feat: add hybrid quick-insertion-selection sorting algorithm with tests

sorting/hybrid_quick_insertion_selection.cpp

@@ -0,0 +1,209 @@
+/**
+ * @file
+ * @brief Hybrid of QuickSort, InsertionSort and SelectionSort
+ * https://es.wikipedia.org/wiki/Quicksort
+ * https://en.wikipedia.org/wiki/Selection_sort
+ * https://en.wikipedia.org/wiki/Insertion_sort
+ * @details
+ * this is a hybrid sorting algorithm
+ * uses quicksort to split the array in two
+ * sorts the left half with insertion sort
+ * sorts the right half with selection sort
+ * created for educational purposes not optimized for speed.
+ * @author Cesar (https://github.com/cesar-011)
+ * @see quick_sort.cpp, insertion_sort.cpp, selection_sort_iterative.cpp
+ */
+
+#include <algorithm>  // for std::is_sorted
+#include <cassert>    // for assert
+#include <iostream>   // for IO
+#include <vector>     // for vector in test
+
+/**
+ * @brief swap two elements of an array
+ */
+template <typename T>
+void swap(T *arr, int i, int j) {
+    T aux = arr[i];
+    arr[i] = arr[j];
+    arr[j] = aux;
+}
+
+/**
+ * @brief print the array
+ */
+template <typename T>
+void print_array(T *arr, int size) {
+    for (int i = 0; i < size; i++) {
+        std::cout << arr[i] << " ";
+    }
+}
+
+/**
+ * @namespace sorting
+ * @brief Sorting algorithms
+ */
+namespace sorting {
+
+/**
+ * @namespace hybrid_quick_insert_select
+ * @brief Hybrid of QuickSort, InsertionSort and SelectionSort algorithms
+ */
+namespace hybrid_quick_insert_select {
+
+/**
+ * @brief Sorts an array using a hybrid of QuickSort, Insertion Sort, and
+ * Selection Sort.
+ *
+ * This algorithm partitions the array using QuickSort's partitioning scheme.
+ * It then applies Insertion Sort to the left half and Selection Sort to the
+ * right half. This hybrid is intended for educational purposes and not
+ * optimized for performance.
+ *
+ * @tparam T Type of the elements in the array. Must support comparison
+ * operators.
+ * @param arr Pointer to the array to be sorted.
+ * @param low Starting index of the subarray to sort.
+ * @param high Ending index of the subarray to sort (inclusive).
+ */
+template <typename T>
+void hybrid_quick_insertion_selection(T *arr, int low, int high) {
+    if (low >= high)
+        return;  // Empty range
+    // A single iteration of Quicksort partitioning to divide the array into two
+    // halves
+    int i = low;
+    int f = high - 1;
+    T pivot = arr[(i + f) / 2];
+    while (i <= f) {
+        while (arr[i] < pivot) i++;
+        while (arr[f] > pivot) f--;
+        if (i <= f) {
+            swap(arr, i, f);
+            i++;
+            f--;
+        }
+    }
+
+    // Insertion at the left
+    if (low < f) {
+        for (int k = low + 1; k <= f; k++) {
+            int key = arr[k];
+            int j = k - 1;
+            while (j >= low && arr[j] > key) {
+                arr[j + 1] = arr[j];
+                j--;
+            }
+            arr[j + 1] = key;
+        }
+    }
+
+    // Selection at the right
+    if (i < high) {
+        for (int k = i; k < high; k++) {
+            int minimum = arr[k];
+            int min_ind = k;
+            int j = k + 1;
+            while (j < high) {
+                if (arr[j] < minimum) {
+                    minimum = arr[j];
+                    min_ind = j;
+                }
+                j++;
+            }
+            swap(arr, k, min_ind);
+        }
+    }
+}
+}  // namespace hybrid_quick_insert_select
+}  // namespace sorting
+
+static void test() {
+    using sorting::hybrid_quick_insert_select::hybrid_quick_insertion_selection;
+
+    // Test 1: empty
+    {
+        std::vector<int> arr = {};
+        hybrid_quick_insertion_selection(arr.data(), 0,
+                                         static_cast<int>(arr.size()));
+        assert(std::is_sorted(arr.begin(), arr.end()));
+    }
+
+    // Test 2: one element
+    {
+        std::vector<int> arr = {42};
+        hybrid_quick_insertion_selection(arr.data(), 0,
+                                         static_cast<int>(arr.size()));
+        assert(std::is_sorted(arr.begin(), arr.end()));
+    }
+
+    // Test 3: positive numbers
+    {
+        std::vector<int> arr = {1, 2, 3, 4, 5};
+        hybrid_quick_insertion_selection(arr.data(), 0,
+                                         static_cast<int>(arr.size()));
+        assert(std::is_sorted(arr.begin(), arr.end()));
+    }
+
+    // Test 4: positive and negative numbers
+    {
+        std::vector<int> arr = {-5, 4, -3, 2, 1};
+        hybrid_quick_insertion_selection(arr.data(), 0,
+                                         static_cast<int>(arr.size()));
+        assert(std::is_sorted(arr.begin(), arr.end()));
+    }
+
+    // Test 5: repeated elements
+    {
+        std::vector<int> arr = {3, 1, 2, 3, 2, 1, 4};
+        hybrid_quick_insertion_selection(arr.data(), 0,
+                                         static_cast<int>(arr.size()));
+        assert(std::is_sorted(arr.begin(), arr.end()));
+    }
+
+    // Test 6: negative numbers
+    {
+        std::vector<int> arr = {-10, -7, -8, -9, -1, -5};
+        hybrid_quick_insertion_selection(arr.data(), 0,
+                                         static_cast<int>(arr.size()));
+        assert(std::is_sorted(arr.begin(), arr.end()));
+    }
+
+    // Test 7: big array
+    {
+        std::vector<int> arr(1000);
+        for (int i = 0; i < 1000; ++i) {
+            arr[i] = 1000 - i;
+        }
+        hybrid_quick_insertion_selection(arr.data(), 0,
+                                         static_cast<int>(arr.size()));
+        assert(std::is_sorted(arr.begin(), arr.end()));
+    }
+
+    std::cout << "All tests passed successfully!\n";
+}
+
+/**
+ * @brief Main program to demonstrate the hybrid sorting algorithm.
+ *
+ * Runs the built-in self-tests, then sorts a sample array using the hybrid
+ * algorithm that combines QuickSort, Insertion Sort, and Selection Sort.
+ *
+ * The array is printed before and after sorting to show the result.
+ *
+ * @return int Program exit code (0 indicates successful execution).
+ */
+int main() {
+    test();  // run self-test implementations
+
+    // An example
+    int N = 8;
+    int array[N] = {8, 5, 9, 20, 2, 13, 3, 1};
+    print_array(array, N);
+    std::cout << '\n';
+    sorting::hybrid_quick_insert_select::hybrid_quick_insertion_selection(array,
+                                                                          0, N);
+    print_array(array, N);
+    std::cout << '\n';
+    return 0;
+}