Solve problem 95

python/e095.py

@@ -0,0 +1,48 @@
+from lib_misc import sum_proper_divisors
+
+
+def euler_095():
+    NO_CHAIN = set()
+    PROPER_DIVISOR_CACHE = {}
+
+    def sum_proper_divisors_cached(n):
+        if n in PROPER_DIVISOR_CACHE:
+            return PROPER_DIVISOR_CACHE[n]
+        r = sum_proper_divisors(n)
+        PROPER_DIVISOR_CACHE[n] = r
+        return r
+
+    def chain(n):
+        chain = []
+        next_number = n
+
+        while next_number not in chain:
+            if next_number >= 10**6 or next_number == 0 or next_number in NO_CHAIN:
+                for c in chain:
+                    NO_CHAIN.add(c)
+                return None
+            chain.append(next_number)
+            next_number = sum_proper_divisors_cached(next_number)
+        chain.append(next_number)
+        return chain
+
+    chains = [[]]
+    for i in range(1, 10**6 + 1):
+        c = chain(i)
+        if c and c[0] == c[-1]:
+            if len(c) == len(chains[0]):
+                # There might be multiple different chains with the same length
+                # so keep all of them to get the smalles element.
+                chains.append(c)
+            elif len(c) > len(chains[0]):
+                chains = [c]
+
+    elems = [e for c in chains for e in c]
+    return min(elems)
+
+
+if __name__ == "__main__":
+    solution = euler_095()
+    print("e095.py: " + str(solution))
+    assert(solution == 14316)
+