326. Power of Three

EasyLeetCode

Given an integer n, return true if it is a power of three. Otherwise, return false.

An integer n is a power of three, if there exists an integer x such that n == 3^x.

Example 1:

Input: n = 27

Output: true

Explanation: 27 = 3³

Example 2:

Input: n = 0

Output: false

Explanation: There is no x where 3^x = 0.

Example 3:

Input: n = -1

Output: false

Explanation: There is no x where 3^x = (-1).

Constraints:

-2³¹ <= n <= 2³¹ - 1

How to solve the problem

1. Using loop to check if n is divisible by 3, and if n/3 is also divisible by 3, and so on.

2. Using logrithm, if a number is a power of 3, then its log₃(n) must be an integer. Combining the logarithmic base conversion formula: log₃(n) = log₁₀(n) / log₁₀(3)

Code

• Loop

class Solution:
    def isPowerOfThree(self, n: int) -> bool:
        if n <= 0: return False
        while n > 1:
            if n % 3 != 0: return False
            n //= 3
        return True

• Logarithm

class Solution:
    def isPowerOfThree(self, n: int) -> bool:
        if n <= 0: return False
        return (math.log10(n) / math.log10(3)).is_integer()

Complexity

Time complexity: O(log₃(n))

Space complexity: O(1)