feat: add Hamming distance algorithm

DIRECTORY.md

@@ -19,6 +19,7 @@
   * Bit Manipulation
     * [Binary Coded Decimal](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/binary_coded_decimal.rs)
     * [Counting Bits](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/counting_bits.rs)
+    * [Hamming Distance](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/hamming_distance.rs)
     * [Highest Set Bit](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/highest_set_bit.rs)
     * [Is Power of Two](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/is_power_of_two.rs)
     * [Missing Number](https://github.com/TheAlgorithms/Rust/blob/master/src/bit_manipulation/find_missing_number.rs)

src/bit_manipulation/hamming_distance.rs

@@ -0,0 +1,136 @@
+//! Hamming Distance
+//!
+//! This module implements the [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance)
+//! algorithm for both integers and strings.
+//!
+//! The Hamming distance between two values is the number of positions at which
+//! the corresponding symbols differ.
+
+/// Counts the number of set bits (1s) in a 64-bit unsigned integer.
+///
+/// # Arguments
+///
+/// * `value` - The number to count set bits in
+///
+/// # Returns
+///
+/// The number of set bits in the value
+///
+/// # Example
+///
+/// ```
+/// // This is a private helper function
+/// let value: u64 = 11; // 1011 in binary has 3 set bits
+/// ```
+fn bit_count(mut value: u64) -> u64 {
+    let mut count = 0;
+    while value != 0 {
+        if value & 1 == 1 {
+            count += 1;
+        }
+        value >>= 1;
+    }
+    count
+}
+
+/// Calculates the Hamming distance between two unsigned 64-bit integers.
+///
+/// The Hamming distance is the number of bit positions at which the
+/// corresponding bits differ. This is computed by taking the XOR of the
+/// two numbers and counting the set bits.
+///
+/// # Arguments
+///
+/// * `a` - The first integer
+/// * `b` - The second integer
+///
+/// # Returns
+///
+/// The number of differing bits between `a` and `b`
+///
+/// # Example
+///
+/// ```
+/// use the_algorithms_rust::bit_manipulation::hamming_distance;
+///
+/// let distance = hamming_distance(11, 2);
+/// assert_eq!(distance, 2);
+/// ```
+pub fn hamming_distance(a: u64, b: u64) -> u64 {
+    bit_count(a ^ b)
+}
+
+/// Calculates the Hamming distance between two strings of equal length.
+///
+/// The Hamming distance is the number of positions at which the
+/// corresponding characters differ.
+///
+/// # Arguments
+///
+/// * `a` - The first string
+/// * `b` - The second string
+///
+/// # Returns
+///
+/// The number of differing characters between `a` and `b`
+///
+/// # Panics
+///
+/// Panics if the strings have different lengths
+///
+/// # Example
+///
+/// ```
+/// use the_algorithms_rust::bit_manipulation::hamming_distance_str;
+///
+/// let distance = hamming_distance_str("1101", "1111");
+/// assert_eq!(distance, 1);
+/// ```
+pub fn hamming_distance_str(a: &str, b: &str) -> u64 {
+    assert_eq!(
+        a.len(),
+        b.len(),
+        "Strings must have the same length for Hamming distance calculation"
+    );
+
+    a.chars()
+        .zip(b.chars())
+        .filter(|(ch_a, ch_b)| ch_a != ch_b)
+        .count() as u64
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_bit_count() {
+        assert_eq!(bit_count(0), 0);
+        assert_eq!(bit_count(11), 3); // 1011 in binary
+        assert_eq!(bit_count(15), 4); // 1111 in binary
+    }
+
+    #[test]
+    fn test_hamming_distance_integers() {
+        assert_eq!(hamming_distance(11, 2), 2);
+        assert_eq!(hamming_distance(2, 0), 1);
+        assert_eq!(hamming_distance(11, 0), 3);
+        assert_eq!(hamming_distance(0, 0), 0);
+    }
+
+    #[test]
+    fn test_hamming_distance_strings() {
+        assert_eq!(hamming_distance_str("1101", "1111"), 1);
+        assert_eq!(hamming_distance_str("1111", "1111"), 0);
+        assert_eq!(hamming_distance_str("0000", "1111"), 4);
+        assert_eq!(hamming_distance_str("alpha", "alphb"), 1);
+        assert_eq!(hamming_distance_str("abcd", "abcd"), 0);
+        assert_eq!(hamming_distance_str("dcba", "abcd"), 4);
+    }
+
+    #[test]
+    #[should_panic(expected = "Strings must have the same length")]
+    fn test_hamming_distance_strings_different_lengths() {
+        hamming_distance_str("abc", "abcd");
+    }
+}

src/bit_manipulation/mod.rs

@@ -4,6 +4,7 @@ mod counting_bits;
 mod find_missing_number;
 mod find_previous_power_of_two;
 mod find_unique_number;
+mod hamming_distance;
 mod highest_set_bit;
 mod is_power_of_two;
 mod n_bits_gray_code;
@@ -19,6 +20,7 @@ pub use self::counting_bits::count_set_bits;
 pub use self::find_missing_number::find_missing_number;
 pub use self::find_previous_power_of_two::find_previous_power_of_two;
 pub use self::find_unique_number::find_unique_number;
+pub use self::hamming_distance::{hamming_distance, hamming_distance_str};
 pub use self::highest_set_bit::find_highest_set_bit;
 pub use self::is_power_of_two::is_power_of_two;
 pub use self::n_bits_gray_code::generate_gray_code;