This repository contains implementations of various algorithmic problems, each organized in its own directory with comprehensive documentation and testing.

• Find and analyze ways to decompose numbers into sums of distinct perfect squares
• Implementation includes visualization of patterns and interactive interface
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• Implementation of Karatsuba's algorithm for large integer multiplication
• Comparison with grade school multiplication method
• Performance analysis and visualization
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• Calculate distance between permutations
• Efficient implementation without using sort operations
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• Find longest increasing sequence in a matrix with neighboring constraints
• Includes visualization with colored output
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• Find longest paths in directed acyclic graphs
• Handles various graph sizes with performance constraints
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• Count intervals in a list summing to a target value
• Efficient implementation without using Python's sum operator
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.
├── README.md
├── asd_assignment/           # Assignment 1
│   ├── src/
│   ├── tests/
│   └── README.md
├── integer_multiplication/   # Assignment 2
│   ├── src/
│   ├── tests/
│   └── README.md
├── kendall_tau/             # Assignment 3
│   ├── src/
│   ├── tests/
│   └── README.md
├── snake_matrix/            # Assignment 4
│   ├── src/
│   ├── tests/
│   └── README.md
├── longest_paths/           # Assignment 5
│   ├── src/
│   ├── tests/
│   └── README.md
└── interval_sum/            # Assignment 6
    ├── src/
    ├── tests/
    └── README.md

1. Python Environment Setup:

pip install matplotlib numpy tqdm

2. Running Tests:

python -m unittest discover -s <assignment_directory>/tests

Each assignment has specific performance constraints:

• ASD: < 1 second for n ≤ 10^4
• Integer Multiplication: < 10 seconds for n ≤ 10^4
• Kendall Tau: ~ 1 second for n ≤ 10^5
• Snake Matrix: < 1 second for m,n ≤ 10^3
• Longest Paths: varies by graph size (1-10 seconds)
• Interval Sum: ~ 1 second for n ≤ 10^6

Each assignment directory contains:

1. Source code with core implementation
2. Test suite with comprehensive test cases
3. Documentation with examples and analysis
4. Visualization tools where applicable

Each assignment includes:

• Problem description
• Implementation details
• Example inputs/outputs
• Performance analysis
• Visualization (where applicable)
• Usage instructions

For detailed information about each assignment, refer to the README.md file in the respective assignment directory.