Power of Four - Practice Coding Problems

Power of Four - Problem

Given an integer n, determine whether it represents a power of four. Return true if n is a power of four, otherwise return false.

A number is a power of four if there exists an integer x such that n = 4^x. In other words, n must be one of the values: 1, 4, 16, 64, 256, 1024, ...

Examples:

n = 16 → true (since 16 = 4²)
n = 5 → false (no integer x exists where 4^x = 5)
n = 1 → true (since 1 = 4⁰)

This problem tests your understanding of mathematical properties, bit manipulation, and optimization techniques.

Input & Output

example_1.py — Basic Power of Four

$ Input: n = 16

› Output: true

💡 Note: 16 = 4² = 4^2, so 16 is a power of four with x = 2

example_2.py — Not Power of Four

$ Input: n = 5

› Output: false

💡 Note: There is no integer x such that 4^x = 5. The closest powers of 4 are 4¹ = 4 and 4² = 16

example_3.py — Edge Case

$ Input: n = 1

› Output: true

💡 Note: 1 = 4⁰ = 4^0, so 1 is a power of four with x = 0

Constraints

-2³¹ ≤ n ≤ 2³¹ - 1
Follow-up: Could you solve it without loops/recursion?

Visualization

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Understanding the Visualization

Identify Powers of 4

1, 4, 16, 64, 256, 1024... follow 4^x pattern

Binary Representation

Each has exactly one bit set: 1₂, 100₂, 10000₂, 1000000₂...

Bit Position Pattern

The single bit is always at even positions (0, 2, 4, 6...)

Apply Bit Magic

Use (n & (n-1)) == 0 and position checking for O(1) solution

Key Takeaway

🎯 Key Insight: Powers of four are the subset of powers of two where the single bit appears at even positions (0, 2, 4, 6...), enabling O(1) verification through bit manipulation.

Asked in

G Google 45 a Amazon 38 ⊞ Microsoft 32 Apple 28

The optimal solution uses bit manipulation to check three conditions in O(1) time: the number must be positive, have exactly one bit set (power of 2), and that bit must be at an even position (making it a power of 4). The key insight is using (n & (n-1)) == 0 to check for single bit and masking with appropriate patterns to verify the bit position.

Common Approaches

Approach	Time	Space	Notes
✓ Bit Manipulation (Optimal)	O(1)	O(1)	Use bit operations to check if n is a power of 4 in O(1) time

Bit Manipulation (Optimal) — Algorithm Steps

Check if n > 0 (powers of 4 are positive)
Check if n has exactly one bit set: (n & (n-1)) == 0
Check if the set bit is at an odd position: (n & 0x55555555) != 0
Return true only if all conditions are met

Visualization

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Step-by-Step Walkthrough

Check n > 0

Powers of 4 must be positive

Check single bit

n & (n-1) == 0 means exactly one bit is set

Check odd position

n & 0x55555555 checks if bit is at odd position

Code -

solution.c — C

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

bool isPowerOfFour(int n) {
    // Check: n > 0, exactly one bit set, bit at odd position
    return n > 0 && (n & (n - 1)) == 0 && (n & 0x55555555) != 0;
}

int main() {
    int n;
    scanf("%d", &n);
    printf("%s\n", isPowerOfFour(n) ? "true" : "false");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

All operations are constant time bit manipulations

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra space for variables

✓ Linear Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Bit Manipulation (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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