/*

Totient permutation

Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.
The number 1 is considered to be relatively prime to every positive number, so φ(1)=1.

Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.

Find the value of n, 1 < n < 107, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.

*/

#include <bits/stdc++.h>

using namespace std;

const int MAX = pow(10, 7);

vector<int> sieve(int n){
    vector<bool> numbers(n+1, true);
    vector<int> result;

    int i = 2;
    while(i <= n){
        if(numbers[i]){
            result.push_back(i);

            int j = 2 * i;
            while(j <= n){
                numbers[j] = false;
                j += i;
            }
        }
        ++i;
    }

    return result;
}

vector<int> prime_terms(int n){
    vector<int> result;

    if(n % 2 == 0){
        result.push_back(2);

        while(n % 2 == 0){
            n /= 2;
        }
    }

    for(int i = 3; i <= sqrt(n); i += 2){
        if(n % i == 0){
            result.push_back(i);

            while(n % i == 0){
                n /= i;
            }
        }
    }

    if(n > 2){
        result.push_back(n);
    }

    return result;
}

int main(){

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

    int n_min = 0;
    float min_ratio = 2;

    for(int n = 2; n < MAX; ++n){
        auto terms = prime_terms(n);

        float phi = n;
        for(float term : terms){
            phi *= 1.0 - 1.0 / term;
        }

        int p = phi;
        string s_phi = to_string(p), s_n = to_string(n);
        sort(s_phi.begin(), s_phi.end());
        sort(s_n.begin(), s_n.end());

        if(s_phi == s_n){
            if((float)n / phi < min_ratio){
                min_ratio = (float)n / phi;
                n_min = n;
            }
        }
    }

    cout << n_min << endl;

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