From 4c35bb8cc9ade7445f717cf64c2d1ca947839794 Mon Sep 17 00:00:00 2001
From: Mohammed Abdoon <mohammedabdoon1996@gmail.com>
Date: Thu, 16 Jul 2026 11:11:14 +0100
Subject: [PATCH] refactored fibonacci funcs

---
 .../fibonacci/fibonacci.py                    |  8 +++-
 .../making_change/making_change.py            | 39 ++++++++-----------
 2 files changed, 23 insertions(+), 24 deletions(-)

diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
index 60cc667..1a18f7a 100644
--- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
+++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
@@ -1,4 +1,10 @@
+cache = {}
+
 def fibonacci(n):
+    if n in cache:
+        return cache[n]
     if n <= 1:
         return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+    result = fibonacci(n - 1) + fibonacci(n - 2)
+    cache[n] = result
+    return result
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..13e77a5 100644
--- a/Sprint-2/improve_with_caches/making_change/making_change.py
+++ b/Sprint-2/improve_with_caches/making_change/making_change.py
@@ -1,32 +1,25 @@
 from typing import List
 
+cache = {}
 
 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))
 
-    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]) -> int:
-    """
-    Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
-    """
-    if total == 0 or len(coins) == 0:
+def ways_to_make_change_helper(total: int, coins) -> int:
+    key = (total, coins)
+    if key in cache:
+        return cache[key]
+    
+    if total == 0:
+        return 1
+    if 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 in range(total // coin + 1):
+        intermediate = ways_to_make_change_helper(total - coin * count, coins[1:])
+        ways += intermediate
+    
+    cache[key] = ways
     return ways