二分查找

date

Jan 6, 2022

slug

BinarySearch

status

Published

二分查找

二分的本质并非“单调性”，而是“边界”，只要找到某种性质，使得整个区间一分为二，那么就可以用二分把边界点二分出来。

模板1

boolean check(int x) {}

int search(int left, int right) {
    while (left < right) {
        int mid = (left + right) >> 1;
        if (check(mid)) {
            right = mid;
        } else {
            left = mid + 1;
        }
    }
    return left;
}

模板2

boolean check(int x) {}

int search(int left, int right) {
    while (left < right) {
        int mid = (left + right + 1) >> 1;
        if (check(mid)) {
            left = mid;
        } else {
            right = mid - 1;
        }
    }
    return left;
}

模板3

	public int search(int[] nums, int target) {
        int left = 0;
        int right = nums.length - 1;
        while (left <= right) {
            int middle = left + ((right - left) / 2);
            if (target < nums[middle]) {
                right = middle - 1;
            } else if (target > nums[middle]) {
                left = middle + 1;
            } else {
                return middle;
            }
        }
        return -1;
   }