Detailed explanation of C++ function recursion: recursive application in divide and conquer method

Recursion is a function self-calling technique, suitable for problems that can be decomposed into smaller-scale sub-problems. The divide-and-conquer method uses recursion to decompose the problem into independent sub-problems and solve them step by step. For example, the findMaximum() function recursively searches for the maximum value in an array by checking the basic situation (single element), calculating the midpoint, recursively calling the subarray, and finally returning the maximum value of the left and right subarrays. This divide-and-conquer recursion is widely used in problems such as sorting, searching, and merging operations.

C Detailed explanation of function recursion: Recursive application in divide and conquer method

What is recursion?

Recursion is a programming technique in which a function calls itself, directly or indirectly. Recursion is useful when a problem can be broken down into smaller sub-problems. The recursive process ends when the subproblem reaches the base case (i.e. no further decomposition is required).

Recursive application in divide-and-conquer method

The divide-and-conquer method is a problem-solving algorithm that decomposes the problem into smaller sub-problems and then solves them recursively. these sub-questions. This approach works well for problems that can be broken down into independent parts.

For example, consider the following recursive application of the C function in the divide-and-conquer method:

int findMaximum(int arr[], int low, int high) {
  // 基本情况检查
  if (low == high) {
    return arr[low];
  }

  // 找到中点
  int mid = (low + high) / 2;

  // 递归调用
  int leftMax = findMaximum(arr, low, mid);
  int rightMax = findMaximum(arr, mid + 1, high);

  // 返回左右子数组中的最大值
  return max(leftMax, rightMax);
}

Practical case: finding the maximum value in an array

Above Recursive function findMaximum() is used to find the maximum value of elements in a given array. It uses the divide-and-conquer method, splitting the array into two sub-arrays and calling the function recursively on those sub-arrays. The process continues until the base case (a single element in the subarray) is reached.

Code explanation

• Basic situation check: If low is equal to high means If there is only one element in the array, this element is directly returned as the maximum value.
• Find the midpoint: Calculate the middle index of the array mid.
• Recursive call: Divide the array into two sub-arrays and call the findMaximum() function on these sub-arrays respectively.
• Return the maximum value: Return the larger value of the two recursive call results.

With this recursive method, we can efficiently find the maximum value in the array. This divide-and-conquer approach can be applied in several problems, such as sorting, searching, and merging operations.

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