Divide-and-conquer splits a problem into smaller subproblems, solves each one independently, and then combines the results. It’s used in algorithms like merge sort and quicksort.

The divide-and-conquer approach is a popular algorithmic technique used in competitive programming to solve complex problems by breaking them down into smaller, more manageable subproblems. The basic idea is to divide the original problem into several smaller subproblems, solve each subproblem independently, and then combine their solutions to solve the overall problem. This approach works best when the subproblems are similar to the original problem but smaller in size. One of the most well-known examples of divide-and-conquer is merge sort, where the array is recursively divided into smaller subarrays, each subarray is sorted, and then the sorted subarrays are merged back together to form the sorted array. Another common example is quicksort, which partitions the array around a pivot element and recursively sorts the subarrays on either side of the pivot. Divide-and-conquer can also be applied to problems like finding the closest pair of points, matrix multiplication, and many other geometric and numerical problems. The key advantage of divide-and-conquer is that it often leads to more efficient algorithms, with time complexities that are significantly better than brute-force approaches. Understanding when and how to apply divide-and-conquer is an essential skill for competitive programmers, as it can dramatically reduce the time complexity of many problems.