Solve 74 in Python.

python/e074.py

@@ -1,8 +1,58 @@
+from functools import lru_cache
+
+
+@lru_cache(maxsize=10)
+def fac(n):
+    r = 1
+    if n <= 1:
+        return 1
+    for i in range(2, n + 1):
+        r *= i
+    return r
+
+
+@lru_cache(maxsize=1000000)
+def get_factorial_sum(n):
+    s = 0
+    for d in get_digits(n):
+        s += fac(d)
+    return s
+
+
+current_numbers_set = set()
+
+
+@lru_cache(maxsize=10000000)
+def get_chain_length(n):
+    """ Could be further optimized by caching all permutations
+    of the given number. All permutations of a number
+    have the same factorial sum because they consist of the
+    same digits. """
+    global current_numbers_set
+    next_value = get_factorial_sum(n)
+    if next_value in current_numbers_set:
+        return 1
+    else:
+        current_numbers_set.add(next_value)
+        return 1 + get_chain_length(next_value)
+
+
+def get_digits(n):
+    return map(int, str(n))
+
 
 def euler_074():
-    return 0
+    c = 0
+    for n in range(10**6):
+        global current_numbers_set
+        current_numbers_set = set([n])
+        chain_len = get_chain_length(n)
+        if chain_len == 60:
+            # print("n: {} length: {}".format(n, chain_len))
+            c += 1
+    return c
 
 
 if __name__ == "__main__":
     print("e074.py: " + str(euler_074()))
-    assert(euler_074() == 0)
+    assert(euler_074() == 402)