Find closest integer with the same weight

Difficulty Level : Basic
Last Updated : 09 Nov, 2021

Given a positive integer X the task is to find an integer Y such that:

The count of set bits is Y is equal to the count of set bits in X.
X != Y.
|X – Y| is minimum.

Examples:

Input: X = 92
Output: 90
90 is the closest number to 92 having
equal number of set bits.
Input: X = 17
Output: 18

Approach: A little math can lead us to the solution approach. Since the number of bits in both the numbers has to be the same, if a set bit is flipped then an unset bit will also have to be flipped.
Now the problem reduces to choosing two bits for the flipping. Suppose one bit at index i is flipped and another bit at index j (j < i) from the LSB (least significant bit). Then the absolute value of the difference between the original integer and the new one is 2ⁱ – 2^j. To minimize this, i has to be as small as possible and j has to be as close to i as possible.
Since the number of set bits have to be equal, so the bit at index i must be different from the bit at index j. This means that the smallest can be the rightmost bit that’s different from the LSB, and j must be the very next bit. In summary, the correct approach is to swap the two rightmost consecutive bits that are different.
Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
const int NumUnsignBits = 64;
 
// Function to return the number
// closest to x which has equal
// number of set bits as x
unsigned long findNum(unsigned long x)
{
    // Loop for each bit in x and
    // compare with the next bit
    for (int i = 0; i < NumUnsignBits - 1; i++) {
        if (((x >> i) & 1) != ((x >> (i + 1)) & 1)) {
            x ^= (1 << i) | (1 << (i + 1));
            return x;
        }
    }
}
 
// Driver code
int main()
{
    int n = 92;
 
    cout << findNum(n);
 
    return 0;
}

Java

// Java implementation of the approach
class GFG
{
static int NumUnsignBits = 64;
 
// Function to return the number
// closest to x which has equal
// number of set bits as x
static long findNum(long x)
{
    // Loop for each bit in x and
    // compare with the next bit
    for (int i = 0; i < NumUnsignBits - 1; i++)
    {
        if (((x >> i) & 1) != ((x >> (i + 1)) & 1))
        {
            x ^= (1 << i) | (1 << (i + 1));
            return x;
        }
    }
    return Long.MIN_VALUE;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 92;
 
    System.out.println(findNum(n));
}
}
 
// This code is contributed by PrinciRaj1992

Python3

# Python3 implementation of the approach
NumUnsignBits = 64;
 
# Function to return the number
# closest to x which has equal
# number of set bits as x
def findNum(x) :
 
    # Loop for each bit in x and
    # compare with the next bit
    for i in range(NumUnsignBits - 1) :
        if (((x >> i) & 1) != ((x >> (i + 1)) & 1)) :
            x ^= (1 << i) | (1 << (i + 1));
            return x;
 
# Driver code
if __name__ == "__main__" :
    n = 92;
    print(findNum(n));
 
# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;
     
class GFG
{
static int NumUnsignBits = 64;
 
// Function to return the number
// closest to x which has equal
// number of set bits as x
static long findNum(long x)
{
    // Loop for each bit in x and
    // compare with the next bit
    for (int i = 0; i < NumUnsignBits - 1; i++)
    {
        if (((x >> i) & 1) != ((x >> (i + 1)) & 1))
        {
            x ^= (1 << i) | (1 << (i + 1));
            return x;
        }
    }
    return long.MinValue;
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 92;
 
    Console.WriteLine(findNum(n));
}
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
    // Javascript implementation of the approach
     
    let NumUnsignBits = 64;
   
    // Function to return the number
    // closest to x which has equal
    // number of set bits as x
    function findNum(x)
    {
        // Loop for each bit in x and
        // compare with the next bit
        for (let i = 0; i < NumUnsignBits - 1; i++)
        {
            if (((x >> i) & 1) != ((x >> (i + 1)) & 1))
            {
                x ^= (1 << i) | (1 << (i + 1));
                return x;
            }
        }
        return Number.MIN_VALUE;
    }
     
    let n = 92;
   
    document.write(findNum(n));
 
</script>

Output:

Time Complexity: O(logn)

Auxiliary Space: O(1)

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Table of Contents

Find closest integer with the same weight

C++

Java

Python3

C#

Javascript

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