Check if Number is a Sum of Powers of Three

class Solution {
public:
    bool canRepresentInPowersOfThree(int num) {
        while (num > 0) {
            if (num % 3 == 2) return false;
            num /= 3;
        }
        return true;
    }
};

The given solution in C++ checks if a number can be represented as a sum of powers of three. Here is how the function operates:

• Initiate a loop that continues until the number becomes zero.
• In each iteration, check if the remainder when the number is divided by 3 is equal to 2. If it is, the number cannot be represented as a sum of powers of three, and the function returns false.
• Divide the number by 3 to reduce it and continue to the next iteration.
• If the loop completes without finding a remainder of 2, return true, indicating that the number can indeed be represented as a sum of powers of three.

This approach effectively uses division and modulus operations to decompose the number and verify its composition in relation to the powers of three.

class Solution {

    public boolean isSumOfPowersOfThree(int input) {
        while (input > 0) {
            if (input % 3 == 2) {
                return false;
            }
            input /= 3;
        }
        return true;
    }
}

This summary explains the Java code designed to check if a given number can be expressed as a sum of powers of Three.

Here's a breakdown of how the code functions:

• Define a class Solution that includes a method isSumOfPowersOfThree.
• This method accepts an integer, input, and processes it to determine if it can be expressed as a sum of various powers of 3.
• Employ a while loop that continues as long as input is greater than zero.
  • Inside the loop, verify if input % 3 == 2. If true, the method immediately returns false, since a remainder of 2 implies the number cannot be broken down into a sum of powers of three without fractions.
  • Reduce input by dividing it by 3 in each iteration of the loop.
• If the loop completes without finding a remainder of 2, return true, indicating the number can be expressed as the sum of powers of three.

This solution efficiently checks the condition using a loop and a simple modulus operation. By continually dividing the number by 3, the code progressively tests each digital position in the base-3 representation of the number for compatibility with the condition. If at any point a digit exceeds 1, the function quits early, optimizing performance.

class Solution:
    def isPossible(self, number: int) -> bool:
        while number > 0:
            if number % 3 == 2:
                return False
            number //= 3
        return True

This Python 3 solution addresses the problem of checking if a given number can be represented as a sum of powers of three. The approach utilizes a while loop to continuously reduce the number by dividing it by 3. During each iteration, the solution assesses whether the remainder of the division by 3 is 2. If it is, the function immediately returns False, indicating that the number cannot be expressed as a sum of powers of three. If the number successfully reduces to zero without hitting a remainder of 2, the function returns True, confirming that such a representation is possible. This method is both time-efficient and straightforward, leveraging the properties of numbers in base 3.