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

using namespace std;

// This function should only work on positive integer n
int rootDigitSum(unsigned int n, int decimals=99){

    // Integer roots don't have decimals of course
    int check = sqrt(n);
    if(check * check == n){
        return 0;
    }

    int result = check;
    vector<int> digits;
    
    while(n > 0){
        int last = n % 10;
        n /= 10;

        digits.push_back(last);
    }

    // Initialize method
    InfInt remainder;
    if(digits.size() % 2 == 0){
        remainder = 10 * digits.back();
        digits.pop_back();
        remainder += digits.back();
        digits.pop_back();
    } else{
        remainder = digits.back();
        digits.pop_back();
    }

    InfInt minus = remainder.intSqrt();
    InfInt root = minus;
    remainder -= minus * minus;

    while(decimals != 0){
        // cout << remainder << " " << root << endl;
        remainder *= 100;

        bool decimalPart = true;
        if(!digits.empty()){
            decimalPart = false;

            remainder += digits.back() * 10;
            digits.pop_back();
            remainder += digits.back();
            digits.pop_back();
        }

        for(int guess = 0; guess < 10; ++guess){
            InfInt lower = (root * 20 + guess) * guess;
            InfInt upper = (root * 20 + guess + 1) * (guess + 1);
            
            if(lower <= remainder && remainder < upper){
                remainder -= lower;
                root = root * 10 + guess;

                if(decimalPart) result += guess;

                // cout << remainder << " " << root << " " << lower << " " << upper << endl;

                break;
            }
        }

        --decimals;
    }
    
    return result;
}

int main(){

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

    int result = 0;

    for(int i = 1; i <= 100; ++i){
        result += rootDigitSum(i);
    }

    cout << result << endl;

    // cout << rootDigitSum(2) << endl;

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