#include <iostream>
#include <stack>

using namespace std;

int recAck(int, int);
int stackAck(int, int);

int main () {
    int i,j;

    for(i=0;i<4;i++) {
       for(j=0;j<5;j++) {
        cout  << i << ", " << j << " = "  << endl;
        cout  << "\tstackAck  " << stackAck(i,j) << endl;
        cout << "\treaAck " << recAck(i,j) << endl;
       }
    }

    return(0);
}

int recAck(int m, int n) {
    if (m == 0) {
        return(n+1);
    }
    if (n == 0) {
       return(recAck(m-1,1));
    }
    return(recAck(m-1, recAck(m,n-1)));
}

int stackAck(int m, int n) {
    stack <int > S;
    int rv;
    bool done = false;

    do {
       if  (m == 0) {
          rv = n+1;
          if (!S.empty()) {
            n = rv;
            m = S.top(); 
            S.pop();
          } else {
             done = true;
          }
       } else if (n == 0) {
          //ack(m,0) -> Ack(m-1,1)->Ack(m-2,Ack(m-1,0));
          if (m > 1) {
              S.push(m-2);
              m = m - 1;
              n = 0;
          } else {
             // ack(1,0) -> ack(0,1) = 2
             rv = 2;
             if(!S.empty()) {
                n = rv;
                m = S.top();
                S.pop();
             } else {
                done = true;
             }
          }
       } else {
          // ack(m,n) -> Ack(m-1, Ack(m,n-1));
          S.push(m-1);
          n = n - 1;
       }
    } while  (!done);

    return(rv);
}