London | 25-SDC-NOV | Jesus del Moral | Sprint 2 | Improve with Caches

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,11 @@
-def fibonacci(n):
-    if n <= 1:
+
+def fibonacci(n, memo={}): 
+    if n in memo: 
+        return memo[n] 
+    if n <= 1: 
         return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+    memo[n] = fibonacci(n-1, memo) + fibonacci(n-2, memo)
+    return memo[n]
+
+# Time complexity: O(n) 
+# # Space complexity: O(n) due to the memo dictionary

Sprint-2/improve_with_caches/fibonacci/fibonacci_test.py

@@ -1,5 +1,4 @@
 import unittest
-
 from fibonacci import fibonacci
 
 class FibonacciTest(unittest.TestCase):

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,19 +1,26 @@
 from typing import List
 
-
 def ways_to_make_change(total: int) -> int:
     """
-    Given access to coins with the values 1, 2, 5, 10, 20, 50, 100, 200, returns a count of all of the ways to make the passed total value.
-
-    For instance, there are two ways to make a value of 3: with 3x 1 coins, or with 1x 1 coin and 1x 2 coin.
+    Given access to coins with the values 1, 2, 5, 10, 20, 50, 100, 200,
+    returns a count of all of the ways to make the passed total value.
     """
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
+    cache = {}
+    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], cache)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def ways_to_make_change_helper(total: int, coins: List[int], cache: dict) -> int:
     """
-    Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
+    Helper function with memoization.
+    Cache key is (total, index of first coin in list) — but since we pass
+    the coins list by slicing, we can cache using tuple(total, tuple(coins)).
     """
+
+    key = (total, tuple(coins))
+
+    if key in cache:
+        return cache[key]
+
     if total == 0 or len(coins) == 0:
         return 0
 
@@ -26,7 +33,13 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
             if total_from_coins == total:
                 ways += 1
             else:
-                intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
+                intermediate = ways_to_make_change_helper(
+                    total - total_from_coins,
+                    coins=coins[coin_index + 1:],
+                    cache=cache
+                )
                 ways += intermediate
             count_of_coin += 1
-    return ways
+
+    cache[key] = ways
+    return ways

Sprint-2/improve_with_caches/making_change/making_change_test.py

@@ -1,5 +1,4 @@
 import unittest
-
 from making_change import ways_to_make_change
 
 class MakingChangeTest(unittest.TestCase):