数组 704.二分查找法

左闭右闭

class Solution {
    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]) {
                left = middle + 1;
            } else if (target < nums[middle]) {
                right = middle - 1;
            } else {
                return middle;
            }
        }return -1;
    }
}

middle = (left + right)/2  与  left+ (right - left)/2 

两个最大值的int类型相加，可能会造成越界，目的是求均值，故先减后加，防止越界

左闭右开

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

一是初始right的取值，当左闭右开时，不包括右边的区间，应该等于nums.length

二是 目标在左半区间，因为右开，所以搜索时也不包含右边界，故此时搜索区间应该是[0,middle)

左开右闭 

class Solution {
    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]) {
                left = middle + 1;
            } else if (target < nums[middle]) {
                right = middle - 1 ;
            } else {
                return middle;
            }
        }return -1;
    }
}

一同上

二 left左区间取值，因为middle = （right + left) /2 是向下取整的，导致后续区间的middle取不对，所以需要middle +1