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

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 = 2Output:10Input:X = 29, K = 2Output: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 <iostream>` `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

`<script>` `// Javascript implementation of the above approach` `// Function to get no of set` `// bits in binary representation` `// of positive integer n` `function` `countSetBits( n)` `{` ` ` `let 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.` `function` `greatestKBits( X, K)` `{` ` ` `let set_bit_count = countSetBits(X);` ` ` `if` `(set_bit_count <= K)` ` ` `return` `X;` ` ` `// Remove rightmost set bits one` ` ` `// by one until we count becomes k` ` ` `let diff = set_bit_count - K;` ` ` `for` `(let i = 0; i < diff; i++)` ` ` `X &= (X - 1);` ` ` `// Return the required number` ` ` `return` `X;` `}` `// Driver Code` `let X = 21, K = 2;` `document.write(greatestKBits(X, K));` `</script>` |

**Output:**

20

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