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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

Example 4:

Input: n = 45 Output: false

Constraints:

- -231 <= n <= 231 - 1

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

Topic: Given an integer, write a function to determine if it is a power of 3. If it is, return true; otherwise, return false. Advanced does this without loops or recursion.

This question is similar to 231. Power of Two and 342. Power of Four But the power of 2 and the power of 4 are more similar.

### Solution 1 Iteration+Trial

The simple solution is to keep adding n n n pairs 3 3 3 Trial until n n n is no longer associated with 3 3 3 is multiplied, then judge n n Is n equal to 3 0 = 1 3^0 = 1 30 = 1. Note that nonpositive integers are not 3 3 The time complexity of the algorithm is O ( log 3 n ) O(\log_3 n) O(log3 n), spatial complexity is O ( 1 ) O(1) O(1) :

//C++ version class Solution { public: bool isPowerOfThree(int n) { if (n <= 0) return false; while (n % 3 == 0) n /= 3; return n == 1; } }; //Execution time: 8 ms, defeated 96.39% of all C++ submissions //Memory consumption: 5.6 MB, beating 94.77% of all C++ submissions

I am here Power of 4 The sx method in can also be used here. n n n to a floating point number and divide by 3 3 3, and finally decide if it's equal to 1.0 1.0 1.0 (not recommended):

//C++ version class Solution { public: bool isPowerOfThree(int n) { double tn = n; while (tn > 1.0) tn /= 3; return tn == 1.0; } }; //Execution time: 16 ms, beat 71.42% of all C++ submissions //Memory consumption: 5.9 MB, beating 40.15% of all C++ submissions

### Solution 2 Math Library Functions + Processing Errors (not recommended)

Use the math library functions log(), round(), but first determine if n is a positive integer and handle the error (probably the test case ratio) 231. Power of Two and 342. Power of Four Much more, over 20,000):

//C++ version class Solution { public: bool isPowerOfThree(int n) { if (n <= 0) return false; double k = log(n) / log(3); return fabs(k - round(k)) <= 1e-10; } }; //Execution time: 8 ms, defeated 96.39% of all C++ submissions //Memory consumption: 6 MB, beating 6.12% of all C++ submissions

### Solution 3 Tables

One of the easiest ways to think of "do not use loops/recursions" is to do table preprocessing. The time complexity of the algorithm is O ( 1 ) O(1) O(1), spatial complexity is O ( 1 ) O(1) O(1) :

//C++ version int ans[25] = {1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,4782969,14348907,43046721,129140163,387420489,1162261467}; class Solution { public: bool isPowerOfThree(int n) { if (n <= 0) return false; for (int i = 0; i < 20; ++i) if (n == ans[i]) return true; return false; } }; //Execution time: 16 ms, beat 71.42% of all C++ submissions //Memory consumption: 5.6 MB, beating 94.77% of all C++ submissions

### Solution 4 Mathematics (multiples/approximations)

n n The data type of n is int. As you can see from the table, the maximum third power in the range of int is 1162261467 1162261467 1162261467. If n n n is 3 3 The power of 3 must be satisfied n ∗ 3 k = 1162261467 n * 3^k = 1162261467 n_3k=1162261467, i.e. n n n and 1162261467 1162261467 1162261467 has a multiplier relationship. So you just need to decide n n n is a positive integer and is 1162261467 1162261467 The time complexity of the algorithm is O ( 1 ) O(1) O(1), spatial complexity is O ( 1 ) O(1) O(1) .

It is important to note that this is not a quick judgement x x General practice for the power of x if and only if x x x is a prime number, so it cannot be generalized to 342. Power of Four A simple example is, 64 64 64 is 4 4 The power of 4 must also be some of the largest 4 4 Power of 4 z z The approximate number of z, however 32 32 32 is not 4 4 The power of 4, but it must be 64 64 64, thus z z The approximate number of z.

//C++ version class Solution { public: bool isPowerOfThree(int n) { return n > 0 && 1162261467 % n == 0; } }; //Execution time: 16 ms, beat 71.42% of all C++ submissions //Memory consumption: 5.8 MB, beating 58.63% of all C++ submissions

- Power of 3

https://leetcode-cn.com/problems/power-of-three/