LeetCode Online Judge 题目C# 练习 - Sqrt(x)

Implement int sqrt(int x).
Compute and return the square root of x.

 1         public static int Sqrt(int x)
 2         {
 3             if (x == 0) return 0;
 4 
 5             ulong x2 = (ulong)x;
 6             ulong l = 0;
 7             ulong r = (ulong)x;
 8             ulong mid;
 9 
10             while (l <= r)
11             {
12                 mid = l + (r - l) / 2;
13 
14                 //if Square(mid) < x < Square(mid + 1)
15                 if (mid * mid == x2 || (x2 > mid * mid && x2 < (mid + 1) * (mid + 1)))
16                     return (int)mid;
17                 else if (mid * mid > x2)
18                     r = mid - 1;
19                 else
20                     l = mid + 1;
21             }
22 
23             return -1;
24         }

代码分析：

　　二分法找平方根。

　　复习一下牛顿法求平方根。

　　xk+1 = (xk + n / xk) / 2   (X0 = 1)

　　C code:

 1 float Sqrt(int n)
 2 {
 3     float x = 1;
 4     //收敛1000次，越多越准
 5     for(int i = 1; i <= 1000; i++)   
 6     {
 7         x = (x + n / 2) / 2;
 8     }
 9     
10     return x;
11 }
posted @ 2012-10-17 23:52  ETCOW  阅读(484)  评论(0)  编辑  收藏  举报