Power of Four

LeetCode 342 | Difficulty: Easy

Easy

Problem Description

Given an integer n, return true if it is a power of four. Otherwise, return false.

An integer n is a power of four, if there exists an integer x such that n == 4^x.

Example 1:

Input: n = 16
Output: true

Example 2:

Input: n = 5
Output: false

Example 3:

Input: n = 1
Output: true

Constraints:

- `-2^31 <= n <= 2^31 - 1`

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

Topics: Math, Bit Manipulation, Recursion

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Approach

Bit Manipulation

Operate directly on binary representations. Key operations: AND (&), OR (|), XOR (^), NOT (~), shifts (<<, >>). XOR is especially useful: a ^ a = 0, a ^ 0 = a.

When to use

Finding unique elements, power of 2 checks, subset generation, toggling flags.

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

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Solutions

Solution 1: C# (Best: 44 ms)

Metric	Value
Runtime	44 ms
Memory	N/A
Date	2018-04-12

Solution

public class Solution {
    public bool IsPowerOfFour(int num) {
        return num > 0 && (num & (num - 1)) == 0 && (num - 1) % 3 == 0;
    }
}

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Complexity Analysis

Approach	Time	Space
Bit Manipulation	$O(n) or O(1)$	$O(1)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.