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Power of Two

Expert Answer & Key Takeaways

A complete guide to understanding and implementing Bit Manipulation.

Power of Two

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==2xn == 2^x.
Easy

Examples

Input: n = 1
Output: true
Input: n = 16
Output: true
Input: n = 3
Output: false
Approach 1

Level I: Brute Force (Division)

Intuition

Keep dividing the number by 2 until it hits 1. If at any point the remainder is not 0, it's not a power of two.
⏱ $O(\\log N)$💾 $O(1)$
java
class Solution {
    public boolean isPowerOfTwo(int n) {
        if (n <= 0) return false;
        while (n % 2 == 0) n /= 2;
        return n == 1;
    }
}
Approach 2

Level II: Math (Max Power of Two)

Intuition

Since the input is a 32-bit signed integer, the largest power of two is 230=10737418242^{30} = 1073741824. If n is a power of two, it must be a divisor of 2302^{30}.
⏱ $O(1)$💾 $O(1)$
java
class Solution {
    public boolean isPowerOfTwo(int n) {
        return n > 0 && 1073741824 % n == 0;
    }
}
Approach 3

Level III: Optimal (Bit Manipulation)

Intuition

A power of two in binary has exactly one bit set. The expression n & (n - 1) clears the rightmost set bit. If n is a power of two, clearing its only set bit should result in 0.
⏱ $O(1)$💾 $O(1)$
java
class Solution {
    public boolean isPowerOfTwo(int n) {
        return n > 0 && (n & (n - 1)) == 0;
    }
}

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