Merge sort

 public class MergeSort {

    public static void mergeSort(int[] arr) {

        if (arr.length <= 1) {

            return; // If the array has 0 or 1 element, it's already sorted, so we're done.

        }

        // Find the middle of the array.

        int mid = arr.length / 2;

        // Create two subarrays, one for the left half and one for the right half.

        int[] left = new int[mid];

        int[] right = new int[arr.length - mid];

        // Copy elements from the original array into the left and right subarrays.

        System.arraycopy(arr, 0, left, 0, mid);

        System.arraycopy(arr, mid, right, 0, arr.length - mid);

        // Recursively sort the left and right subarrays.

        mergeSort(left);

        mergeSort(right);

        // Merge the sorted left and right subarrays to produce the final sorted array.

        merge(arr, left, right);

    }

    private static void merge(int[] arr, int[] left, int[] right) {

        int i = 0, j = 0, k = 0;

        // Compare elements from the left and right subarrays and merge them into the original array.

        while (i < left.length && j < right.length) {

            if (left[i] < right[j]) {

                arr[k++] = left[i++];

            } else {

                arr[k++] = right[j++];

            }

        }

        // Copy any remaining elements from the left subarray (if any).

        while (i < left.length) {

            arr[k++] = left[i++];

        }

        // Copy any remaining elements from the right subarray (if any).

        while (j < right.length) {

            arr[k++] = right[j++];

        }

    }

    public static void main(String[] args) {

        int[] arr = {12, 11, 13, 5, 6, 7};

        // Call the mergeSort function to sort the array.

        mergeSort(arr);

        // Print the sorted array.

        System.out.println("Sorted array: " + Arrays.toString(arr));

    }

}

public class MergeSort {

    public static void mergeSort(int[] arr) {

        if (arr.length <= 1) {

            return;

        }

        int mid = arr.length / 2;

        // Divide the array into two halves.

        int[] left = new int[mid];

        int[] right = new int[arr.length - mid];

        System.arraycopy(arr, 0, left, 0, mid);

        System.arraycopy(arr, mid, right, 0, arr.length - mid);

        // Sort the two halves recursively.

        mergeSort(left);

        mergeSort(right);

        // Merge the two sorted halves back together.

        merge(arr, left, right);

    }

    private static void merge(int[] arr, int[] left, int[] right) {

        int i = 0, j = 0, k = 0;

        while (i < left.length && j < right.length) {

            if (left[i] <= right[j]) {

                arr[k++] = left[i++];

            } else {

                arr[k++] = right[j++];

            }

        }

        while (i < left.length) {

            arr[k++] = left[i++];

        }

        while (j < right.length) {

            arr[k++] = right[j++];

        }

    }

}

public class MergeSort {

    public static void mergeSort(int[] arr) {

        if (arr.length <= 1) {

            return;

        }

        int mid = arr.length / 2;

        // Divide the array into two halves.

        int[] left = new int[mid];

        int[] right = new int[arr.length - mid];

        System.arraycopy(arr, 0, left, 0, mid);

        System.arraycopy(arr, mid, right, 0, arr.length - mid);

        // Sort the two halves recursively.

        mergeSort(left);

        mergeSort(right);

        // Merge the two sorted halves back together.

        merge(arr, left, right);

    }

    private static void merge(int[] arr, int[] left, int[] right) {

        int i = 0, j = 0, k = 0;

        while (i < left.length && j < right.length) {

            if (left[i] <= right[j]) {

                arr[k++] = left[i++];

            } else {

                arr[k++] = right[j++];

            }

        }

        while (i < left.length) {

            arr[k++] = left[i++];

        }

        while (j < right.length) {

            arr[k++] = right[j++];

        }

    }

    public static void main(String[] args) {

        int[] arr = {5, 3, 2, 1, 4};

        mergeSort(arr);

        System.out.println("Sorted array:");

        for (int i = 0; i < arr.length; i++) {

            System.out.print(arr[i] + " ");

        }

    }

}

WITH TIME COMPLEXITY

public class MergeSort {

    public static void mergeSort(int[] arr) {

        if (arr.length <= 1) {

            return;

        }

        int mid = arr.length / 2;

        // Divide the array into two halves.

        int[] left = new int[mid];

        int[] right = new int[arr.length - mid];

        System.arraycopy(arr, 0, left, 0, mid);

        System.arraycopy(arr, mid, right, 0, arr.length - mid);

        // Sort the two halves recursively.

        mergeSort(left);

        mergeSort(right);

        // Merge the two sorted halves back together.

        merge(arr, left, right);

    }

    private static void merge(int[] arr, int[] left, int[] right) {

        int i = 0, j = 0, k = 0;

        while (i < left.length && j < right.length) {

            if (left[i] <= right[j]) {

                arr[k++] = left[i++];

            } else {

                arr[k++] = right[j++];

            }

        }

        while (i < left.length) {

            arr[k++] = left[i++];

        }

        while (j < right.length) {

            arr[k++] = right[j++];

        }

    }

    public static long timeComplexity(int[] arr) {

        long startTime = System.nanoTime();

        mergeSort(arr);

        long endTime = System.nanoTime();

        return endTime - startTime;

    }

    public static void main(String[] args) {

        int[] arr = {5, 3, 2, 1, 4};

        long timeComplexity = timeComplexity(arr);

        System.out.println("Sorted array:");

        for (int i = 0; i < arr.length; i++) {

            System.out.print(arr[i] + " ");

        }

        System.out.println("\nTime complexity: " + timeComplexity + " nanoseconds");

    }

}