From 6157818ad0d0e958ab0058225d5da614b5eb5213 Mon Sep 17 00:00:00 2001
From: daviddoji <daviddoji@pm.me>
Date: Sat, 4 Dec 2021 17:39:28 +0100
Subject: [PATCH] Solution to problem 60 in Python

---
 src/Python/Problem060.py | 32 +++++++++++++++++++++-----------
 1 file changed, 21 insertions(+), 11 deletions(-)

diff --git a/src/Python/Problem060.py b/src/Python/Problem060.py
index fa78520..2dcaba1 100644
--- a/src/Python/Problem060.py
+++ b/src/Python/Problem060.py
@@ -1,6 +1,6 @@
 #!/usr/bin/env python3
 """
-Created on 13 Oct 2021
+Created on 04 Dic 2021
 
 @author: David Doblas Jiménez
 @email: daviddoji@pm.me
@@ -9,8 +9,7 @@ Solution for problem 60 of Project Euler
 https://projecteuler.net/problem=60
 """
 
-from itertools import permutations
-from utils import timeit, list_primes
+from utils import timeit, list_primes, is_prime
 
 
 @timeit("Problem 60")
@@ -28,15 +27,26 @@ def compute():
 
     primes_list = list_primes(10_000)
 
-    for nums in permutations(primes_list, 5):
-        for n1, n2 in permutations(nums, 2):
-            if int(str(n1) + str(n2)) not in primes_list:
-                break
-    primes = sum(nums)
-    print(nums)
-    # break
+    def solve_backtrack(max_chain_length, chain):
+        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
 
-    return primes
+    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
+
+    result = solve_backtrack(5, [])
+    return sum(result)
 
 
 if __name__ == "__main__":