Java Program for Merge Sort

Merge Sort is a divide-and-conquer algorithm. It divides the input array into two halves, calls itself the two halves, and then merges the two sorted halves. The merge() function is used for merging two halves. The merge(arr, l, m, r) is a key process that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the two sorted sub-arrays into one.

Merge Sort Algorithm

There are only five steps to understand Merge Sort Algorithm:

Step 1: Divide Array into Two Parts.
Step 2: Merge Sort the first part of the array.
Step 3: Merge Sort the second part of the array.
Step 4: Merge Both the parts.
Step 5: Return the Sorted Array

Base Conditions for Merge Sort is:

Divide the Array till the size of Array is greater than 1.

Program of Merge Sort in Java

Java

// Java program for Merge Sort
// Driver Class
class MergeSort {
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(int arr[], int l, int m, int r)
    {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        // Create temp arrays
        int L[] = new int[n1];
        int R[] = new int[n2];

        // Copy data to temp arrays
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];

        // Merge the temp arrays
        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarray array
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            }
            else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        // Copy remaining elements of L[] if any
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }

        // Copy remaining elements of R[] if any
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(int arr[], int l, int r)
    {
        if (l < r) {
            // Find the middle point
            int m = (l + r) / 2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr, m + 1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

    // A utility function to print array of size n
    static void printArray(int arr[])
    {
        int n = arr.length;
        for (int i = 0; i < n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    // Driver method
    public static void main(String args[])
    {
        int arr[] = { 12, 11, 13, 5, 6, 7 };

        System.out.println("Given Array");
        printArray(arr);

        // Calling of Merge Sort
        MergeSort ob = new MergeSort();
        ob.sort(arr, 0, arr.length - 1);

        System.out.println("\nSorted array");
        printArray(arr);
    }
}

Output

Given Array
12 11 13 5 6 7 

Sorted array
5 6 7 11 12 13

The complexity of the above method:

Time Complexity: O(n log n)
Auxiliary Space: O(n)

Advantages of Merge Sort

The advantages of Merge Sort are mentioned below:

Stability: Merge sort is a stable sorting algorithm, which means it maintains the relative order of equal elements in the input array.
Guaranteed worst-case performance: Merge sort has a worst-case time complexity of O(n log n), which means it performs well even on large datasets.
Parallelizable: Merge sort is a naturally parallelizable algorithm, which means it can be easily parallelized to take advantage of multiple processors or threads.

References: Please refer complete article on Merge Sort for more details.

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Java Programs

Merge Sort