo só ao almoço
+181	Le Villageois	Vila do Conde	Vila do Conde	Tradicional portuguesa	Espetos de pescada e camarão	2ª feira
+182	Pedra Alta	Vila do Conde	Vila do Conde	Marisco	Grelhado de marisco, bacalhau à pescador	
+183	Praiamar	Vila do Conde	Vila do Conde	Marisco	Picanha, espetada de marisco	
+184	Ramon	Vila do Conde	Vila do Conde	Tradicional portuguesa	"Cabrito assado no forno, tamboril;parrilhada de peixes e arroz à valenciana"	3ª feira
+185	Romando 	Vila do Conde	Vila do Conde	Requintada	Peixe fresco  e carne mirandesa, charolesa e barrosã. Carta de vinhos/Garrafeira	3ª feira
+186	S. Roque	Vila do Conde	Vila do Conde	Tradicional portuguesa	Cabrito no Forno e Filetes de pescada.	2ª feira
+187	Santana Hotel	Vila do Conde	Vila do Conde	Tradicional portuguesa	Bacalhau com brôa ou Posta Barrosã	Não encerra
+188	Os Lázaros	Carvalho de Egas	Vila Flor	Tradicional portuguesa	Naco (vitela) na Pedra, Açorda de Marisco	2ª feira
+189	Casa das Velhas	Vila Nova Cerveira	Vila Nova Cerveira	Variada		Domingo à noite e 2ª feira
+190	Casa do Lau	Vila Nova Cerveira	Vila Nova Cerveira	Tradicional portuguesa	Polvo à lagareiro e cabrito	5ª feira
+191	Costa do Sol	Estrada do Minho	Vila Pouca Aguiar	Regional	Assado de maronesa.	
+192	Adega Regional Passos Perdidos	Vila Real	Vila Real	Regional		Domingo à noite e 2ª feira
+193	Albergaria Rio Beça	Boticas	Vila Real	Regional		Domingo à noite
+194	Casa de Souto Velho (Taberna)	Chaves	Vila Real	Regional		Não encerra
+195	Chaxoila	Vila Real	Vila Real	Regional		Domingo
+196	Espadeiro	Vila Real	Vila Real	Variada		Domingo à noite e 3ª feira
+197	Estalagem Qtaª do Paço	Vila Real	Vila Real	Tradicional portuguesa	Bacalhau cozido com grão e cabrito assado no forno …	Não encerra
+198	Lameirão	Vila Real	Vila Real	Tradicional portuguesa	Tripas aos molhos	Não encerra
+199	Maria do Carmo	Vila Real	Vila Real	Tradicional portuguesa	Polvo Grelhado, Joelho da Porca, Arroz de Pato 	2ª feira
+200	Museu dos Presuntos	Vila Real	Vila Real	Tradicional portuguesa	Petiscos e fumeiro	Domingo
+201	O Barriguinha Cheia	Vila Real	Vila Real	Tradicional portuguesa		Não encerra
+202	O Mateus	Vila Real	Vila Real	Específica	Rodízio	Não encerra
+203	Ponte Romana	Sabrosa	Vila Real	Regional		Não encerra
+204	Terra da Montanha	Vila Real	Vila Real	Regional	Bacalhau assado/ Joelho de porco	Domingo à noite e feriados
+205	Churrasqueira Barros	Vila Verde	Vila Verde	Tradicional portuguesa	Espetada mista	Domingo
+206	Manjar do Mar	Braga	Vila Verde	Marisqueira	"Mariscos; Peixe grelhado e posta barrosã"	2ª feira
+207	Sevilhana	Braga	Vila Verde	Grelhados/ Pratos Sul Americanos	Parrilhada Argentina / Lombo grelhado	3ª feira
+208	Torres	Braga	Vila Verde	Tradicional portuguesa	Cabrito, Bacalhau	5ª feira
+209	Cidadela Transmontana	Vinhais	Vinhais	Regional	Pratos relacionados com caça e fumeiro.	Domingo
+210	Madre Garcia	Vinhais	Vinhais	Regional	Posta  Mirandesa	Sábado
+211	O Delfim	Vinhais	Vinhais	Regional	"Vitela no churrasco; variedade de fumeiro e caça."	Sábado
+212	Solar de Montemuro	Cinfães	Viseu	Regional	"Papas de perdiz; Vitela assada "	Não encerra
+213	Xisto	Vizela	Vizela	Regional	Folhados de aves 	2ª. feira
