SOTF Combinatorics MMO-B W9/H4

#include <iostream>
#include <set>
#include <bitset>
using namespace std;

/*

This is a bruteforce solution to the following COMBINATORICS problem,
intended to be solved purely mathematically.

"Plus and minus signs are arranged in a 4x4 table as shown below.

    + | + | - | +
    + | + | + | +
    + | + | + | +
    + | + | + | +

It is permissible to reverse all the signs in one row, one column,
or along any line parallel to a diagonal of the table (in particular,
in any corner unit square). Does there exist a sequence of these
operations leading to a table with only plus signs?"

*/

set<int> all;

void f(int g) {
    if (all.find(g) != all.end())
        return;
    all.insert(g);
    //perform all possible operations
    //f(g XOR mask), where each active bit in the mask
    //signifies whether to flip the bit
    f(g^0b1111000000000000);
    f(g^0b0000111100000000);
    f(g^0b0000000011110000);
    f(g^0b0000000000001111);
    f(g^0b1000100010001000);
    f(g^0b0100010001000100);
    f(g^0b0010001000100010);
    f(g^0b0001000100010001);
    f(g^0b1000010000100001);
    f(g^0b0001001001001000);
    f(g^0b0100001000010000);
    f(g^0b0010000100000000);
    f(g^0b0001000000000000);
    f(g^0b0010010010000000);
    f(g^0b0100100000000000);
    f(g^0b1000000000000000);
    f(g^0b0000000100100100);
    f(g^0b0000000000010010);
    f(g^0b0000000000000001);
    f(g^0b0000100001000010);
    f(g^0b0000000010000100);
    f(g^0b0000000000001000);
}

int main() {
    int initial = 0b1101111111111111;
    f(initial);

    cout << "Number of possible tables: " << all.size() << '\n';
    bitset<16> best = *prev(all.end());
    cout << "Closest table to all pluses: " << best << '\n';
}