#include <iostream>
#include <iomanip>
#include <vector>

using namespace std;

const int HIGH_LIMIT = 44;
const int LOW_LIMIT = 0;

unsigned long Fib(int n);
unsigned long MemoFib(int n);
unsigned long ItFib(int n);

vector<unsigned long> CALLS(HIGH_LIMIT+1,0);

int main() {
    int i{20};

    cout << "Recursive regular fib " << endl;

    for(i = LOW_LIMIT; i <= HIGH_LIMIT; i++) {
        cout << setw(3) << i << setw(20) << Fib(i) << endl;
    }
    cout << endl << endl;

    cout << "Call Record " << endl;
    for(i =0; i <= HIGH_LIMIT; i ++) {
        cout << i << "  " << CALLS[i] << endl;
    }


    cout << endl << endl;

    cout << "MemoFib " << endl;
    for(i = LOW_LIMIT; i <= HIGH_LIMIT; i++) {
        cout << setw(3) << i << setw(20) << MemoFib(i) << endl;
    }

    cout << endl << endl;
    cout << "Iterative Fib" << endl;
    for(i = LOW_LIMIT; i <= HIGH_LIMIT; i++) {
        cout << setw(3) << i << setw(20) << ItFib(i) << endl;
    }

    return 0;
}

unsigned long Fib(int n){
    CALLS[n] ++;
    if (n <= 1) {
        return 1l;
    }
    return Fib(n-1) + Fib(n-2);
}

unsigned long MemoFib(int n){
    static vector<unsigned long> history{1,1};
    unsigned long tmp;

    if (static_cast<size_t>(n) >= history.size()) {
       tmp = MemoFib(n-1) + MemoFib(n-2);
       history.push_back(tmp);
    }
    return history[n];
}

unsigned long ItFib(int n) {
    unsigned long prev {1};
    unsigned long last {1};
    int i;
    unsigned long sum{1};

    for(i = 2; i <= n; i++) {
         sum = prev + last;
         last = prev;
         prev = sum;
    }

    return sum;
}