二分查找

//C语言 
int binarySearch(int *arr,int len,int key) {
    if(arr == NULL || len <= 0)
    return -1;
    int start = 0;
    int end = len - 1;
    int mid = 0;
    while(start < end) {
        if(arr[start] == key)
        return start;
        if(arr[end] == key)
        return end;
        mid = start + (end - start) / 2;
        if(arr[mid] == key)
        return mid;
        else if(arr[mid] < key)
        start = mid+1;//必须+1，否则死循环 
        else
        end = mid-1;//必须-1，否则死循环 
    }
    return -1;
}

 

//C++
const size_t arraySize = 10;
template<typename T>
int binarySearch(const array<T, arraySize> &arr, const T &key) {
    int mid = 0;
    int low = 0;
    int high = arraySize - 1;
    while (low < high) {
        mid = low + (high - low);
        if (arr[low] == key)
            return low;
        if (arr[high] == key)
            return high;
        if (arr[mid] == key)
            return mid;
        if (arr[mid] < key)
            low = mid + 1;
        else
            high = mid - 1;
    }
    return -1;
}

时间复杂度：O(log₂N)

证明：