MD lines ending with two spaces removed

Author: lee-naish

src/algorithms/explanations/ASTExp.md

@@ -19,7 +19,7 @@ Others of these algorithms work with weighted graphs
 where the aim is to find the least cost path(s), while BFS and DFS
 ignore edge weights and Prim's
 algorithm finds a minumum spanning tree of the graph (the least cost 
-set of edges that connects all nodes, if the graph is connected).  
+set of edges that connects all nodes, if the graph is connected).
 
 These graph traversal algorithms can be used for both directed
 and undirected graphs; in AIA we use undirected graphs for simplicity.

src/algorithms/explanations/AVLExp original Dec 2024.md

@@ -13,7 +13,7 @@ structure.
 Others of these algorithms work with weighted graphs (with positive weights
 for all edges), where the aim is to find the least cost path(s), while Prim's
 algorithm finds a minumum spanning tree of the graph (the least cost 
-set of edges that connects all nodes, if the graph is connected).  
+set of edges that connects all nodes, if the graph is connected).
 
 These graph traversal algorithms can be used for both directed
 and undirected graphs; in AIA we use undirected graphs for simplicity.

src/algorithms/explanations/BFSExp.md

@@ -16,7 +16,7 @@ structure.
 Others of these algorithms work with weighted graphs (with positive weights
 for all edges), where the aim is to find the least cost path(s), while Prim's
 algorithm finds a minumum spanning tree of the graph (the least cost 
-set of edges that connects all nodes, if the graph is connected).  
+set of edges that connects all nodes, if the graph is connected).
 
 These graph traversal algorithms can be used for both directed
 and undirected graphs; in AIA we use undirected graphs for simplicity.

src/algorithms/explanations/DFSExp.md

@@ -13,7 +13,7 @@ Others of these algorithms work with weighted graphs
 where the aim is to find the least cost path(s), while BFS and DFS
 ignore edge weights and Prim's
 algorithm finds a minumum spanning tree of the graph (the least cost 
-set of edges that connects all nodes, if the graph is connected).  
+set of edges that connects all nodes, if the graph is connected).
 
 These graph traversal algorithms can be used for both directed
 and undirected graphs; in AIA we use undirected graphs for simplicity.

src/algorithms/explanations/DIJKExp.md

@@ -3,11 +3,11 @@
 Horspool's algorithm uses a preprocessing of the pattern P to limit the number of partial matches attempted, compared to the brute-force method. 
 As with the brute-force method, we can think of P as "sliding along" the text T. Horspool's method, however, matches the pattern P from right to left. 
 Its preprocessing generates a Shift Table which gives, for each character, the number of places to shift the pattern along, in case of a failed partial match. 
-The shift table has a value for every character in the alphabet, including characters that are not in pattern P, but could be in text T. The alphabet contains all characters that might possibly be in the text and pattern.  
+The shift table has a value for every character in the alphabet, including characters that are not in pattern P, but could be in text T. The alphabet contains all characters that might possibly be in the text and pattern.
 
-In this visualization, the alphabet contains all letters in the Roman alphabet (A-Z) plus the Space character.  Alphabets might be smaller, e.g. for DNA sequences the alphabet would be the four bases, or they might be larger, e.g. the characters found in English literature, which would include both upper and lower case letters, space, punctuation, numbers, etc.  
+In this visualization, the alphabet contains all letters in the Roman alphabet (A-Z) plus the Space character.  Alphabets might be smaller, e.g. for DNA sequences the alphabet would be the four bases, or they might be larger, e.g. the characters found in English literature, which would include both upper and lower case letters, space, punctuation, numbers, etc.
 
-As an example of how the Shift Table is used:  
+As an example of how the Shift Table is used:
 
 If the pattern is "wally" and matching fails (immediately) because the
     'y' gets compared against an 'x' in the text, a character not found in the pattern,
@@ -19,4 +19,4 @@ If the failure was due to comparing 'y' against an 'a', a character
     we need to start another attempted match from the rightmost end of the pattern. Where a
     character appears repeatedly in the pattern, as 'l' does in the "wally"
     example, it is the last occurrence that counts, so in this example
-    the shift therefore will be 1, not 2.	 
+    the shift therefore will be 1, not 2.	 

src/algorithms/explanations/HSSExp.md

@@ -3,7 +3,7 @@
 ---
 
 Warshalls algorithm computes the transitive closure of a directed 
-graph, that is, what nodes can be reached from other nodes.  
+graph, that is, what nodes can be reached from other nodes.
 