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/turistas1.data b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/turistas1.data
new file mode 100644
index 0000000..e78bb6e
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2023-v2/turistas1.data
@@ -0,0 +1,11533 @@
+   1.5800000e+02	   5.9000000e+01	   2.4000000e+01	   4.0000000e+00	
+   2.0400000e+02	   1.3100000e+02	   6.0000000e+00	   5.0000000e+00	
+   4.2400000e+02	   1.7600000e+02	   1.6000000e+01	   2.0000000e+00	
+   6.1100000e+02	   1.3400000e+02	   1.8000000e+01	   1.0000000e+00	
+   3.6300000e+02	   1.6100000e+02	   1.6000000e+01	   1.0000000e+00	
+   3.3200000e+02	   1.3400000e+02	   6.0000000e+00	   3.0000000e+00	
+   2.5400000e+02	   9.4000000e+01	   5.0000000e+00	   2.0000000e+00	
+   3.6800000e+02	   1.3600000e+02	   2.6000000e+01	   1.0000000e+00	
+   1.1300000e+02	   9.0000000e+00	   2.3000000e+01	   3.0000000e+00	
+   1.5500000e+02	   1.3800000e+02	   1.6000000e+01	   5.0000000e+00	
+   4.6500000e+02	   5.4000000e+01	   4.0000000e+00	   3.0000000e+00	
+   2.2100000e+02	   7.8000000e+01	   1.8000000e+01	   5.0000000e+00	
+   4.0500000e+02	   8.0000000e+01	   1.6000000e+01	   5.0000000e+00	
+   7.5000000e+01	   1.2000000e+02	   3.0000000e+01	   5.0000000e+00	
+   7.8200000e+02	   5.2000000e+01	   1.4000000e+01	   5.0000000e+00	
+   1.7300000e+02	   1.2000000e+01	   2.2000000e+01	   3.0000000e+00	
+   2.7000000e+02	   5.1000000e+01	   1.2000000e+01	   5.0000000e+00	
+   3.1800000e+02	   1.6400000e+02	   3.0000000e+01	   1.0000000e+00	
+   4.9400000e+02	   9.5000000e+01	   9.0000000e+00	   3.0000000e+00	
+   7.0300000e+02	   1.0000000e+02	   5.0000000e+00	   2.0000000e+00	
+   4.0000000e+02	   1.2000000e+01	   2.4000000e+01	   1.0000000e+00	
+   4.5400000e+02	   1.1300000e+02	   2.6000000e+01	   3.0000000e+00	
+   8.0500000e+02	   2.0500000e+02	   1.4000000e+01	   4.0000000e+00	
+   2.1600000e+02	   5.7000000e+01	   8.0000000e+00	   4.0000000e+00	
+   2.2400000e+02	   1.6900000e+02	   9.0000000e+00	   3.0000000e+00	
+   7.1300000e+02	   8.1000000e+01	   3.0000000e+00	   5.0000000e+00	
+   2.2000000e+01	   2.5000000e+01	   1.5000000e+01	   4.0000000e+00	
+   4.4500000e+02	   1.2500000e+02	   5.0000000e+00	   5.0000000e+00	
+   1.6200000e+02	   7.1000000e+01	   2.8000000e+01	   5.0000000e+00	
+   2.4500000e+02	   1.1800000e+02	   1.5000000e+01	   5.0000000e+00	
+   8.2900000e+02	   3.2000000e+01	   1.3000000e+01	   3.0000000e+00	
+   5.6700000e+02	   1.0000000e+00	   2.2000000e+01	   3.0000000e+00	
+   5.7400000e+02	   1.8200000e+02	   2.1000000e+01	   5.0000000e+00	
+   7.2800000e+02	   2.8000000e+01	   1.0000000e+01	   3.0000000e+00	
+   2.1200000e+02	   9.9000000e+01	   1.8000000e+01	   2.0000000e+00	
+   2.3000000e+01	   1.7200000e+02	   2.1000000e+01	   4.0000000e+00	
+   7.4900000e+02	   1.9200000e+02	   2.3000000e+01	   2.0000000e+00	
+   3.3500000e+02	   3.2000000e+01	   3.0000000e+00	   2.0000000e+00	
+   2.6200000e+02	   1.6200000e+02	   1.6000000e+01	   5.0000000e+00	
+   5.9100000e+02	   1.3400000e+02	   6.0000000e+00	   5.0000000e+00	
+   6.9400000e+02	   9.0000000e+00	   2.3000000e+01	   1.0000000e+00	
+   3.8100000e+02	   1.3500000e+02	   2.4000000e+01	   2.0000000e+00	
