Sorting

Merge Sort (Top-Down)

Split the array recursively, sort each half, then merge two sorted runs into one sorted result.

Algorithm

The checked-in replay follows the same small input and final output across all 21 DSA books, so this Java DSA implementation can be compared directly with the other languages.

divide and conquer Each recursive call solves a smaller sorted subproblem.
merge step Two sorted halves are combined by repeatedly taking the smaller front item.

Visual walkthrough

The pinned input is [5, 1, 4, 2, 8]. The diagrams show the split into recursive halves, the sorted subarrays, and the final merge choices.

Step 1 - Split the input

The first midpoint splits [5, 1, 4, 2, 8] into left [5, 1] and right [4, 2, 8].

Top-down split used by merge_sort.[5,1,4,2,8]mid = 2[5,1]left[4,2,8]right

Step 2 - Sorted halves return

Recursive calls return [1, 5] and [2, 4, 8] before the final merge begins.

Returned subarrays before the final merge.sidebefore sortafter sortleft[5, 1][1, 5]right[4, 2, 8][2, 4, 8]

Step 3 - Merge by taking smaller fronts

Take 1 from left, then 2 and 4 from right, then the remaining 5 and 8.

Final merge produces [1, 2, 4, 5, 8].choiceleft frontright frontmergedtake 112[1]take 252[1, 2]take 454[1, 2, 4]extend58[1, 2, 4, 5, 8]

Basic Implementation

Basic.java 
class Basic {
	public static void main(String[] args) {
		int[] arr = new int[] { 5, 1, 4, 2, 8 };
		int[] sorted = mergeSort(arr);
		printArray(sorted);
	}

	static void printArray(int[] arr) {
		System.out.print("[");
		for (int i = 0; i < arr.length; i++) {
			if (i > 0) System.out.print(", ");
			System.out.print(arr[i]);
		}
		System.out.println("]");
	}
	static int[] mergeSort(int[] values) {
		if (values.length <= 1) return values;
		int mid = values.length / 2;
		int[] left = java.util.Arrays.copyOfRange(values, 0, mid);
		int[] right = java.util.Arrays.copyOfRange(values, mid, values.length);
		return merge(mergeSort(left), mergeSort(right));
	}

	static int[] merge(int[] left, int[] right) {
		int[] merged = new int[left.length + right.length];
		int i = 0, j = 0, k = 0;
		while (i < left.length && j < right.length) {
			if (left[i] <= right[j]) merged[k++] = left[i++];
			else merged[k++] = right[j++];
		}
		while (i < left.length) merged[k++] = left[i++];
		while (j < right.length) merged[k++] = right[j++];
		return merged;
	}
}

Complexity

  • Time: O(n log n)
  • Space: O(n)
  • Stable: yes

Implementation notes

  • Java stores values in primitive int[] arrays. mergeSort returns an int[] result instead of sorting the original array in place, and the base case returns the same one-element or empty array reference.
  • Each recursive split computes mid = values.length / 2 and allocates copied halves with java.util.Arrays.copyOfRange(values, 0, mid) and copyOfRange(values, mid, values.length).
  • merge allocates a fresh int[] merged and uses index variables i, j, and k to copy primitive values from the sorted halves. The left[i] <= right[j] comparison preserves left-side ties before the tail-copy loops run.
  • The replay shows the top-level copied halves [5, 1] and [4, 2, 8], their sorted recursive results, then the final merged array [1, 2, 4, 5, 8]. Split and merge arrays are JVM heap objects while referenced; temporary arrays become reclaimable after returns, while the final merged array remains referenced as sorted.