(69)Sqrt(x)

Implement int sqrt(int x).

Compute and return the square root of x.

example:

sqrt(3) = 1

sqrt(4) = 2

sqrt(5) = 2

sqrt(10) = 3
 
challenge:O(log(x))
 
 
we start with two initial values - one value a below √Q and another value b above √Q, where Q is a positive real number. Since a is a low value, let us denote it by L. Similarly, denote b by H. Let m = (L+H)/2.
If m^2 < Q, let L = m.
If m^2 > Q, let H = m.
Let us find √5. So Q = 5.
since 2^2 <= 5 < 3^2, let L = 2, H = 3.
 
 1     public int sqrt(int x) {
 2         long lo = 0;
 3         long hi = x;
 4         while (hi >= lo) {
 5             long mid = lo + (hi - lo) / 2;
 6             System.out.println("befor " + "lo:" + lo + " hi:" + hi + " mid:" + mid);
 7             if (x < mid * mid) {
 8                 hi = mid - 1; // not hi = mid
 9             } else {
10                 lo = mid + 1;
11             }
12             System.out.println("after " + "lo:" + lo + " hi:" + hi + " mid:" + mid);
13         }
14         return (int)hi;
15     }

 

posted on 2015-02-09 14:27  lh_chuang  阅读(416)  评论(0)  编辑  收藏  举报

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