Solve problem 77.

python/e077.py

@@ -1,8 +1,44 @@
+from lib_prime import primes
+from functools import lru_cache 
+
 
 def euler_077():
-    return 0
+
+    def get_prime_sequence_dict(n_max):
+        """ Returns a dict that maps a
+        current prime to the following prime. """
+        ps = primes(n_max)
+        ps_current = ps[0]
+        ps_dict = {}
+
+        for p in ps[1:]:
+            ps_dict[ps_current] = p
+            ps_current = p
+
+        return ps_dict
+
+    prime_dict = get_prime_sequence_dict(10000)
+
+    @lru_cache(maxsize=1000000)
+    def possible_sums(n, n_orig, d):
+        if d == n_orig:
+            return 0
+        if n == 0:
+            return 1
+        if n < 0:
+            return 0
+        if d > n:
+            return 0
+
+        s_1 = possible_sums(n - d, n_orig, d)
+        s_2 = possible_sums(n, n_orig, prime_dict[d])
+        return s_1 + s_2
+
+    for n in range(1000):
+        if possible_sums(n, n, 2) > 5000:
+            return n
 
 
 if __name__ == "__main__":
     print("e077.py: " + str(euler_077()))
-    assert(euler_077() == 0)
+    assert(euler_077() == 71)