feat(divide-and-conquer): implement space-optimized merge sort using shared temp array

Author: PavithraSharma14

15-divide-and-conquer/MergeSortOptimized.java

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+/**
+ * Merge Sort - Space Optimized Implementation
+ *
+ * 📌 Concept:
+ * Same Divide and Conquer approach as basic Merge Sort,
+ * but optimized to avoid repeated creation of temporary arrays.
+ *
+ * 🔥 Optimization:
+ * Instead of creating a new temp array in every merge call,
+ * we create a single temp array once and reuse it.
+ *
+ * 📊 Time Complexity:
+ * Best Case   : O(n log n)
+ * Average Case: O(n log n)
+ * Worst Case  : O(n log n)
+ *
+ * 📦 Space Complexity:
+ * O(n) - but avoids repeated allocations (more efficient in practice)
+ *
+ * ✅ Stable Sorting Algorithm
+ */
+public class MergeSortOptimized {
+
+    public static void main(String[] args) {
+        int[] arr = {38, 27, 43, 3, 9, 82, 10};
+
+        System.out.println("Before Sorting:");
+        printArray(arr);
+
+        // Create temp array once
+        int[] temp = new int[arr.length];
+
+        mergeSort(arr, temp, 0, arr.length - 1);
+
+        System.out.println("After Sorting:");
+        printArray(arr);
+    }
+
+    /**
+     * Recursive divide function
+     */
+    public static void mergeSort(int[] arr, int[] temp, int left, int right) {
+
+        if (left >= right) {
+            return;
+        }
+
+        int mid = left + (right - left) / 2;
+
+        // Divide
+        mergeSort(arr, temp, left, mid);
+        mergeSort(arr, temp, mid + 1, right);
+
+        // Merge using shared temp array
+        merge(arr, temp, left, mid, right);
+    }
+
+    /**
+     * Merge function using reusable temp array
+     */
+    private static void merge(int[] arr, int[] temp, int left, int mid, int right) {
+
+        int i = left;      // left half pointer
+        int j = mid + 1;   // right half pointer
+        int k = left;      // temp array index (same indexing)
+
+        // Merge both halves into temp[]
+        while (i <= mid && j <= right) {
+
+            if (arr[i] <= arr[j]) {
+                temp[k++] = arr[i++];
+            } else {
+                temp[k++] = arr[j++];
+            }
+        }
+
+        // Copy remaining elements of left half
+        while (i <= mid) {
+            temp[k++] = arr[i++];
+        }
+
+        // Copy remaining elements of right half
+        while (j <= right) {
+            temp[k++] = arr[j++];
+        }
+
+        // Copy back from temp[] to original array
+        for (int p = left; p <= right; p++) {
+            arr[p] = temp[p];
+        }
+    }
+
+    /**
+     * Utility method to print array
+     */
+    private static void printArray(int[] arr) {
+        for (int num : arr) {
+            System.out.print(num + " ");
+        }
+        System.out.println();
+    }
+}