// Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.
// Probably good to know that e can be written as [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, ..., 1, 2k, 1, ...]

#include <bits/stdc++.h>
#include "../bigint.h"

using namespace std;

InfInt gcd(InfInt a, InfInt b){
    if(b == 0){
        return a;
    }
    return gcd(b, a % b);
}

pair<InfInt, InfInt> fracAdd(const pair<InfInt, InfInt>& f1, const pair<InfInt, InfInt>& f2){
    pair<InfInt, InfInt> result = {f1.first*f2.second + f2.first*f1.second, f1.second * f2.second};
    InfInt g = gcd(result.first, result.second);

    result.first /= g;
    result.second /= g;

    return result;
}

pair<InfInt, InfInt> fracInv(const pair<InfInt, InfInt>& f){
    return pair<InfInt, InfInt>(f.second, f.first);
}

pair<InfInt, InfInt> cfApprox(const vector<int>& seq){
    pair<InfInt, InfInt> result = {seq[0], 1};
    pair<InfInt, InfInt> carry = {0, 1};
    if(seq.size() > 1){
        carry = {1, seq[1]};
        for(size_t i = seq.size() - 2; i > 0; --i){
            pair<InfInt, InfInt> newp = {seq[i], 1};
            carry = fracInv(fracAdd(carry, newp));
        }
    }

    result = fracAdd(result, carry);

    return result;
}

int main(){

    cout << "HeInfInto this is Patrick" << endl;
    auto start = chrono::high_resolution_clock::now();

    // Generate the e sequence
    vector<int> seq;
    seq.push_back(2);
    for(int i = 0; i < 99; ++i){
        if(i % 3 == 0 || i % 3 == 2){
            seq.push_back(1);
        } else{
            seq.push_back(((i / 3) + 1) * 2);
        }
    }

    auto f = cfApprox(seq);
    InfInt frac = f.first;
    InfInt result = 0;
    
    while(frac > 0){
        result += frac % 10;
        frac /= 10;
    }

    cout << "Fraction of " << f.first << " / " << f.second << " resulting in sum of: ";
    cout << result << endl;

    auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
    cout << (float)duration.count()/1000 << endl;
    return 0;
}