Power of Four

Power of Four - Problem

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.

Input & Output

Example 1 — Power of Four

$ Input: n = 16

› Output: true

💡 Note: 16 = 4², so it is a power of four

Example 2 — Not a Power of Four

$ Input: n = 5

› Output: false

💡 Note: 5 cannot be expressed as 4^x for any integer x

Example 3 — Edge Case

$ Input: n = 1

› Output: true

💡 Note: 1 = 4⁰, so it is a power of four

Constraints

-2³¹ ≤ n ≤ 2³¹ - 1

Visualization

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Asked in

G Google 15 a Amazon 12 M Microsoft 8 f Facebook 6

The key insight is that powers of 4 have exactly one bit set at even positions (0,2,4,6...). Best approach is bit manipulation using masks to check the pattern. Time: O(1), Space: O(1)

Common Approaches

✓ Bit Manipulation

⏱️ Time: O(1) Space: O(1)

Powers of 4 have a specific bit pattern: they have exactly one bit set, and that bit is at an even position (0, 2, 4, 6, ...). We can check this using bitwise AND operations with specific masks.

Division Method

⏱️ Time: O(log n) Space: O(1)

Start with the number and keep dividing by 4. If we can divide evenly until we reach 1, it's a power of 4. If at any point we can't divide evenly or reach 0, it's not a power of 4.

Logarithm Method

⏱️ Time: O(1) Space: O(1)

A number n is a power of 4 if and only if log₄(n) is an integer. We can compute this using the change of base formula: log₄(n) = log(n) / log(4). If this result is very close to an integer, then n is a power of 4.

Bit Manipulation — Algorithm Steps

Check if n is positive and has exactly one bit set
Verify the single bit is at an even position
Use mask 0x55555555 to check even positions
Return true if both conditions are met

Visualization

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Step-by-Step Walkthrough

Check Power of 2

Verify exactly one bit is set

Check Even Position

Use mask to verify bit position

Result

Both conditions must be true

Code -

solution.c — C

#include <stdio.h>
#include <stdbool.h>

bool solution(int n) {
    if (n <= 0) {
        return false;
    }
    
    // Check if n is a power of 2 (has exactly one bit set)
    if ((n & (n - 1)) != 0) {
        return false;
    }
    
    // Check if the single bit is at an even position
    // 0x55555555 = 01010101010101010101010101010101 in binary
    return (n & 0x55555555) != 0;
}

int main() {
    int n;
    scanf("%d", &n);
    
    bool result = solution(n);
    printf(result ? "true\n" : "false\n");
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Constant time bitwise operations

⚡ Linearithmic

Space Complexity

O(1)

Only using constant extra space

✓ Linear Space

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Medium Frequency

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Bit Manipulation — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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