feat: Add IntroSort algorithm in C

sorting/intro_sort.c

@@ -0,0 +1,147 @@
+// Implementation of IntroSort (Introspective Sort)
+// Author: sgindeed
+// Description:
+// IntroSort is a hybrid sorting algorithm that starts with QuickSort,
+// switches to HeapSort when recursion depth exceeds a limit, and uses
+// InsertionSort for small arrays. It combines average-case speed of QuickSort
+// with the worst-case performance guarantee of HeapSort.
+//
+// Time Complexity: O(n log n)
+// Space Complexity: O(log n) due to recursion stack
+//
+// References:
+// - Musser, David R. "Introspective Sorting and Selection Algorithms." Software: Practice and Experience (1997)
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#define SIZE 50
+#define INSERTION_SORT_THRESHOLD 16
+
+/* -------------------- Utility Functions -------------------- */
+
+void swap(int *a, int *b) {
+    int temp = *a;
+    *a = *b;
+    *b = temp;
+}
+
+/* -------------------- Insertion Sort -------------------- */
+
+void insertionSort(int arr[], int left, int right) {
+    for (int i = left + 1; i <= right; i++) {
+        int key = arr[i];
+        int j = i - 1;
+        while (j >= left && arr[j] > key) {
+            arr[j + 1] = arr[j];
+            j--;
+        }
+        arr[j + 1] = key;
+    }
+}
+
+/* -------------------- Heap Sort -------------------- */
+
+void heapify(int arr[], int n, int i, int start) {
+    int largest = i;
+    int left = 2 * (i - start) + 1 + start;
+    int right = 2 * (i - start) + 2 + start;
+
+    if (left < n && arr[left] > arr[largest])
+        largest = left;
+    if (right < n && arr[right] > arr[largest])
+        largest = right;
+
+    if (largest != i) {
+        swap(&arr[i], &arr[largest]);
+        heapify(arr, n, largest, start);
+    }
+}
+
+void heapSort(int arr[], int start, int end) {
+    int n = end - start + 1;
+
+    // Build heap (rearrange array)
+    for (int i = start + n / 2 - 1; i >= start; i--)
+        heapify(arr, end + 1, i, start);
+
+    // Extract elements one by one
+    for (int i = end; i >= start; i--) {
+        swap(&arr[start], &arr[i]);
+        heapify(arr, i, start, start);
+    }
+}
+
+/* -------------------- Quick Sort (used in IntroSort) -------------------- */
+
+int partition(int arr[], int low, int high) {
+    int pivot = arr[high];
+    int i = low - 1;
+
+    for (int j = low; j < high; j++) {
+        if (arr[j] <= pivot) {
+            i++;
+            swap(&arr[i], &arr[j]);
+        }
+    }
+    swap(&arr[i + 1], &arr[high]);
+    return (i + 1);
+}
+
+void introSortUtil(int arr[], int low, int high, int depthLimit) {
+    int size = high - low + 1;
+
+    // Use insertion sort for small arrays
+    if (size < INSERTION_SORT_THRESHOLD) {
+        insertionSort(arr, low, high);
+        return;
+    }
+
+    // If depth limit is 0, use heap sort
+    if (depthLimit == 0) {
+        heapSort(arr, low, high);
+        return;
+    }
+
+    // Otherwise, use QuickSort
+    int pivot = partition(arr, low, high);
+
+    introSortUtil(arr, low, pivot - 1, depthLimit - 1);
+    introSortUtil(arr, pivot + 1, high, depthLimit - 1);
+}
+
+/* -------------------- Main IntroSort Function -------------------- */
+
+void introSort(int arr[], int n) {
+    int depthLimit = 2 * log(n);
+    introSortUtil(arr, 0, n - 1, depthLimit);
+}
+
+/* -------------------- Display Utility -------------------- */
+
+void display(int arr[], int n) {
+    for (int i = 0; i < n; i++)
+        printf("%d ", arr[i]);
+    printf("\n");
+}
+
+/* -------------------- Driver Code -------------------- */
+
+int main() {
+    int arr[SIZE];
+
+    // Generate random numbers
+    for (int i = 0; i < SIZE; i++)
+        arr[i] = rand() % (SIZE << 1); // random numbers from 0 to 2*SIZE
+
+    printf("Original array:\n");
+    display(arr, SIZE);
+
+    introSort(arr, SIZE);
+
+    printf("\nSorted array:\n");
+    display(arr, SIZE);
+
+    return 0;
+}