Power of Two

LeetCode 231 | Difficulty: Easy

Easy

Problem Description

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

An integer n is a power of two, if there exists an integer x such that n == 2^x.

Example 1:

Input: n = 1
Output: true
Explanation: 2^0 = 1

Example 2:

Input: n = 16
Output: true
Explanation: 2^4 = 16

Example 3:

Input: n = 3
Output: false

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 IsPowerOfTwo(int n) {
        if(n<=0) return false;
        var x = n & n-1;
        return x==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.