DP Fibonacci

#include <iostream>
#include <vector>
#include <chrono>
using namespace std;
using namespace std::chrono;
typedef unsigned long long ull;

//Simplest timer i can implement
class Timer {
public:
    Timer() : start{ clock_t::now() } {}
    void restart() {
        start = clock_t::now();
    }
    double get_elapsed() const {
        auto micro_elapsed = duration_cast<microseconds>(clock_t::now() - start).count();
        return micro_elapsed / 1e3;
    }
private:
    using clock_t = high_resolution_clock;
    time_point<clock_t> start;
};


ull calls_fib = 0, calls_fib_dp = 0;
vector<ull> fib_dp_res;

ull fib(ull pos) {
    //we are counting the number of function calls
    calls_fib += 1;

    // Fibonacci sequence starts with 0, then 1:
    // Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21...
    if (pos == 0) return 0;
    if (pos == 1) return 1;
    return fib(pos - 1) + fib(pos - 2);
}

ull fib_dp(ull pos) {
    //we are counting the number of function calls
    calls_fib_dp += 1;

    if (pos < fib_dp_res.size())
        return fib_dp_res[pos];
    // Fibonacci sequence starts with 0, then 1:
    // Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21...
    if (pos == 0) {
        fib_dp_res.push_back(0);
        return fib_dp_res[pos];
    }
    fib_dp(pos - 1);
    if (pos == 1 and fib_dp_res.size() == 1) {
        fib_dp_res.push_back(1);
        return fib_dp_res[pos];
    }
    fib_dp_res.push_back(fib_dp_res[pos - 1] + fib_dp_res[pos - 2]);
    return fib_dp_res[pos];
}

int main() {
    ull position = 40;
    ull fib_res, fib_dp_res;

    Timer fib_res_timer;
    fib_res = fib(position);
    auto fib_res_time = fib_res_timer.get_elapsed();

    Timer fib_dp_res_timer;
    fib_dp_res = fib_dp(position);
    auto fib_dp_res_time = fib_dp_res_timer.get_elapsed();

    cout << "fib(" << position << ") was called. Result is " << fib_res
        << ". fib() was called " << calls_fib << " times." << " Elapsed time is: " << fib_res_time << " ms" << endl;

    cout << "fib_dp(" << position << ") was called. Result is " << fib_dp_res
        << ". fib_dp() was called " << calls_fib_dp << " times." << " Elapsed time is: " << fib_dp_res_time << " ms" << endl;
}