Maximum XOR using K numbers from 1 to n

Given an positive integer n and k. Find maximum xor of 1 to n using at most k numbers. Xor sum of 1 to n is defined as 1 ^ 2 ^ 3 ^ … ^ n.

Examples :

Input :  n = 4, k = 3
Output : 7
Explanation
Maximum possible xor sum is 1 ^ 2 ^ 4 = 7.

Input : n = 11, k = 1
Output : 11
Explanation
Maximum Possible xor sum is 11.



If we have k = 1 then the maximum possible xor sum is 1. Now for k > 1 we can always have an number with its all bits set to 1. So result will be maximum number greater than n with its all bits set to 1.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to find max xor sum
// of 1 to n using atmost k numbers
#include <bits/stdc++.h>
using namespace std;
  
// To return max xor sum of 1 to n
// using at most k numbers
int maxXorSum(int n, int k)
{
    // If k is 1 then maximum
    // possible sum is n
    if (k == 1)
        return n;
  
    // Finding number greater than
    // or equal to n with most significant 
    // bit same as n. For example, if n is
    // 4, result is 7. If n is 5 or 6, result 
    // is 7
    int res = 1;
    while (res <= n)
        res <<= 1;
  
    // Return res - 1 which denotes
    // a number with all bits set to 1
    return res - 1;
}
  
// Driver program 
int main()
{
    int n = 4, k = 3;
    cout << maxXorSum(n, k);
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find max xor sum
// of 1 to n using atmost k numbers
public class Main {
  
    // To return max xor sum of 1 to n
    // using at most k numbers
    static int maxXorSum(int n, int k)
    {
        // If k is 1 then maximum
        // possible sum is n
        if (k == 1)
            return n;
  
        // Finding number greater than
        // or equal to n with most significant 
        // bit same as n. For example, if n is
        // 4, result is 7. If n is 5 or 6, result 
        // is 7
        int res = 1;
        while (res <= n)
            res <<= 1;
  
        // Return res - 1 which denotes
        // a number with all bits set to 1
        return res - 1;
    }
  
    // Driver program to test maxXorSum()
    public static void main(String[] args)
    {
        int n = 4, k = 3;
        System.out.print(maxXorSum(n, k));
    }
}

chevron_right


Python

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 code to find max xor sum
# of 1 to n using atmost k numbers
  
# To return max xor sum of 1 to n
# using at most k numbers
def maxXorSum( n , k ):
    # If k is 1 then maximum
    # possible sum is n
    if k == 1:
        return n
      
    # Finding number greater than
    # or equal to n with most significant
    # bit same as n. For example, if n is
    # 4, result is 7. If n is 5 or 6, result
    # is 7
    res = 1
    while res <= n:
        res <<= 1
      
    # Return res - 1 which denotes
    # a number with all bits set to 1
    return res - 1
  
# Driver code
n = 4
k = 3
print( maxXorSum(n, k) )
  
# This code is contributed by Abhishek Sharma44.

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find max xor sum
// of 1 to n using atmost k numbers
using System;
  
public class main {
  
    // To return max xor sum of 1 to n
    // using at most k numbers
    static int maxXorSum(int n, int k)
    {
        // If k is 1 then maximum
        // possible sum is n
        if (k == 1)
            return n;
  
        // Finding number greater than
        // or equal to n with most significant 
        // bit same as n. For example, if n is
        // 4, result is 7. If n is 5 or 6, result 
        // is 7
        int res = 1;
        while (res <= n)
            res <<= 1;
  
        // Return res - 1 which denotes
        // a number with all bits set to 1
        return res - 1;
    }
  
    // Driver program
    public static void Main()
    {
        int n = 4, k = 3;
        Console.WriteLine(maxXorSum(n, k));
    }
}
  
// This code is contributed by vt_m.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to find max xor sum
// of 1 to n using atmost k numbers
  
// To return max xor sum of 1 to n
// using at most k numbers
function maxXorSum($n, $k)
{
    // If k is 1 then maximum
    // possible sum is n
    if ($k == 1)
        return $n;
  
    // Finding number greater than
    // or equal to n with most 
    // significant bit same as n. 
    // For example, if n is 4, result 
    // is 7. If n is 5 or 6, result is 7
    $res = 1;
    while ($res <= $n)
        $res <<= 1;
  
    // Return res - 1 which denotes
    // a number with all bits set to 1
    return $res - 1;
}
  
// Driver code 
$n = 4;
$k = 3;
echo maxXorSum($n, $k);
  
// This code is contributed by Mithun Kumar
?>

chevron_right



Output :

7


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Mithun Kumar



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.