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C语言：二分搜索函数

news 2025/7/19 15:37:41

一、二分搜索基本概念

二分搜索（Binary Search）是一种在有序数组中查找特定元素的高效算法，时间复杂度为O(log n)。

基本特点：

仅适用于有序数组（升序或降序）
每次比较将搜索范围减半
比线性搜索(O(n))高效得多

二、标准二分搜索实现

1. 迭代版本（最常用）

int binarySearch(int arr[], int size, int target) {int left = 0;int right = size - 1;while (left <= right) {int mid = left + (right - left) / 2; // 防止溢出if (arr[mid] == target) {return mid; // 找到目标，返回索引} else if (arr[mid] < target) {left = mid + 1; // 目标在右半部分} else {right = mid - 1; // 目标在左半部分}}return -1; // 未找到
}

2. 递归版本

int binarySearchRecursive(int arr[], int left, int right, int target) {if (left > right) {return -1;}int mid = left + (right - left) / 2;if (arr[mid] == target) {return mid;} else if (arr[mid] < target) {return binarySearchRecursive(arr, mid + 1, right, target);} else {return binarySearchRecursive(arr, left, mid - 1, target);}
}

三、二分搜索变种

1. 查找第一个等于目标的值

int findFirst(int arr[], int size, int target) {int left = 0;int right = size - 1;int result = -1;while (left <= right) {int mid = left + (right - left) / 2;if (arr[mid] == target) {result = mid;right = mid - 1; // 继续在左半部分查找} else if (arr[mid] < target) {left = mid + 1;} else {right = mid - 1;}}return result;
}

2. 查找最后一个等于目标的值

int findLast(int arr[], int size, int target) {int left = 0;int right = size - 1;int result = -1;while (left <= right) {int mid = left + (right - left) / 2;if (arr[mid] == target) {result = mid;left = mid + 1; // 继续在右半部分查找} else if (arr[mid] < target) {left = mid + 1;} else {right = mid - 1;}}return result;
}

3. 查找第一个大于等于目标的值

int findFirstGreaterOrEqual(int arr[], int size, int target) {int left = 0;int right = size - 1;int result = -1;while (left <= right) {int mid = left + (right - left) / 2;if (arr[mid] >= target) {result = mid;right = mid - 1;} else {left = mid + 1;}}return result;
}