feat: add cycle sort algorithm (#1252)

* feat: add cycle sort algorithm

* feat: add cycle sort algorithm

* feat: add cycle sort algorithm

* feat: add cycle sort algorithm

* feat: add cycle sort algorithm

* feat: add cycle sort algorithm

* feat: add cycle sort algorithm

* updating DIRECTORY.md

* Add namespace decription

* fix: add assert and template

* fix: add some comment

* fix: update some suggested changes

* fix: update some suggested changes

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

DIRECTORY.md

@@ -240,6 +240,7 @@
   * [Comb Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/comb_sort.cpp)
   * [Counting Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort.cpp)
   * [Counting Sort String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort_string.cpp)
+  * [Cycle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/cycle_sort.cpp)
   * [Gnome Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/gnome_sort.cpp)
   * [Heap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/heap_sort.cpp)
   * [Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/insertion_sort.cpp)

sorting/cycle_sort.cpp

@@ -0,0 +1,104 @@
+/**
+ * @file
+ * @brief Implementation of [Cycle sort](https://en.wikipedia.org/wiki/Cycle_sort) algorithm
+ *
+ * @details
+ * Cycle Sort is a sorting algorithm that works in \f$O(n^2)\f$ time in best cas and works in \f$O(n^2)\f$ in worst case.
+ * If a element is already at its correct  position, do nothing.
+ * If a element is not at its correct position, we then need to move it to its correct position by computing the correct positions.Therefore, we should make sure the duplicate elements.
+ *
+ * @author [TsungHan Ho](https://github.com/dalaoqi)
+ */
+
+#include <algorithm> /// for std::is_sorted, std::swap
+#include <cassert>     /// for assert
+#include <iostream> /// for io operations
+#include <vector>    /// for std::vector 
+
+/**
+ * @namespace sorting
+ * @brief Sorting algorithms
+ */
+namespace sorting {
+/**
+ * @namespace cycle_sort
+ * @brief Functions for [Cycle sort](https://en.wikipedia.org/wiki/Cycle_sort) algorithm
+ */
+namespace cycle_sort { 
+/**
+ * @brief The main function implements cycleSort
+ * @tparam T type of array
+ * @param in_arr array to be sorted
+ * @returns void
+ */
+template <typename T>
+std::vector<T> cycleSort(const std::vector<T> &in_arr) {
+    std::vector<T> arr(in_arr);
+    for (size_t cycle_start = 0; cycle_start <= arr.size() - 1; cycle_start++) {
+        // initialize item
+        T item = arr[cycle_start];
+
+        // Count the number of elements smaller than item, this  number is the correct index of item.
+        int pos = cycle_start;
+        for (size_t i = cycle_start + 1; i < arr.size(); i++) {
+            if (arr[i] < item) {
+                pos++;
+            }
+        }
+
+        // item is already in correct position
+        if (pos == cycle_start) {
+            continue;
+        }
+
+        // duplicate  elements
+        while (item == arr[pos]) pos += 1;
+        std::swap(item, arr[pos]);
+
+        // Rest of the  elements
+        while (pos != cycle_start) {
+            pos = cycle_start;
+            // Find position where we put the element
+            for (size_t i = cycle_start + 1; i < arr.size(); i++) {
+                if (arr[i] < item) {
+                    pos += 1;
+                }
+            }
+            // duplicate  elements
+            while (item == arr[pos]) pos += 1;
+            std::swap(item, arr[pos]);
+        }
+    }
+    return arr;
+}
+} // namespace cycle_sort
+} // namespace sorting
+
+/**
+ * @brief Test implementations
+ * @returns void
+ */
+static void test() {
+    // [506, 48, 123, 79, 0, 362, 951, 500, 0] return [0, 0, 48, 79, 123, 362, 500, 506, 951]
+    std::vector<int> array1 = {506, 48, 123, 79, 0, 362, 951, 500, 0};
+    std::cout << "Test 1... ";
+    std::vector<int> arr1  = sorting::cycle_sort::cycleSort(array1);
+    assert(std::is_sorted(std::begin(arr1), std::end(arr1)));
+    std::cout << "passed" << std::endl;
+
+    // [4.3, -6.5, -7.4, 0, 2.7, 1.8] return [-7.4, -6.5, 0, 1.8, 2.7, 4.3]
+    std::vector<double> array2 = {4.3, -6.5, -7.4, 0, 2.7, 1.8};
+    std::cout << "Test 2... ";
+    std::vector<double> arr2 = sorting::cycle_sort::cycleSort(array2);
+    assert(std::is_sorted(std::begin(arr2), std::end(arr2)));
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // execute the test
+    return 0;
+}