C program to set K-th bit of a number N

Given a number N and an integer K, the task is to set the Kth bit of the number N, i.e., if the Kth bit is 0, then set it to 1 and if it is 1 then leave it unchanged.

Examples: 

Input: N = 5, K = 2
Output: 7
Explanation: 
5 is represented as 101 in binary and has its second bit 0, so setting it will result in 111 i.e. 7.

Input: N = 5, K = 1
Output: 5
Explanation: 
5 is represented as 101 in binary and has its first bit is already 1, so setting it will result in 101 i.e. 5.

Naive Approach: A simple approach would be to add the 2’s pow if that bit is not set in number. Following are steps for our idea. 

• Check if bit is set or not.

N = 4, K = 1

5 -> 100

so if take the bitwise and of N and  2^K-1   if that bit is set it result 1 else it result 0. 

since 1 & 0 = 0 and 0 & 1 = 0 

1 & 1 = 1 and 0 & 0 = 1

K = 1 -> 2^1-1 = 2⁰ = 1 -> 001

N & 2^k-1 = 100 & 001 = 000  so bit is not set.

• If bit is not set then set the bit with the adding 2^K-1to the number.

N = 4 -> 100 , K = 2⁰ = 1

N + K = 4 +1 = 5

So we set the 1’s bit and result is 5 -> 101  

• If bit is set then do not add number. 

Below is the program to implement the above idea.

C

// Online C compiler to run C program online
#include <stdio.h>
#include<math.h>

// Function to set Kth bit
int number( int n, int k){

    int x = (int)pow(2,k-1);
    // Checking the Kth bit is set or not
    if(n & x) return n;
    else{
        return n + x;
    }
}
// Driver code
int main() {

    int result = number(5, 2);
    printf("%d",result);

    return 0;
}

Output

7

Time Complexity: O(log k)

Auxiliary Space: O(1)

Effective Approach: The approach to solve this problem is based on bitmasking technique with help of bitwise OR operator.

• Since bitwise OR of any bit with a set bit results in a set bit, i.e.

Any bit  <bitwise OR> Set bit = Set bit

which means,

0 | 1 = 1

1 | 1 = 1

• So for setting a bit, performing a bitwise OR of the number with a set bit is the best idea.

n = n | 1 << K

OR

n |= 1 << K

where K is the bit that is to be set

Below is the C++ program to implement the above approach-

C++

// C++ program to implement the above approach
#include <stdio.h>

// Function to set the
// kth bit of n
int setBit(int N, int K)
{
    return (N | (1 << (K - 1)));
}

// Driver code
int main()
{
    int N = 5, K = 2;
    printf("%d\n", setBit(N, K));
    return 0;
}

Time Complexity: O(1)

Auxiliary Space: O(1)

Output

7