Staircase Game

#include <bits/stdc++.h>
using namespace std;
#define ve vector

ve<int> Max = { 40, 40, 10 };
int A = 0;
int B = 1;
int C = 2;

map<ve<int>, bool> Win;

bool f(ve<int>& State) {

    bool win;
    ve<int> StateNew;

    if (Win.find(State) == Win.end()) {
        win = false;

        for (int i = 0; i < State.size(); i++) {
            for (int k = 1; k <= State[i]; k++) {

                StateNew = State;
                StateNew[i] -= k;
                if (!f(StateNew)) win = true;

                for (int j = 0; j < i; j++) {
                    StateNew = State;
                    StateNew[i] -= k;
                    StateNew[j] += k;
                    if (!f(StateNew)) win = true;
                }
            }
        }

        Win[State] = win;
    }

    return Win[State];
}

int main() {

    ve<int> State;

    State = Max;
    for (int k = 0; k <= Max[C]; k++) {
        State[C] = k;

        cout << k << endl;
        cout << endl;

        for (int i = 0; i <= Max[A]; i++) {
            State[A] = i;

            for (int j = 0; j <= Max[B]; j++) {
                State[B] = j;

                if (f(State)) cout << ". ";
                else cout << "X ";
            }
            cout << endl;
        }
        cout << endl;
    }

    return 0;
}