NW | 26-SDC-Mar | Zabihollah Namazi | Sprint 2 | improve with caches

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,13 @@
-def fibonacci(n):
-    if n <= 1:
-        return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+fib_cache = {}
+def fibonacci(n: int) -> int:
+    if n == 0:
+        return 0
+    if n == 1:
+        return 1
+
+    if n in fib_cache:
+        return fib_cache[n]
+
+    fib_cache[n] = fibonacci(n - 1) + fibonacci(n - 2)
+
+    return fib_cache[n]

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -2,31 +2,36 @@
 
 
 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.
+
+    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1], coin_index = 0, cache = None)
 
-    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])
 
+def ways_to_make_change_helper(total: int, coins: List[int], coin_index: int = 0, cache: dict = None) -> int:
+    if cache == None:
+        cache = {}
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
-    """
-    Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
-    """
-    if total == 0 or len(coins) == 0:
+    current_key = (total, coin_index)
+    if current_key in cache:
+        return cache[current_key]
+
+    if total == 0:
+        return 1
+
+    if coin_index == len(coins) - 1:
+        return 1 if total % coins[coin_index] == 0 else 0
+
+    if total < 0 or coin_index >= len(coins):
         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
-    return ways
+
+    remaining_value = total - coins[coin_index]
+
+    taken_the_coin = ways_to_make_change_helper(remaining_value, coins, coin_index, cache)
+
+    left_the_coin = ways_to_make_change_helper(total, coins, coin_index + 1, cache)
+
+    ways = taken_the_coin + left_the_coin
+
+    cache[current_key] = ways
+    return ways