London | March-2025 | Elhadj Abdoul Diallo | improve_with_caches

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,12 @@
-def fibonacci(n):
+def fibonacci(n, memo=None):
     if n <= 1:
         return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+
+    if memo is None:
+        memo = {}
+
+    if n in memo: return memo[n]
+
+    memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo)
+    return memo[n]
+

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,4 +1,4 @@
-from typing import List
+from typing import List, Tuple, Dict
 
 
 def ways_to_make_change(total: int) -> int:
@@ -10,23 +10,24 @@ def ways_to_make_change(total: int) -> int:
     return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def ways_to_make_change_helper(total: int, coins: List[int], memo: Dict[Tuple[int, int], int] = None) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
+    Uses memoization to optimize repeated subproblems.
     """
-    if total == 0 or len(coins) == 0:
+    if memo is None:
+        memo = {}
+    key = (total, len(coins))
+    if key in memo:
+        return memo[key]
+    if total == 0:
+        return 1
+    if total < 0 or len(coins) == 0:
         return 0
-
     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
+    coin = coins[0]
+    for count_of_coin in range(0, total // coin + 1):
+        remaining = total - coin * count_of_coin
+        ways += ways_to_make_change_helper(remaining, coins[1:], memo)
+    memo[key] = ways
     return ways