Divide and Conquer Algorithm: How Does the Divide and Conquer Idea Solve Problems? The Principle of Merge Sort

The core of the divide-and-conquer algorithm is "divide and conquer," which solves complex problems through three steps: divide (split into smaller subproblems), conquer (recursively solve subproblems), and combine (integrate results). It is suitable for scenarios with recursive structures. Taking array sum calculation as an example, the array is divided, the sum of subarrays is recursively computed, and the total sum is obtained through combination. Merge sort is a typical application: the array is first divided into individual elements (which are inherently ordered), and then the ordered subarrays are merged using the two-pointer technique. Its time complexity is O(n log n) and space complexity is O(n) (requiring a temporary array). Divide-and-conquer simplifies problems through recursion, and merge sort efficiently demonstrates its advantages. It serves as a foundation for understanding recursive and sorting algorithms.