 The algorithm starts with an adjacency matrix A for a directed graph G
 with n nodes. In the adjacency matrix, A[i,j] = 1 indicates that 
@@ -14,12 +14,12 @@ i to j, possibly with several intermediate steps between i and j.
 
 The algorithm uses three nested loops that iterate over all the nodes
 but the order of the nesting is crucial for correctness. 
-    
+
 ## The logic is as follows.
-    
+
 We start with the matrix describing direct reachability
 (using a single edge and no intermediate nodes). 
-    
+
 We first compute reachability that may include node 1 as an intermediate node 
 (as well as direct reachability), then compute reachability that may include 
 nodes 1 and/or 2, and so on, up to n. 

src/algorithms/explanations/TCExp.md

@@ -15,7 +15,7 @@ less than the keys in child2.
 Three-nodes have two keys and three subtrees, named and
 ordered child1, key1, child2, key2, child3.  Four-nodes have three keys
 and four subtrees, named and ordered child1, key1, child2, key2, child3,
-key3, child4.  
+key3, child4.
 
 For simplicity, equal keys have been ignored in this module. One way of handling duplicate
 keys would be to have a linked list of records originating in the node. Alternatively an
@@ -36,7 +36,7 @@ it is simplest to implement the
 encountered as we traverse down the tree. There is a more complicated
 "bottom up" version that waits to split four-nodes until the split is actually needed.  The
 "bottom-up" version can slightly reduce the number of nodes in the
-tree in some cases, potentially improving efficiency.  
+tree in some cases, potentially improving efficiency.
 
 ---
 

src/algorithms/explanations/TTFExp.md

@@ -2,25 +2,25 @@
 
 ---
 
-Natural merge sort is a variation of the merge sort algorithm that 
-takes advantage of the natural order present in the input array. 
-Natural merge sort scans through the array to identify naturally 
-occurring sorted sequences (runs) and merges consecutive pairs of 
+Natural merge sort is a variation of the merge sort algorithm that
+takes advantage of the natural order present in the input array.
+Natural merge sort scans through the array to identify naturally
+occurring sorted sequences (runs) and merges consecutive pairs of
 runs, until a single run remains.
 
-The merge operation is not in-place - it requires O(n) extra space.  
-A simple solution (used here) is to merge the two sorted sub-arrays 
-to a temporary array then copy them back to the original array. 
-Merge uses three pointers/indices that scan from left to right; 
-one for each of the input sub-arrays and one for the output array.  
-At each stage the minimum input array element is copied to the 
-output array and the indices for those two arrays are incremented. 
-When one input array has been completely copied, any additional 
-elements in the other input array are copied to the output array. 
+The merge operation is not in-place - it requires O(n) extra space.
+A simple solution (used here) is to merge the two sorted sub-arrays
+to a temporary array then copy them back to the original array.
+Merge uses three pointers/indices that scan from left to right;
+one for each of the input sub-arrays and one for the output array.
+At each stage the minimum input array element is copied to the
+output array and the indices for those two arrays are incremented.
+When one input array has been completely copied, any additional
+elements in the other input array are copied to the output array.
 
-Natural merge sort is stable meaning the relative order of equal 
-elements is preserved. In the bottom-up merge sort, shown elsewhere, 
-the starting point assumes each run is one item long. In practice, 
-random input data will have many short runs that just happen to be 
-sorted. In the typical case, the natural merge sort may not need 
+Natural merge sort is stable meaning the relative order of equal
+elements is preserved. In the bottom-up merge sort, shown elsewhere,
+the starting point assumes each run is one item long. In practice,
+random input data will have many short runs that just happen to be
+sorted. In the typical case, the natural merge sort may not need
 as many passes because there are fewer runs to merge.