How do you solve Check if Number is a Sum of Powers of Three on LeetCode?

Check if Number is a Sum of Powers of Three (LeetCode #1780) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: The ternary representation of a number provides insight into whether it can be expressed as a sum of distinct powers of three.

What is the brute force solution for Check if Number is a Sum of Powers of Three?

The brute force approach for Check if Number is a Sum of Powers of Three is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible sums of distinct powers of three and checking if the given number can be formed. This method is straightforward but inefficient as it explores all combinations. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Check if Number is a Sum of Powers of Three?

Check if Number is a Sum of Powers of Three uses the following concepts: Math. The recommended patterns to study are: Mathematical Properties, Base Conversion.

What are the interview tips for Check if Number is a Sum of Powers of Three?

Always consider the properties of the number system (like binary, ternary) when dealing with sums of powers. Be prepared to explain your thought process clearly, especially when transitioning from brute force to optimal solutions. Practice recognizing patterns in problems to improve your problem-solving speed.

What are common mistakes when solving Check if Number is a Sum of Powers of Three?

Failing to recognize the significance of the ternary representation. Overcomplicating the problem by trying to generate combinations instead of checking the base 3 digits.

#1780

Check if Number is a Sum of Powers of Three

Medium

MathMathematical PropertiesBase Conversion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(log n)
Space	O(1)	O(1)

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Intuition

Time O(log n)Space O(1)

The optimal solution leverages the properties of numbers in base 3. If the number can be represented as a sum of distinct powers of three, its ternary representation should not contain the digit '2'. This is because '2' indicates that we would need to use the same power of three more than once.

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Algorithm

3 steps

1Step 1: Convert the number n to its base 3 representation.
2Step 2: Check if any digit in the base 3 representation is '2'.
3Step 3: Return true if no '2' is found, otherwise return false.

solution.py6 lines

1def checkPowersOfThree(n):
2    while n > 0:
3        if n % 3 == 2:
4            return False
5        n //= 3
6    return True

ℹ

Complexity note: The time complexity is O(log n) because we are effectively dividing the number by 3 in each iteration, which reduces the number of digits we need to check. The space complexity is O(1) as we are using a constant amount of space.

1The ternary representation of a number provides insight into whether it can be expressed as a sum of distinct powers of three.
2If any digit in the base 3 representation is '2', it cannot be formed by distinct powers.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.