+   5.5000000e+02	   2.9000000e+01	   9.0000000e+00	   4.0000000e+00	
+   3.0700000e+02	   1.8000000e+01	   2.9000000e+01	   5.0000000e+00	
+   8.3400000e+02	   1.7000000e+02	   9.0000000e+00	   4.0000000e+00	
+   1.6500000e+02	   3.4000000e+01	   2.7000000e+01	   5.0000000e+00	
+   5.4300000e+02	   1.6000000e+02	   1.6000000e+01	   5.0000000e+00	
+   4.7000000e+01	   3.3000000e+01	   1.3000000e+01	   3.0000000e+00	
+   2.5700000e+02	   1.3000000e+01	   4.0000000e+00	   1.0000000e+00	
+   3.0500000e+02	   1.0900000e+02	   1.2000000e+01	   2.0000000e+00	
+   3.8300000e+02	   2.1200000e+02	   1.9000000e+01	   2.0000000e+00	
+   1.0700000e+02	   1.0700000e+02	   1.2000000e+01	   4.0000000e+00	
+   7.1000000e+02	   1.4000000e+02	   2.1000000e+01	   5.0000000e+00	
+   7.8400000e+02	   1.8200000e+02	   1.8000000e+01	   1.0000000e+00	
+   4.7500000e+02	   8.9000000e+01	   9.0000000e+00	   2.0000000e+00	
+   2.3500000e+02	   1.3100000e+02	   9.0000000e+00	   4.0000000e+00	
+   2.8700000e+02	   5.7000000e+01	   1.1000000e+01	   1.0000000e+00	
+   5.0700000e+02	   6.0000000e+01	   1.9000000e+01	   5.0000000e+00	
+   3.3700000e+02	   5.0000000e+00	   1.9000000e+01	   4.0000000e+00	
+   3.2700000e+02	   1.8900000e+02	   1.5000000e+01	   3.0000000e+00	
+   3.7900000e+02	   3.4000000e+01	   1.0000000e+01	   1.0000000e+00	
+   5.7000000e+02	   4.3000000e+01	   1.0000000e+01	   4.0000000e+00	
+   1.8100000e+02	   2.0500000e+02	   3.0000000e+01	   4.0000000e+00	
+   2.8600000e+02	   1.8500000e+02	   2.1000000e+01	   1.0000000e+00	
+   5.8300000e+02	   6.1000000e+01	   1.6000000e+01	   3.0000000e+00	
+   7.7300000e+02	   1.6200000e+02	   2.0000000e+01	   5.0000000e+00	
+   5.7400000e+02	   1.0100000e+02	   2.6000000e+01	   2.0000000e+00	
+   5.3300000e+02	   1.9900000e+02	   9.0000000e+00	   1.0000000e+00	
+   6.0200000e+02	   1.0300000e+02	   6.0000000e+00	   2.0000000e+00	
+   3.0900000e+02	   5.6000000e+01	   1.1000000e+01	   1.0000000e+00	
+   5.2700000e+02	   2.0500000e+02	   2.0000000e+01	   5.0000000e+00	
+   5.5900000e+02	   1.8700000e+02	   8.0000000e+00	   4.0000000e+00	
+   8.4000000e+01	   5.2000000e+01	   2.1000000e+01	   1.0000000e+00	
+   1.8400000e+02	   5.7000000e+01	   1.4000000e+01	   4.0000000e+00	
+   1.3600000e+02	   8.2000000e+01	   2.6000000e+01	   4.0000000e+00	
+   1.6900000e+02	   1.0000000e+01	   2.4000000e+01	   3.0000000e+00	
+   7.1500000e+02	   1.3400000e+02	   3.0000000e+01	   2.0000000e+00	
+   4.6600000e+02	   1.8200000e+02	   2.6000000e+01	   3.0000000e+00	
+   3.6600000e+02	   1.8300000e+02	   2.8000000e+01	   1.0000000e+00	
+   3.7200000e+02	   5.0000000e+01	   1.6000000e+01	   5.0000000e+00	
+   1.1500000e+02	   1.2500000e+02	   1.6000000e+01	   4.0000000e+00	
+   1.2800000e+02	   1.8200000e+02	   1.3000000e+01	   5.0000000e+00	
+   6.4600000e+02	   1.4000000e+02	   2.8000000e+01	   4.0000000e+00	
+   8.1800000e+02	   1.0900000e+02	   4.0000000e+00	   4.0000000e+00	
+   3.5900000e+02	   3.3000000e+01	   3.0000000e+01	   3.0000000e+00	
+   4.2000000e+02	   1.9900000e+02	   1.3000000e+01	   2.0000000e+00	
+   8.3500000e+02	   1.6800000e+02	   1.3000000e+01	   2.0000000e+00	
+   3.3300000e+02	   1.2200000e+02	   2.0000000e+01	   4.0000000e+00	
