1. Introduction to Divide and Conquer Strategy

The Divide and Conquer strategy is an algorithm design paradigm used to solve problems efficiently. The idea is to break down a problem into smaller subproblems, solve each subproblem recursively, and then combine their results to solve the original problem.

The general structure for divide and conquer algorithms:

  1. Divide: Break the problem into smaller subproblems of the same type.
  2. Conquer: Recursively solve each subproblem.
  3. Combine: Combine the results from the subproblems to get the final solution.

This paradigm is commonly used in algorithms like Binary Search, Merge Sort, and Quick Sort.

2. Binary Search Algorithm

The Binary Search Algorithm is a classic example of the divide and conquer strategy. It is used to find an element in a sorted array efficiently.

How Binary Search Works:

  1. Divide: Check the middle element of the array.
  2. Conquer: If the middle element is equal to the target, return its index. If the target is smaller, search in the left half; otherwise, search in the right half.
  3. Combine: Since the problem is divided in half each time, there's no need to combine results; the search either continues or ends.

Binary Search Implementation in Java:

class BinarySearch {
    // Function to perform binary search
    public int binarySearch(int[] arr, int target) {
        int left = 0, right = arr.length - 1;
        while (left <= right) {
            int mid = left + (right - left) / 2;

            // Check if target is present at mid
            if (arr[mid] == target) return mid;

            // If target is smaller than mid, it can only be in the left half
            if (arr[mid] > target) right = mid - 1;
            else left = mid + 1;
        }
        return -1;  // Element not found
    }

    public static void main(String[] args) {
        BinarySearch bs = new BinarySearch();
        int[] arr = {2, 3, 4, 10, 40};
        int result = bs.binarySearch(arr, 10);
        if (result != -1)
            System.out.println("Element found at index " + result);
        else
            System.out.println("Element not found");
    }
}

Time Complexity: