London | 26-SDC-March | Jamal Laqdiem| Sprint 2 | Improve code with caches

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,10 @@
-def fibonacci(n):
+
+def fibonacci(n: int, fib_cache: dict[int, int] = {0: 0, 1: 1}) -> int:
     if n <= 1:
         return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+    #check if already calc this num.
+    if n in fib_cache:
+        return fib_cache[n]
+    # if not in cache, calculate it, store it, and return
+    fib_cache[n] = fibonacci(n - 1) + fibonacci(n - 2)
+    return fib_cache[n]

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,32 +1,46 @@
-from typing import List
-
+from typing import List, Tuple, Dict
 
+change_cache: Dict[Tuple[int, int], int] = {}
 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.
     """
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
+    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1],0)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def ways_to_make_change_helper(total: int, coins: List[int], coin_index: int) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
     """
-    if total == 0 or len(coins) == 0:
+
+    # If total is 0, we found 1 valid way
+    if total == 0:
+        return 1
+
+    # If total becomes negative or we ran out of coins, 0 ways
+    if total < 0 or coin_index >= len(coins):
         return 0
 
+    # shortcut if only one coin is left
+    if coin_index == len(coins) - 1:
+        return 1 if total % coins[coin_index] == 0 else 0
+
+    # Cache check
+    cache_key = (total, coin_index)
+    if cache_key in change_cache:
+        return change_cache[cache_key]
+
     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
+    current_coin = coins[coin_index]
+
+    # One level of loop to try taking 0, 1, 2... of the current coin
+    current_total = 0
+    while current_total <= total:
+        ways += ways_to_make_change_helper(total - current_total, coins, coin_index + 1)
+        current_total += current_coin
+
+    # Store the result in the cache before returning      
+    change_cache[cache_key] = ways
     return ways