feat: Hamming distance algorithm. (#1376)

* Added bit manipulation algorithms.

* Removed Power of 2 and xor swap.

* Update bit_manipulation/hamming_distance.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update bit_manipulation/hamming_distance.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update bit_manipulation/hamming_distance.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for ae4d4707

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* test: docs: Added tests and docs for hamming distance.

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for 94fb407b

* Update bit_manipulation/hamming_distance.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* feat: Added string method for hamming distance.

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for 455dce1d

* fix: Make hamming distance algorithm work for all strings.

* clang-format and clang-tidy fixes for ba18ec04

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -10,6 +10,9 @@
   * [Rat Maze](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/rat_maze.cpp)
   * [Sudoku Solve](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/sudoku_solve.cpp)
 
+## Bit Manipulation
+  * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/hamming_distance.cpp)
+
 ## Ciphers
   * [Caesar Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/caesar_cipher.cpp)
   * [Hill Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/hill_cipher.cpp)

bit_manipulation/hamming_distance.cpp

@@ -0,0 +1,107 @@
+/**
+ * @file
+ * @brief Returns the [Hamming
+ * distance](https://en.wikipedia.org/wiki/Hamming_distance) between two
+ * integers
+ *
+ * @details
+ * To find hamming distance between two integers, we take their xor, which will
+ * have a set bit iff those bits differ in the two numbers.
+ * Hence, we return the number of such set bits.
+ *
+ * @author [Ravishankar Joshi](https://github.com/ravibitsgoa)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for io operations
+
+/**
+ * @namespace bit_manipulation
+ * @brief Bit Manipulation algorithms
+ */
+namespace bit_manipulation {
+/**
+ * @namespace hamming_distance
+ * @brief Functions for [Hamming
+ * distance](https://en.wikipedia.org/wiki/Hamming_distance) implementation
+ */
+namespace hamming_distance {
+/**
+ * This function returns the number of set bits in the given number.
+ * @param value the number of which we want to count the number of set bits.
+ * @returns the number of set bits in the given number.
+ */
+uint64_t bitCount(uint64_t value) {
+    uint64_t count = 0;
+    while (value) {       // until all bits are zero
+        if (value & 1) {  // check lower bit
+            count++;
+        }
+        value >>= 1;  // shift bits, removing lower bit
+    }
+    return count;
+}
+
+/**
+ * This function returns the hamming distance between two integers.
+ * @param a the first number
+ * @param b the second number
+ * @returns the number of bits differing between the two integers.
+ */
+uint64_t hamming_distance(uint64_t a, uint64_t b) { return bitCount(a ^ b); }
+
+/**
+ * This function returns the hamming distance between two strings.
+ * @param a the first string
+ * @param b the second string
+ * @returns the number of characters differing between the two strings.
+ */
+uint64_t hamming_distance(const std::string& a, const std::string& b) {
+    assert(a.size() == b.size());
+    size_t n = a.size();
+    uint64_t count = 0;
+    for (size_t i = 0; i < n; i++) {
+        count += (b[i] != a[i]);
+    }
+    return count;
+}
+}  // namespace hamming_distance
+}  // namespace bit_manipulation
+
+/**
+ * @brief Function to the test hamming distance.
+ * @returns void
+ */
+static void test() {
+    assert(bit_manipulation::hamming_distance::hamming_distance(11, 2) == 2);
+    assert(bit_manipulation::hamming_distance::hamming_distance(2, 0) == 1);
+    assert(bit_manipulation::hamming_distance::hamming_distance(11, 0) == 3);
+
+    assert(bit_manipulation::hamming_distance::hamming_distance("1101",
+                                                                "1111") == 1);
+    assert(bit_manipulation::hamming_distance::hamming_distance("1111",
+                                                                "1111") == 0);
+    assert(bit_manipulation::hamming_distance::hamming_distance("0000",
+                                                                "1111") == 4);
+
+    assert(bit_manipulation::hamming_distance::hamming_distance("alpha",
+                                                                "alphb") == 1);
+    assert(bit_manipulation::hamming_distance::hamming_distance("abcd",
+                                                                "abcd") == 0);
+    assert(bit_manipulation::hamming_distance::hamming_distance("dcba",
+                                                                "abcd") == 4);
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();           // execute the tests
+    uint64_t a = 11;  // 1011 in binary
+    uint64_t b = 2;   // 0010 in binary
+
+    std::cout << "Hamming distance between " << a << " and " << b << " is "
+              << bit_manipulation::hamming_distance::hamming_distance(a, b)
+              << std::endl;
+}