📌 About the Project

The objective of this project is to find the median of two sorted arrays without fully merging them. This is a common algorithmic problem, especially in interview settings, where optimal performance is expected.

The implemented solution uses a non-recursive, linear-time approach that tracks only the necessary elements to determine the median efficiently.

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⚙️ System Workflow

🔁 Iterative Logic

1. Use two pointers i and j to iterate over arr1 and arr2.

2. At each step, select the smaller element and update the variables med1 and med2.

3. Repeat until reaching the middle index of the combined length.

4. Return:

   • med1 if the total number of elements is odd.
   • (med1 + med2) / 2 if the total number of elements is even.

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🗃️ Project Files Overview

File Name	Description
Main.py	Contains the main function median_of_two() and test arrays.
Pseudocode.md	Structured pseudocode version of the algorithm logic.
Code analysis.md	Explains how the algorithm works with examples and key observations.
Time complexity.md	Time complexity analysis and breakdown of each step in the algorithm.

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🧪 Sample Input & Output

Example 1 (Odd total):

arr1 = [1, 2, 6, 9, 13]
arr2 = [3, 5, 14, 17]

# Combined sorted: [1, 2, 3, 5, 6, 9, 13, 14, 17]
# Output: 6

Example 2 (Even total):

arr1 = [1, 2]
arr2 = [3, 5, 6, 9]

# Combined sorted: [1, 2, 3, 5, 6, 9]
# Output: (3 + 5) / 2 = 4.0

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🧠 Key Features

• ✅ Supports both even and odd array lengths.
• 📉 No full merge of arrays required.
• ⏱️ Runs in O(n) time where n = total number of elements.
• 🧮 Simple, readable logic.
• 📄 Pseudocode and analysis files included for educational use.

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🛠️ How to Run the Project

1. Ensure Python 3.x is installed.
2. Clone or download the repository files.
3. (Optional) Sort input arrays before calling the function, as the algorithm assumes sorted input.
4. Run the main script:

python Main.py

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👨‍💻 Team Members

Project Leader: Amr Yasser Badr

Team Members:

• Youssef Mahmoud Younes
• Sama Saeed El-Fishawy