367. Valid Perfect Square

Given a positive integer num, write a function which returns True if num is a perfect square else False.

Note: Do not use any built-in library function such as sqrt.

Example 1:

Input: 16

Returns: True

 

Solution 1: use BST,O(logn)

class Solution {
public:
    bool isPerfectSquare(int num) {
        if (num==1) return true;
        int begin=0,end=num;
        while (begin<end-1){
            long long mid=(begin+end)/2;
            if (mid*mid==num) return true;
            if (mid*mid<num) begin=mid;
            if (mid*mid>num) end=mid;
        } 
        return false;
    }
};

Solution 2: Newton's method,  http://blog.csdn.net/wangxiaojun911/article/details/18203333

class Solution {
public:
    bool isPerfectSquare(int num) {
        long long x=num;
        while(x*x>num) x=(x+num/x)/2;
        return x*x==num;
    }
};

Soulution 3:  q_math.c special method, O(1)