Power of Three

Problem

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

Example 2:

Input: n = 0
Output: false

Example 3:

Input: n = 9
Output: true

 

Constraints:

• -231 <= n <= 231 - 1

Solution

/**
 * @param {number} n
 * @return {boolean}
 */
var isPowerOfThree = function(n) {
    if (n < 1) return false;
    while (n % 3 === 0) n /= 3;
    return n === 1;
};

Keep dividing n by 3 until there is a non-zero remainder.

Follow-up

Could you solve it without loops/recursion?

Solution

/**
 * @param {number} n
 * @return {boolean}
 */
var isPowerOfThree = function(n) {
    if (n <= 0) {
        return false;
    }
    const epsilon = 10e-12;
    const val = (Math.log(n) / Math.log(3)) % 1;
    return val < epsilon;
};

Using basic logarithmic rules, we can test if $\log_3n = \frac{\log n}{\log 3}$ is an integer. Note that due to limitations of floating point arithmetics, we use an epsilon value to determine if we're "close enough" to be consider an integer.