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

@@ -1,32 +1,52 @@
-from typing import List
+from typing import Dict, Tuple
+
+COINS = [200, 100, 50, 20, 10, 5, 2, 1]
 
 
 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.
+    Returns the number of ways to make `total` using UK coin values.
     """
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
+    cache: Dict[Tuple[int, int], int] = {}
+    return _helper(total, 0, cache)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def _helper(total: int, coin_index: int, cache: Dict[Tuple[int, int], int]) -> int:
     """
-    Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
+    Recursive helper using memoization.
+
+    Parameters:
+    - total: remaining amount to form
+    - coin_index: index into COINS representing which coins we are allowed to use
+    - cache: memoization dictionary
     """
-    if total == 0 or len(coins) == 0:
+
+    # Base case: exact match
+    if total == 0:
+        return 1
+
+    # Base case: no coins left
+    if coin_index == len(COINS):
         return 0
 
+    key = (total, coin_index)
+
+    # If we’ve already solved: return the cached result, We just return the stored answer instead of recomputing it
+    if key in cache:
+        return cache[key]
+
+    # CORE LOGIC: 
     ways = 0
-    for coin_index in range(len(coins)):
-        coin = coins[coin_index]
-        count_of_coin = 1
-        while coin * count_of_coin <= total:
-            total_from_coins = coin * count_of_coin
-            if total_from_coins == total:
-                ways += 1
-            else:
-                intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
-                ways += intermediate
-            count_of_coin += 1
-    return ways
+    coin = COINS[coin_index]
+
+    # Try using this coin 0, 1, 2, ... times
+    # The maximum number of this coin we could use without exceeding total.
+    max_count = total // coin
+
+    # For each possible count of this coin, we compute the remaining amount and recursively call _helper for the next coin.
+    for count in range(max_count + 1):
+        remaining = total - (coin * count)
+        ways += _helper(remaining, coin_index + 1, cache)
+
+    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):