[pull] master from TheAlgorithms:master

DIRECTORY.md

@@ -19,6 +19,7 @@
   * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_set_bits.cpp)
   * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp)
   * [Find Non Repeating Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/find_non_repeating_number.cpp)
+  * [Gray Code](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/gray_code.cpp)
   * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/hamming_distance.cpp)
   * [Next Higher Number With Same Number Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/next_higher_number_with_same_number_of_set_bits.cpp)
   * [Power Of 2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/power_of_2.cpp)
@@ -161,6 +162,7 @@
 ## Greedy Algorithms
   * [Boruvkas Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/boruvkas_minimum_spanning_tree.cpp)
   * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/dijkstra.cpp)
+  * [Gale Shapley](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/gale_shapley.cpp)
   * [Huffman](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/huffman.cpp)
   * [Jump Game](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/jump_game.cpp)
   * [Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/knapsack.cpp)
@@ -377,6 +379,7 @@
   * [Pigeonhole Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/pigeonhole_sort.cpp)
   * [Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/quick_sort.cpp)
   * [Quick Sort 3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/quick_sort_3.cpp)
+  * [Quick Sort Iterative](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/quick_sort_iterative.cpp)
   * [Radix Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/radix_sort.cpp)
   * [Radix Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/radix_sort2.cpp)
   * [Random Pivot Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/random_pivot_quick_sort.cpp)

search/binary_search.cpp

@@ -4,16 +4,16 @@
  * algorithm](https://en.wikipedia.org/wiki/Binary_search_algorithm)
  * @details
  * Binary search is a search algorithm that finds the position of a target value
- * within a sorted array. Binary search compares the target value to the middle
- * element of the array. If they are not equal, the half in which the target
+ * within a sorted array.Just like looking for a word in a dictionary, in binary search we compare the target value to the middle
+ * element of the array. If they are not equal, then the half in which the target
  * cannot lie is eliminated and the search continues on the remaining half,
  * again taking the middle element to compare to the target value, and repeating
  * this until the target value is found. If the search ends with the remaining
  * half being empty, the target is not in the array.
  *
  * ### Implementation
  *
- * Binary search works on sorted arrays. Binary search begins by comparing an
+ * Binary search works on sorted arrays. It begins by comparing an
  * element in the middle of the array with the target value. If the target value
  * matches the element, its position in the array is returned. If the target
  * value is less than the element, the search continues in the lower half of
@@ -28,6 +28,7 @@
  * Worst-case time complexity	O(log n)
  * Best-case time complexity	O(1)
  * Average time complexity	    O(log n)
+ * space complexity  0(1)
  * Worst-case space complexity  0(1)
  *
  * @author [Lajat Manekar](https://github.com/Lazeeez)

strings/duval.cpp

@@ -0,0 +1,118 @@
+/**
+ * @file duval.cpp
+ * @brief Implementation of [Duval's algorithm](https://en.wikipedia.org/wiki/Lyndon_word).
+ *
+ * @details
+ * Duval's algorithm is an algorithm to find the lexicographically smallest
+ * rotation of a string. It is based on the concept of Lyndon words.
+ * Lyndon words are defined as the lexicographically smallest string in a
+ * rotation equivalence class. A rotation equivalence class is a set of strings
+ * that can be obtained by rotating a string. For example, the rotation
+ * equivalence class of "abc" is {"abc", "bca", "cab"}. The lexicographically
+ * smallest string in this class is "abc".
+ *
+ * Duval's algorithm works by iterating over the string and finding the
+ * smallest rotation of the string that is a Lyndon word. This is done by
+ * comparing the string with its suffixes and finding the smallest suffix that
+ * is lexicographically smaller than the string. This suffix is then added to
+ * the result and the process is repeated with the remaining string.
+ * The algorithm has a time complexity of O(n) where n is the length of the
+ * string.
+ *
+ * @note While Lyndon words are described in the context of strings,
+ * Duval's algorithm can be used to find the lexicographically smallest cyclic
+ * shift of any sequence of comparable elements.
+ *
+ * @author [Amine Ghoussaini](https://github.com/aminegh20)
+*/
+
+#include <array>    /// for std::array
+#include <cassert>  /// for assert
+#include <cstddef>  /// for std::size_t
+#include <deque>    /// for std::deque
+#include <iostream> /// for std::cout and std::endl
+#include <string>   /// for std::string
+#include <vector>   /// for std::vector
+
+/**
+ * @brief string manipulation algorithms
+ * @namespace
+ */
+namespace string {
+/**
+ * @brief Find the lexicographically smallest cyclic shift of a sequence.
+ * @tparam T type of the sequence
+ * @param s the sequence
+ * @returns the 0-indexed position of the least cyclic shift of the sequence
+ */
+template <typename T>
+size_t duval(const T& s) {
+    size_t n = s.size();
+    size_t i = 0, ans = 0;
+    while (i < n) {
+        ans = i;
+        size_t j = i + 1, k = i;
+        while (j < (n + n) && s[j % n] >= s[k % n]) {
+            if (s[k % n] < s[j % n]) {
+                k = i;
+            } else {
+                k++;
+            }
+            j++;
+        }
+        while (i <= k) {
+            i += j - k;
+        }
+    }
+    return ans;
+    // returns 0-indexed position of the least cyclic shift
+}
+
+}  // namespace string
+
+/**
+ * @brief self test implementation
+ * returns void
+ */
+static void test() {
+    using namespace string;
+
+    // Test 1
+    std::string s1 = "abcab";
+    assert(duval(s1) == 3);
+
+    // Test 2
+    std::string s2 = "011100";
+    assert(duval(s2) == 4);
+
+    // Test 3
+    std::vector<int> v = {5, 2, 1, 3, 4};
+    assert(duval(v) == 2);
+
+    // Test 4
+    std::array<int, 5> a = {1, 2, 3, 4, 5};
+    assert(duval(a) == 0);
+
+    // Test 5
+    std::deque<char> d = {'a', 'z', 'c', 'a', 'b'};
+    assert(duval(d) == 3);
+
+    // Test 6
+    std::string s3;
+    assert(duval(s3) == 0);
+
+    // Test 7
+    std::vector<int> v2 = {5, 2, 1, 3, -4};
+    assert(duval(v2) == 4);
+
+    std::cout << "All tests passed!" << std::endl;
+}
+
+/**
+ * @brief main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self test implementations
+    return 0;
+}