From 447712f83433859edf0731c64628d84bc2cf4f18 Mon Sep 17 00:00:00 2001
From: Ebrahim Beiaty <ebrahimbeiaty@gmail.com>
Date: Thu, 16 Apr 2026 22:00:48 +0100
Subject: [PATCH] improve_with_caches

---
 .../fibonacci/fibonacci.py                    | 10 ++++-
 .../making_change/making_change.py            | 37 +++++++++++--------
 2 files changed, 30 insertions(+), 17 deletions(-)

diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
index 60cc667..fb79e72 100644
--- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
+++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
@@ -1,4 +1,10 @@
-def fibonacci(n):
+def fibonacci(n, cache=None):
+    if cache is None:
+        cache = {}
+    if n in cache:
+        return cache[n]
     if n <= 1:
         return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+    else:
+        cache[n] = fibonacci(n - 1, cache) + fibonacci(n - 2, cache)
+    return cache[n]
diff --git a/Sprint-2/improve_with_caches/making_change/making_change.py b/Sprint-2/improve_with_caches/making_change/making_change.py
index 255612e..ef7ff87 100644
--- a/Sprint-2/improve_with_caches/making_change/making_change.py
+++ b/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:
@@ -7,26 +7,33 @@ def ways_to_make_change(total: int) -> int:
 
     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])
+    coins = [200, 100, 50, 20, 10, 5, 2, 1]
+    cache: Dict[Tuple[int, int], int] = {}
+    return ways_to_make_change_helper(total, coins, 0, cache)
 
 
-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, cache: Dict[Tuple[int, int], 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 == 0:
+        return 1
+    if total < 0 or coin_index == len(coins):
         return 0
 
+    key = (total, coin_index)
+    if key in cache:
+        return cache[key]
+
+    coin = coins[coin_index]
     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
+    count = 0
+    while count * coin <= total:
+        remaining = total - count * coin
+        ways += ways_to_make_change_helper(remaining, coins, coin_index + 1, cache)
+        count += 1
+
+    cache[key] = ways
     return ways