Maximum xor among all subsets of an array

Question

I have to find maximum value of exclusive xor among the elements of subsets of an array. I have to check every subset of the array and the subset which will yield maximum xo

Answer 1

Gaussian Elimination is what you need.

For example : 3 numbers {9, 8, 5}

First sort them in decreasing order and convert them into binary :

9 : 1001
8 : 1000
5 : 0101

Observe the 1st number. Highest bit is 4.
Now check 4th bit of the 1st number (9). As it is 1, xor the number with the rest of the numbers where 4th bit is 1.

9 : 1001
1 : 0001 > changed
5 : 0101

Now check 3rd bit of 2nd number (1). As it is 0, check rest of the below numbers where 3rd bit is 1.
Number 5 has 1 in 3rd bit. Swap them :

9 : 1001
5 : 0101 > swapped
1 : 0001 >

Now xor 5 with the rest of the numbers where 3rd bit is 1. Here none exists. So there will be no change.

Now check 2nd bit of 3rd number (1). As it is 0 and there is no other number below where 2nd bit is 1, so there will be no change.

Now check 1st bit of 3rd number (1). As it is 1, change the rest of the numbers where 1st bit is 1.

8 : 1000 > changed
4 : 0100 > changed
1 : 0001

No more bit left to consider :)

Now xor the whole remaining array {8 ^ 4 ^ 1} = 13

So 13 is the solution :)

That's pretty much how you solve the problem using Gaussian Elimination :)

Here is my C++ implementation :

#include 
using namespace std;

typedef long long int           ll;
typedef unsigned long long int  ull;

ull check_bit(ull N,int POS){return (N & (1ULL<v;
ull gaussian_elimination()
{
    int n=v.size();
    int ind=0;  // Array index
    for(int bit=log2(v[0]);bit>=0;bit--)
    {
        int x=ind;
        while(x>x;
        v.push_back(x);
    }
    sort(v.rbegin(),v.rend());
    cout<