Maximum XOR-value of at-most k-elements from 1 to n

You are given two positive integer n and k. You have to calculate the maximum possible XOR value of at most k-elements from 1 to n.
Note:k > 1

Examples :

Input : n = 7, k = 3
Output : 7
Explanation : You can select 1, 2, 4 for maximum XOR-value

Input : n = 7, k = 2
Output : 7
Explanation : You can select 3 and 4 for maximum value.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

For any value of k we can select atleast two numbers from 1 to n and for the required result we have to take a closer look on the bit-representation of n. So lets understand it through an example. Suppose n = 6 and k = 2:
Bit representation of 6 = 110
Bit representation of 5 = 101
Bit representation of 4 = 100
Bit representation of 3 = 011
Bit representation of 2 = 010
Bit representation of 1 = 001

Now, you can see that after selecting as much numbers you want and selecting any of them you can not obtain XOR value greater than 111 i.e 7. So, for a given n and k >1 the maximum possible XOR value is 2log2(n)+1-1 (that is the value when all bits of n are turned to 1).

C++

 // Program to obtain maximum XOR value sub-array #include using namespace std;    // function to calculate maximum XOR value int maxXOR(int n, int k) {   int c = log2(n) + 1;      // Return (2^c - 1)   return ((1 << c) - 1); }    // driver program int main() {   int n = 12;   int k = 3;   cout << maxXOR(n, k);   return 0; }

Java

 // Program to obtain maximum // XOR value sub-array import java.lang.*;    class GFG { // function to calculate // maximum XOR value static int maxXOR(int n, int k)  { int c = (int) (Math.log(n) /                 Math.log(2)) + 1;    // Return (2^c - 1) return ((1 << c) - 1); }    // Driver Code public static void main(String[] args)  { int n = 12; int k = 3; System.out.println(maxXOR(n, k)); } }    // This code is contributed by Smitha

Python3

 # Python3 program to obtain maximum # XOR value sub-array import math    # Function to calculate maximum XOR value def maxXOR(n, k):     c = int(math.log(n, 2)) + 1        # Return (2^c - 1)     return ((1 << c) - 1)    # Driver Code n = 12; k = 3 print (maxXOR(n, k))    # This code is contributed by shreyanshi_arun.

C#

 // Program to obtain maximum // XOR value sub-array using System;    class GFG { // function to calculate // maximum XOR value static int maxXOR(int n, int k)  { int c = (int) (Math.Log(n) /                 Math.Log(2)) + 1;    // Return (2^c - 1) return ((1 << c) - 1); }    // Driver Code public static void Main(String[] args) { int n = 12; int k = 3; Console.Write(maxXOR(n, k)) ; } }    // This code is contributed by Smitha

PHP



Output:

15

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