====== Divide and Conquer in Java ======

Divide and Conquer is a fundamental algorithm design paradigm in computer science, used to solve various types of problems by dividing them into smaller subproblems, solving the subproblems recursively, and then combining their solutions.

==== Core Concept ====
The divide and conquer strategy works by:
  - **Dividing** the problem into a number of subproblems that are smaller instances of the same problem.
  - **Conquering** the subproblems by solving them recursively. If the subproblem sizes are small enough, solve them in a straightforward manner.
  - **Combining** the solutions to the subproblems into the solution for the original problem.

==== Common Applications ====
  - **Sorting algorithms** such as Quick Sort and Merge Sort.
  - **Searching algorithms** like Binary Search.
  - Complex number multiplication and other number-theoretic problems.
  - Constructing data structures such as Binary Trees and Segment Trees.

==== Example: Merge Sort in Java ====
Merge Sort is a classic example of divide and conquer.

<code java MergeSort.java>
public class MergeSort {
    // Merges two subarrays of arr[]
    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);
        }
    }
}
</code>