[LeetCode] Valid Perfect Square

Problem

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.

Examples

Example 1:

Input: 16
Returns: True

Example 2:

Input: 14
Returns: False

Solution

Newton's method, close to O(1)

public class Solution {
    public boolean isPerfectSquare(int num) {
      if (num < 1) return false;
      long t = num/2+1;
      while (t*t > num) {
        t = (t+num/t)/2;
      }
      return t*t == num;
    }
}

Binary-Search method, O(logn)

public class Solution {
    public boolean isPerfectSquare(int num) {
        long start = 1, end = num;
        while (start <= end) {
            long mid = start + (end-start)/2;
            long t = mid * mid;
            if (t == num) return true;
            else if (t < num) start = mid+1;
            else end = mid-1;
        }
        return false;
    }
}