// Lock pairs into the candidate graph in order, without creating cycles
void lock_pairs(void)
{
    int W, L;

    for (int i = 0; i < pair_count; i++)
    {
        W = pairs[i].winner;
        L = pairs[i].loser;
        //check the cycle
        if (check_cycle(L, W, i)) //not a cycle
        {
            locked[W][L] = true;
        }

    }
    return;
}

bool check_cycle(int l, int w, int counter)//return the end of the cycle
{
    //if there is a cycle than the counter will exceed the number of possible connections wich is pair count
    if (l == w)
    {
        return false;
    }
    if (counter == 0)
    {
        return true;
    }
    //check if there is a path from l to w so check if there is a edge going from locked[i][l]
    for (int i = 0; i < pair_count; i++)
    {
        if (locked[l][i])
        {
            if (!(check_cycle(i, w, counter--)))
            {
                return false;
            }
        }
    }
    return true;
}
// Print the winner of the election
void print_winner(void)
{
    //find the source of the graph aka the candidate where no one is pointing to
    int winner;
    for (int i = 0; i < candidate_count; i++)
    {
        for (int j = 0; j < candidate_count; j++)
        {
            if (locked[j][i])
            {
                break;
            }
            winner = i;
        }
    }
    printf("%s\n", candidates[winner]);
    return;
}