+   5.9800000e+02	   1.4400000e+02	   1.1000000e+01	   4.0000000e+00	
+   4.8900000e+02	   1.3900000e+02	   2.0000000e+01	   5.0000000e+00	
+   7.8100000e+02	   2.0500000e+02	   2.6000000e+01	   5.0000000e+00	
+   5.7100000e+02	   1.9800000e+02	   2.8000000e+01	   1.0000000e+00	
+   7.7700000e+02	   1.6500000e+02	   1.4000000e+01	   1.0000000e+00	
+   1.6800000e+02	   1.7400000e+02	   1.3000000e+01	   1.0000000e+00	
+   7.9100000e+02	   1.7200000e+02	   6.0000000e+00	   5.0000000e+00	
+   3.5900000e+02	   1.8900000e+02	   1.6000000e+01	   1.0000000e+00	
+   1.7900000e+02	   6.5000000e+01	   1.9000000e+01	   5.0000000e+00	
+   2.5100000e+02	   1.9800000e+02	   1.6000000e+01	   5.0000000e+00	
+   6.9000000e+01	   1.8200000e+02	   2.7000000e+01	   2.0000000e+00	
+   2.0000000e+02	   1.5600000e+02	   1.4000000e+01	   3.0000000e+00	
+   2.5200000e+02	   1.6000000e+02	   6.0000000e+00	   1.0000000e+00	
+   4.4400000e+02	   5.6000000e+01	   9.0000000e+00	   2.0000000e+00	
+   9.0000000e+01	   2.0900000e+02	   2.0000000e+01	   5.0000000e+00	
+   3.9300000e+02	   5.6000000e+01	   3.0000000e+00	   1.0000000e+00	
+   5.2800000e+02	   1.7200000e+02	   3.0000000e+00	   3.0000000e+00	
+   7.1800000e+02	   5.8000000e+01	   3.0000000e+01	   4.0000000e+00	
+   6.2500000e+02	   1.3400000e+02	   2.3000000e+01	   4.0000000e+00	
+   1.3700000e+02	   1.4300000e+02	   2.6000000e+01	   1.0000000e+00	
+   2.9000000e+01	   6.7000000e+01	   1.1000000e+01	   5.0000000e+00	
+   2.9000000e+02	   1.2000000e+02	   7.0000000e+00	   3.0000000e+00	
+   6.8000000e+02	   3.6000000e+01	   1.8000000e+01	   1.0000000e+00	
+   8.1100000e+02	   1.7000000e+02	   1.5000000e+01	   1.0000000e+00	
+   4.1800000e+02	   4.9000000e+01	   7.0000000e+00	   1.0000000e+00	
+   3.2900000e+02	   9.0000000e+01	   1.1000000e+01	   3.0000000e+00	
+   4.2300000e+02	   1.1600000e+02	   2.4000000e+01	   5.0000000e+00	
+   5.9900000e+02	   1.2800000e+02	   2.4000000e+01	   3.0000000e+00	
+   7.7400000e+02	   1.1300000e+02	   1.5000000e+01	   4.0000000e+00	
+   5.4000000e+01	   1.3600000e+02	   1.9000000e+01	   5.0000000e+00	
+   3.1300000e+02	   1.2100000e+02	   2.9000000e+01	   1.0000000e+00	
+   6.0300000e+02	   1.1900000e+02	   1.0000000e+01	   3.0000000e+00	
+   3.5300000e+02	   1.7200000e+02	   1.4000000e+01	   3.0000000e+00	
+   3.1100000e+02	   1.7900000e+02	   1.8000000e+01	   4.0000000e+00	
+   1.3400000e+02	   2.0500000e+02	   6.0000000e+00	   4.0000000e+00	
+   5.3400000e+02	   1.5900000e+02	   3.0000000e+01	   4.0000000e+00	
+   2.6600000e+02	   6.9000000e+01	   1.3000000e+01	   1.0000000e+00	
+   2.7500000e+02	   1.4100000e+02	   1.7000000e+01	   5.0000000e+00	
+   1.0600000e+02	   1.0000000e+01	   2.5000000e+01	   1.0000000e+00	
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+   1.6000000e+01	   6.9000000e+01	   1.3000000e+01	   1.0000000e+00	
+   4.3900000e+02	   1.6000000e+02	   1.3000000e+01	   2.0000000e+00	
diff --git a/2ano1/MPEI/trabalho-pratico-2-2023-2024-v1 b/2ano1/MPEI/trabalho-pratico-2-2023-2024-v1
new file mode 160000
index 0000000..4ed6f70
--- /dev/null
+++ b/2ano1/MPEI/trabalho-pratico-2-2023-2024-v1
@@ -0,0 +1 @@
+Subproject commit 4ed6f70d613dc0a9802c4442c450105c970e1505