feat: add Hamming distance algorithm

[AliAlimohammadi]

Description

This PR adds an implementation of the Hamming distance algorithm to the bit manipulation module. The Hamming distance is a metric for comparing two binary data strings, measuring the minimum number of substitutions required to change one string into the other.

Implementation Details

The implementation provides two public functions:

1. hamming_distance(a: u64, b: u64) -> u64

   • Calculates the Hamming distance between two 64-bit unsigned integers
   • Uses XOR operation to identify differing bits
   • Counts set bits in the XOR result using a helper function

2. hamming_distance_str(a: &str, b: &str) -> u64

   • Calculates the Hamming distance between two strings of equal length
   • Iterates through character pairs and counts differences
   • Panics with a descriptive message if string lengths differ

Algorithm Approach

For integers:

• $XOR$ the two numbers (this sets bits where they differ)
• Count the number of set bits in the result
• Time complexity: $O(log n)$ where n is the value of the larger number
• Space complexity: $O(1)$

For strings:

• Zip the two strings together
• Filter and count positions where characters differ
• Time complexity: $O(n)$ where n is the string length
• Space complexity: $O(1)$

Changes Made

• ✅ Added src/bit_manipulation/hamming_distance.rs with complete implementation
• ✅ Updated src/bit_manipulation/mod.rs to include and export the new module
• ✅ Implemented comprehensive unit tests covering:
  • Integer Hamming distance with multiple test cases
  • String Hamming distance with various scenarios
  • Panic behavior for strings of different lengths
  • Edge cases (identical values, zero values)
• ✅ Added documentation with examples for all public functions
• ✅ Included doctests that demonstrate usage

Type of Change

• New algorithm implementation
• Documentation (docstrings and examples)
• Tests

Testing

All tests pass successfully:

cargo test hamming_distance
cargo test --doc
cargo fmt --check
cargo clippy -- -D warnings

Test Coverage

• ✅ Basic integer Hamming distance calculations
• ✅ Edge cases (zero, identical values)
• ✅ String Hamming distance with binary strings
• ✅ String Hamming distance with alphanumeric strings
• ✅ Panic behavior for mismatched string lengths
• ✅ Doctests for public API

Examples

use the_algorithms_rust::bit_manipulation::{hamming_distance, hamming_distance_str};

// Integer example: 11 (1011) vs 2 (0010) = 2 differing bits
assert_eq!(hamming_distance(11, 2), 2);

// String example
assert_eq!(hamming_distance_str("1101", "1111"), 1);
assert_eq!(hamming_distance_str("alpha", "alphb"), 1);

Checklist

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• I have added tests that prove my implementation is correct
• New and existing unit tests pass locally with my changes
• I have checked my code with cargo fmt
• I have checked my code with cargo clippy
• Any dependent changes have been merged and published

[AliAlimohammadi]

@siriak, this is ready to be merged.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.78%. Comparing base (ba7ca98) to head (4caa180).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #983      +/-   ##
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+ Coverage   95.77%   95.78%   +0.01%     
==========================================
  Files         353      354       +1     
  Lines       23363    23407      +44     
==========================================
+ Hits        22376    22421      +45     
+ Misses        987      986       -1     

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