From 2c5b46885d6c853b9909c31bd3909c4c45c2a4d9 Mon Sep 17 00:00:00 2001
From: Abubakar-Meigag <113248042+Abubakar-Meigag@users.noreply.github.com>
Date: Tue, 30 Jun 2026 10:44:53 +0100
Subject: [PATCH] London | 26-SDC-Mar | beko | Sprint 2 | improve code with
 caches

---
 .../fibonacci/fibonacci.py                    | 12 +++++-
 .../making_change/making_change.py            | 40 ++++++++++++-------
 2 files changed, 36 insertions(+), 16 deletions(-)

diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
index 60cc667..6a2f0f3 100644
--- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
+++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
@@ -1,4 +1,14 @@
+
+cache = {}
+
 def fibonacci(n):
+    
+    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) + fibonacci(n - 2)
+        
+    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..a207fe8 100644
--- a/Sprint-2/improve_with_caches/making_change/making_change.py
+++ b/Sprint-2/improve_with_caches/making_change/making_change.py
@@ -1,5 +1,6 @@
 from typing import List
 
+cache = {}
 
 def ways_to_make_change(total: int) -> int:
     """
@@ -7,26 +8,35 @@ 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]
+    ways = [0] * (total + 1)
+    ways[0] = 1
+    
+    for coin in coins:
+        for amount in range(coin, total + 1):
+            ways[amount] += ways[amount - coin]    
+    
+    
+    return ways[total]
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def ways_to_make_change_helper(total: int, coins: List[int], coin_start_index: int = 0) -> 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_start_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
+    memo_key = (total, coin_start_index)
+    if memo_key in cache:
+        return cache[memo_key]
+
+    coin = coins[coin_start_index]
+    ways = ways_to_make_change_helper(total, coins, coin_start_index + 1)
+    if coin <= total:
+        ways += ways_to_make_change_helper(total - coin, coins, coin_start_index)
+
+    cache[memo_key] = ways
     return ways