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326. Power of Three

Description

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 == 3x.

 

Example 1:

Input: n = 27
Output: true
Explanation: 27 = 33

Example 2:

Input: n = 0
Output: false
Explanation: There is no x where 3x = 0.

Example 3:

Input: n = -1
Output: false
Explanation: There is no x where 3x = (-1).

 

Constraints:

• -231 <= n <= 231 - 1

 

Follow up: Could you solve it without loops/recursion?

Solutions

Solution 1: Trial Division

If $n \gt 2$, we can continuously divide $n$ by $3$. If it’s not divisible, it means $n$ is not a power of $3$, otherwise we continue dividing by $3$ until $n$ is less than or equal to $2$. If $n$ equals $1$, it means $n$ is a power of $3$, otherwise it’s not a power of $3$.

Time complexity $O(\log_3n)$, space complexity $O(1)$.

Solution 2: Mathematics

If $n$ is a power of $3$, then the maximum value of $n$ is $3^{19} = 1162261467$. Therefore, we only need to check if $n$ is a divisor of $3^{19}$.

Time complexity $O(1)$, space complexity $O(1)$.

• Java
• C++
• Python
• Go
• TypeScript
• Javascript
• Rust

• class Solution {
      public boolean isPowerOfThree(int n) {
          return n > 0 && 1162261467 % n == 0;
      }
  }
  
  
  // Solution 2
  class Solution {
      public boolean isPowerOfThree(int n) {
          return n > 0 && 1162261467 % n == 0;
      }
  }
  
  

• class Solution {
  public:
      bool isPowerOfThree(int n) {
          return n > 0 && 1162261467 % n == 0;
      }
  };
  
  
  // Solution 2
  class Solution {
  public:
      bool isPowerOfThree(int n) {
          return n > 0 && 1162261467 % n == 0;
      }
  };
  
  

• class Solution:
      def isPowerOfThree(self, n: int) -> bool:
          return n > 0 and 1162261467 % n == 0
  
  
  # Solution 2
  class Solution:
      def isPowerOfThree(self, n: int) -> bool:
          return n > 0 and 1162261467 % n == 0
  
  

• func isPowerOfThree(n int) bool {
  	return n > 0 && 1162261467%n == 0
  }
  
  
  // Solution 2
  func isPowerOfThree(n int) bool {
  	return n > 0 && 1162261467%n == 0
  }
  
  

• function isPowerOfThree(n: number): boolean {
      return n > 0 && 1162261467 % n == 0;
  }
  
  
  // Solution 2
  function isPowerOfThree(n: number): boolean {
      return n > 0 && 1162261467 % n == 0;
  }
  
  

• /**
   * @param {number} n
   * @return {boolean}
   */
  var isPowerOfThree = function (n) {
      return n > 0 && 1162261467 % n == 0;
  };
  
  
  // Solution 2
  /**
   * @param {number} n
   * @return {boolean}
   */
  var isPowerOfThree = function (n) {
      return n > 0 && 1162261467 % n == 0;
  };
  
  

• impl Solution {
      pub fn is_power_of_three(mut n: i32) -> bool {
          while n > 2 {
              if n % 3 != 0 {
                  return false;
              }
              n /= 3;
          }
          n == 1
      }
  }
  
  
  // Solution 2
  impl Solution {
      pub fn is_power_of_three(mut n: i32) -> bool {
          n > 0 && 1162261467 % n == 0
      }
  }
  
  

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