#!/usr/bin/env python
"""
Created on 04 Dic 2021

@author: David Doblas Jiménez
@email: daviddoji@pm.me

Solution for problem 060 of Project Euler
https://projecteuler.net/problem=60
"""

from utils import is_prime, list_primes, timeit


def solve_backtrack(max_chain_length, chain):
    primes_list = list_primes(10_000)

    for p in primes_list[1:]:
        if p not in chain and is_concatenable(chain, p):
            chain.append(p)
            if len(chain) == max_chain_length:
                return chain
            solve_backtrack(max_chain_length, chain)
            chain.pop()
    return chain


def is_concatenable(chain, candidate):
    for n in chain:
        if not is_prime(int(str(n) + str(candidate))):
            return False
        if not is_prime(int(str(candidate) + str(n))):
            return False
    return True


@timeit("Problem 060")
def compute():
    """
    The primes 3, 7, 109, and 673, are quite remarkable. By taking any two
    primes and concatenating them in any order the result will always be prime.
    For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of
    these four primes, 792, represents the lowest sum for a set of four primes
    with this property.

    Find the lowest sum for a set of five primes for which any two primes
    concatenate to produce another prime.
    """

    ans = solve_backtrack(5, [])

    return sum(ans)


if __name__ == "__main__":
    print(f"Result for Problem 060: {compute()}")