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# Largest number less than X having at most K set bits

• Last Updated : 11 Jun, 2021

Given an integer X > 1 and an integer K > 0, the task is to find the greatest odd number < X such that the number of 1’s in its binary representation is at most K.
Examples:

Input: X = 10, K = 2
Output: 10
Input: X = 29, K = 2
Output: 24

Naive Approach: Starting from X – 1 check all the numbers below X which have at most K set bits, the first number satisfying the condition is the required answer.
Efficient Approach: is to count the set bits. If the count is less than or equal to K, return X. Otherwise, keep removing rightmost set bit while count – k does not become 0.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the greatest number <= X``// having at most K set bits.``int` `greatestKBits(``int` `X, ``int` `K)``{``    ``int` `set_bit_count = __builtin_popcount(X);``    ``if` `(set_bit_count <= K)``        ``return` `X;` `    ``// Remove rightmost set bits one``    ``// by one until we count becomes k``    ``int` `diff = set_bit_count - K;``    ``for` `(``int` `i = 0; i < diff; i++)``        ``X &= (X - 1);` `    ``// Return the required number``    ``return` `X;``}` `// Driver code``int` `main()``{``    ``int` `X = 21, K = 2;``    ``cout << greatestKBits(X, K);``    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.io.*;``  ` `class` `GFG {` `    ``// Function to return the greatest number <= X``    ``// having at most K set bits.``     ``int` `greatestKBits(``int` `X, ``int` `K)``     ``{``       ``int` `set_bit_count = Integer.bitCount(X);``       ``if` `(set_bit_count <= K)``            ``return` `X;` `        ``// Remove rightmost set bits one``        ``// by one until we count becomes k``        ``int` `diff = set_bit_count - K;``        ``for` `(``int` `i = ``0``; i < diff; i++)``            ``X &= (X - ``1``);` `        ``// Return the required number``        ``return` `X;``    ``}` `// Driver code``public` `static` `void` `main (String[] args)``{``    ``int` `X = ``21``, K = ``2``;``    ``GFG g=``new` `GFG();``      ``System.out.print(g.greatestKBits(X, K));``}` `//This code is contributed by Shivi_Aggarwal``}`

## Python3

 `# Python 3 implementation of the approach` `# Function to return the greatest``# number <= X having at most K set bits.``def` `greatestKBits(X, K):``    ``set_bit_count ``=` `bin``(X).count(``'1'``)``    ``if` `(set_bit_count <``=` `K):``        ``return` `X` `    ``# Remove rightmost set bits one``    ``# by one until we count becomes k``    ``diff ``=` `set_bit_count ``-` `K``    ``for` `i ``in` `range``(``0``, diff, ``1``):``        ``X &``=` `(X ``-` `1``)` `    ``# Return the required number``    ``return` `X` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``X ``=` `21``    ``K ``=` `2``    ``print``(greatestKBits(X, K))``    ` `# This code is contributed by``# Shashank_Sharma`

## C#

 `// C# implementation of the above approach``using` `System;` `class` `GFG``{``    ``// Function to get no of set``    ``// bits in binary representation``    ``// of positive integer n``    ``static` `int` `countSetBits(``int` `n)``    ``{``        ``int` `count = 0;``        ``while` `(n > 0)``        ``{``            ``count += n & 1;``            ``n >>= 1;``        ``}``        ``return` `count;``    ``}``    ` `    ``// Function to return the greatest number <= X``    ``// having at most K set bits.``    ``static` `int` `greatestKBits(``int` `X, ``int` `K)``    ``{``        ``int` `set_bit_count = countSetBits(X);``        ``if` `(set_bit_count <= K)``        ``return` `X;` `        ``// Remove rightmost set bits one``        ``// by one until we count becomes k``        ``int` `diff = set_bit_count - K;``        ``for` `(``int` `i = 0; i < diff; i++)``            ``X &= (X - 1);` `        ``// Return the required number``        ``return` `X;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `X = 21, K = 2;``        ``Console.WriteLine(greatestKBits(X, K));``        ` `    ``}``}` `// This code is contributed by Ryuga`

## Javascript

 ``
Output:
`20`

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