Valid Perfect Square
Given a positive integer num, write a function that returns True if num is a perfect square else False.
Note: Do not use any built-in library function such as sqrt.
Example 1:
We have observed the equation and find some similarities, let's discuss with an example.
Input: 16
1 + 3 + 5 + 7 = 16
So 1 + 3 + 5 + 7 + 9 + 11 + ... + (2n -1)
= (2(n-1) + 1) n/2 = n*n
Note: Do not use any built-in library function such as sqrt.
Example 1:
Input: 16 Output: trueBinary Search Approach - O(log n)
public boolean isPerfectSquare(int num) { long left = 1; long right = num; while (left<= right) { long mid = left + (right -left) /2; if (mid * mid == num) return true; if (mid * mid < num) { left = mid + 1; } else right = mid - 1; } return false; }Square Root Approach - O(sqrt(n))
We have observed the equation and find some similarities, let's discuss with an example.
Input: 16
1 + 3 + 5 + 7 = 16
So 1 + 3 + 5 + 7 + 9 + 11 + ... + (2n -1)
= (2(n-1) + 1) n/2 = n*n
public boolean isPerfectSquare(int num) { int i = 1; while (num > 0) { num -= i; i += 2; } return num == 0; }
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