Start practising

K-th Bit is Set or Not

Easy Bit Manipulation Basics Original on GeeksforGeeks

K-th Bit is Set or Not is a easy bit manipulation problem solved with the basics pattern. The best approach, optimal (mask with a left shift), runs in O(1) time and O(1) space. Below are 2 approaches in Java, from divide k times up.

Problem

Check whether the k-th bit (0-indexed from the right) of n is set to 1.

Examples

Example 1

Input
n = 4, k = 2
Output
true
Why
4 = 100 in binary; bit 2 (0-indexed from the right) is 1.

Example 2

Input
n = 4, k = 0
Output
false

Constraints

  • 1 <= n <= 10^9, 0 <= k <= 30; k is 0-indexed from the least significant bit.

Animated walkthrough

A narrated, step-by-step animation that builds the solution from the idea up. Press play, or step through it at your own pace.

Concepts first, then the problem and every approach, step by step.

Space to play or pause · ← → to jump a step · click or drag the bar to seek

Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

ApproachTimeSpace
Divide k timesO(k)O(1)
Optimal (mask with a left shift)O(1)O(1)

1Divide k times

TimeO(k)
SpaceO(1)

Divide n by 2 k times to bring bit k to the bottom, then check whether it is odd.

  1. Repeat k times: n /= 2. Return n % 2 == 1.
Java
class Solution {
    static boolean checkKthBit(int n, int k) {
        for (int i = 0; i < k; i++) n /= 2;
        return n % 2 == 1;
    }
}

2Optimal (mask with a left shift)

TimeO(1)
SpaceO(1)

1 << k has only bit k set. AND with n keeps just that bit.

  1. return (n & (1 << k)) != 0. (Equivalent: ((n >> k) & 1) == 1.)
Java
class Solution {
    static boolean checkKthBit(int n, int k) {
        return (n & (1 << k)) != 0;
    }
}

Edge cases to test

  • k beyond the highest set bit (false)

Hints

Hint 1

Build a mask with only bit k set: 1 << k. Then n & mask is non-zero exactly when bit k is set.

FAQ

What is the best time complexity for K-th Bit is Set or Not?

Optimal (mask with a left shift) runs in O(1) time and O(1) extra space.

Which pattern does K-th Bit is Set or Not use?

It is a bit manipulation problem that uses the basics pattern. Other problems with the same pattern: Decimal to binary, Convert Binary Number in a Linked List to Integer, Odd or Even.

Is there a brute force solution for K-th Bit is Set or Not?

Yes. Divide k times takes O(k) time and O(1) space. Divide n by 2 k times to bring bit k to the bottom, then check whether it is odd.

Which edge cases should I test for K-th Bit is Set or Not?

k beyond the highest set bit (false).