LeetCode-Sqrt(x)

Implement int sqrt(int x).

Compute and return the square root of x.

二分搜索法
class Solution {
public:
    int sqrt(int x) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if(x<=0)return 0;
        if(x<4)return 1;
        else if(x==4)return 2;
        else{
        int start=1,end=46340;
        if(end*end<=x)return end;
        while(start<=end){
            int mid=(start+end)/2;
            int a=mid*mid;
            if(a>x){
                end=mid-1;
            }
            else{
                if(a+mid*2+1>x)return mid;
                start=mid+1;
            }
        }
    }
    }
};

 

牛顿迭代法
class Solution {
public:
    int sqrt(int x) {
        if(x<1)return 0;
    unsigned long x1 = x - 1;
    unsigned s = 1;
    unsigned g0,g1;

    /* 初值设定 */
    if (x1 > 65535) {s += 8; x1 >>= 16;}
    if (x1 > 255)   {s += 4; x1 >>= 8;}
    if (x1 > 15)    {s += 2; x1 >>= 4;}
    if (x1 > 3)     {s += 1; x1 >>= 2;}

    /*迭代*/
    g0 = 1 << s;
    g1 = (g0 + (x >> s)) >> 1;
    while(g1 < g0)
    {
       g0 = g1;
       g1 = (g0 + x/g0) >> 1;
    }
    return g0;
    }
};
参见
http://www.cnblogs.com/Matrix_Yao/archive/2009/07/28/1532883.html