367 Valid Perfect Square[Easy, Math]

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

从1开始加的话会超时。要利用一个数学规律：

1 = 1 4 = 1 + 3 9 = 1 + 3 + 5 16 = 1 + 3 + 5 + 7 25 = 1 + 3 + 5 + 7 + 9 36 = 1 + 3 + 5 + 7 + 9 + 11 .... so 1+3+...+(2n-1) = (2n-1 + 1)n/2 = nn

复杂度O(sqrt(n))

public boolean isPerfectSquare(int num) {
     int i = 1;
     while (num > 0) {
         num -= i;
         i += 2;
     }
     return num == 0;
 }

或者用牛顿法。 https://discuss.leetcode.com/topic/49325/a-square-number-is-1-3-5-7-java-code/2