feat: Add the Wave Sort algorithm (#1525)

* Create wave_sort.cpp

* Update wave_sort.cpp

* Update wave_sort.cpp

* Update wave_sort.cpp

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for 196165e7

* Update wave_sort.cpp

* Update sorting/wave_sort.cpp

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

* Update sorting/wave_sort.cpp

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

* Update sorting/wave_sort.cpp

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

* Update wave_sort.cpp

* clang-format and clang-tidy fixes for b5f9663f

* Update sorting/wave_sort.cpp

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

* Update sorting/wave_sort.cpp

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

* clang-format and clang-tidy fixes for 8651884e

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

DIRECTORY.md

@@ -311,6 +311,7 @@
   * [Strand Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/strand_sort.cpp)
   * [Swap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/swap_sort.cpp)
   * [Tim Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/tim_sort.cpp)
+  * [Wave Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/wave_sort.cpp)
   * [Wiggle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/wiggle_sort.cpp)
 
 ## Strings

sorting/wave_sort.cpp

@@ -0,0 +1,94 @@
+/**
+ * @file
+ * @brief Implementation of the [Wave
+ * sort](https://www.geeksforgeeks.org/sort-array-wave-form-2/) algorithm
+ * @details
+ * Wave Sort is a sorting algorithm that works in \f$O(nlogn)\f$ time assuming
+ * the sort function used works in \f$O(nlogn)\f$ time.
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+
+#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 wave_sort
+ * @brief Functions for the [Wave
+ * sort](https://www.geeksforgeeks.org/sort-array-wave-form-2/) implementation
+ */
+namespace wave_sort {
+/**
+ * @brief The main function implements that implements the Wave Sort algorithm
+ * @tparam T type of array
+ * @param in_arr array to be sorted
+ * @returns arr the wave sorted array
+ */
+template <typename T>
+std::vector<T> waveSort(const std::vector<T> &in_arr, int64_t n) {
+    std::vector<T> arr(in_arr);
+
+    for (int64_t i = 0; i < n; i++) {
+        arr[i] = in_arr[i];
+    }
+    std::sort(arr.begin(), arr.end());
+    for (int64_t i = 0; i < n - 1; i += 2) {  // swap all the adjacent elements
+        std::swap(arr[i], arr[i + 1]);
+    }
+    return arr;
+}
+}  // namespace wave_sort
+}  // namespace sorting
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // [10, 90, 49, 2, 1, 5, 23] return [2, 1, 10, 5, 49, 23, 90]
+    std::vector<int64_t> array1 = {10, 90, 49, 2, 1, 5, 23};
+    std::cout << "Test 1... ";
+    std::vector<int64_t> arr1 = sorting::wave_sort::waveSort(array1, 7);
+    const std::vector<int64_t> o1 = {2, 1, 10, 5, 49, 23, 90};
+    assert(arr1 == o1);
+    std::cout << "passed" << std::endl;
+
+    // [1, 3, 4, 2, 7, 8] return [2, 1, 4, 3, 8, 7]
+    std::vector<int64_t> array2 = {1, 3, 4, 2, 7, 8};
+    std::cout << "Test 2... ";
+    std::vector<int64_t> arr2 = sorting::wave_sort::waveSort(array2, 6);
+    const std::vector<int64_t> o2 = {2, 1, 4, 3, 8, 7};
+    assert(arr2 == o2);
+    std::cout << "passed" << std::endl;
+
+    // [3, 3, 3, 3] return [3, 3, 3, 3]
+    std::vector<int64_t> array3 = {3, 3, 3, 3};
+    std::cout << "Test 3... ";
+    std::vector<int64_t> arr3 = sorting::wave_sort::waveSort(array3, 4);
+    const std::vector<int64_t> o3 = {3, 3, 3, 3};
+    assert(arr3 == o3);
+    std::cout << "passed" << std::endl;
+
+    // [9, 4, 6, 8, 14, 3] return [4, 3, 8, 6, 14, 9]
+    std::vector<int64_t> array4 = {9, 4, 6, 8, 14, 3};
+    std::cout << "Test 4... ";
+    std::vector<int64_t> arr4 = sorting::wave_sort::waveSort(array4, 6);
+    const std::vector<int64_t> o4 = {4, 3, 8, 6, 14, 9};
+    assert(arr4 == o4);
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}