Binary Search

二分的原理是利用区间内值有序的特点, 不断让可行区间减半, 最终可行区间长度减到1得到答案
要保证二分能得到正确答案并且不会死循环, 要保证两个条件:
1. 解一直在可行区间里
2. 每次判断后可行区间都会缩小(特别是左右端点相距为1的时候)

闭区间 [low, high]

普通二分：pass

lower_bound:

初始参数为 low=0, high=n-1

p搜索区间为[low, high], 返回值候选区间[low, high+1]

A[mid]<key时，搜索区间更新为[mid+1,high], 返回值候选区间[mid+1, high+1]

A[mid]>=key时，搜索区间更新为[low,mid-1], 返回值候选区间[low, mid]

while (low<=high) 需要包含等于号，这是因为如果while (low<high)，终止时low=high，返回值候选区间[low, high+1]有两个值。

while (low<=high) 终止时low>high, 即low>=high+1。又由于low<=high+1，所以low=high+1。此时候选区间只有一个元素low，low就是解。

int bsearch(int *A, int low, int high, int key){ //[low,high]
    int mid;
    while (low<=high){
        mid = (low+high)/2;
        if (A[mid]==key) 
            return mid;
        else if (A[mid]<key)
            low = mid+1;
        else
            high = low-1; 
    }
} 

int lower_bound(int *A, int low, int high, int key){ //[low,high]
    int mid;
    while (low<=high){
        mid = (low+high)/2;
        if (A[mid]<key)
            low = mid+1;
        else
            high = low-1; 
    }
    return low;
}

A[mid]<key

Binary Search

原文：https://www.cnblogs.com/hankunyan/p/9028410.html