London | 26-Jul-SDC | Roman Sanaye | Sprint 2 | Improve Code with Caches

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,22 @@
 def fibonacci(n):
-    if n <= 1:
-        return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+    # Initialize the cache as a function attribute if it doesn't exist yet
+    if not hasattr(fibonacci, "cache"):
+        fibonacci.cache = {}
+
+    def helper(number):
+        # Check the function attribute cache at the start
+        if number in fibonacci.cache:
+            return fibonacci.cache[number]
+
+        # Base case
+        if number <= 1:
+            return number
+
+        # Compute the result (making sure number decreases!)
+        result = helper(number - 1) + helper(number - 2)
+
+        # Store the result in the function attribute cache right before returning
+        fibonacci.cache[number] = result
+        return result
+
+    return helper(n)

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,32 +1,53 @@
 from typing import List
 
+# Defined once globally to avoid recreation overhead
+COINS = [200, 100, 50, 20, 10, 5, 2, 1]
 
+
+# ===============> change function <============
 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])
+    # Initialize a cache dictionary
+    cache = {}
+    # Passing 0 (the starting index) instead of the full list
+    return ways_to_make_change_helper(total, 0, cache)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+# =================> change helper function <==============
+def ways_to_make_change_helper(total: int, start_index: int, cache: dict) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
     """
-    if total == 0 or len(coins) == 0:
+    # Create unique key for this subproblem
+    cache_key = (total, start_index)
+
+    # Return cached result if already calculated
+    if cache_key in cache:
+        return cache[cache_key]
+
+    if total == 0 or start_index >= len(COINS):
         return 0
 
     ways = 0
-    for coin_index in range(len(coins)):
-        coin = coins[coin_index]
+    # Iterate through the global COINS list using the integer index
+    for i in range(start_index, len(COINS)):
+        coin = COINS[i]
         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:])
+                # Just pass an integer (i + 1)
+                intermediate = ways_to_make_change_helper(
+                    total - total_from_coins, start_index=i + 1, cache=cache
+                )
                 ways += intermediate
             count_of_coin += 1
+
+    cache[cache_key] = ways
     return ways