Add Edit Distance Algorithm to Dynamic Programming

[staging-devin-ai-integration]

Add Edit Distance Algorithm to Dynamic Programming

This pull request adds the implementation of the Edit Distance algorithm to the Dynamic Programming (DP) section of the algorithms repository.

Description

The Edit Distance algorithm calculates the minimum number of operations (insertion, deletion, substitution) required to transform one string into another. This is a classic dynamic programming problem with applications in spell checking, DNA sequence alignment, and natural language processing.

Implementation Details

• File: dp/edit_distance.py
• Time Complexity: O(m*n), where m and n are the lengths of the input strings
• Space Complexity: O(m*n)

The algorithm uses a 2D DP table to store intermediate results, with each cell representing the minimum edit distance for substrings of the input strings.

Test Cases

A comprehensive set of unit tests has been added in dp/test_edit_distance.py, covering:

1. Basic cases
2. Edge cases (empty strings, identical strings)
3. Single character operations (insertion, deletion, substitution)
4. Long strings

All tests pass successfully, ensuring the correctness of the implementation.

Integration with Existing Codebase

This new algorithm complements the existing DP algorithms in the repository, providing a solution to a fundamental string manipulation problem. It follows the coding style and structure of other algorithms in the project.

Usage Example

from dp.edit_distance import edit_distance

str1 = "kitten"
str2 = "sitting"
distance = edit_distance(str1, str2)
print(f"Edit distance between '{str1}' and '{str2}': {distance}")
# Output: Edit distance between 'kitten' and 'sitting': 3

This PR is ready for review and integration into the main branch.

This Devin run was requested by Federico.

[marcosfede]

can you change this to dog?

[staging-devin-ai-integration]

Closing due to inactivity.