From 8b5f0b6f5b90d476818fb38db1e44246fc4cdf31 Mon Sep 17 00:00:00 2001
From: RahwaZeslusHaile <rahwazeslase@gmail.com>
Date: Fri, 27 Feb 2026 13:26:58 +0000
Subject: [PATCH 1/2] Add memoization to fibonacci and making_change for
 performance improvement

---
 .../fibonacci/fibonacci.py                    | 14 +++++-
 .../making_change/making_change.py            | 43 ++++++++++---------
 2 files changed, 34 insertions(+), 23 deletions(-)

diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
index 60cc667..9e3c76f 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)
+        result = n
+    else:
+        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..f53ec1b 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 +1,33 @@
 from typing import List
 
 
+cache = {}
+coins = [200, 100, 50, 20, 10, 5, 2, 1]
+
+
 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])
+    cache.clear()
+    return ways_to_make_change_helper(total, 0)
 
 
-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, coin_index: int) -> int:
+    key = (total, coin_index)
+    if key in cache:
+        return cache[key]
+    
+    if total == 0:
+        return 1
+    if coin_index >= len(coins) or total < 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[coin_index]
+    count_of_coin = 0
+    
+    while coin * count_of_coin <= total:
+        ways += ways_to_make_change_helper(total - (coin * count_of_coin), coin_index + 1)
+        count_of_coin += 1
+    
+    cache[key] = ways
     return ways

From 19df71f3f5807fffb08c7d1d8f55437dc1f23735 Mon Sep 17 00:00:00 2001
From: RahwaZeslusHaile <rahwazeslase@gmail.com>
Date: Fri, 27 Feb 2026 14:47:59 +0000
Subject: [PATCH 2/2] Optimize making_change: move base checks before cache
 lookup and add last-coin shortcut

---
 .../making_change/making_change.py            | 24 +++++++++++--------
 1 file changed, 14 insertions(+), 10 deletions(-)

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 f53ec1b..babd7e3 100644
--- a/Sprint-2/improve_with_caches/making_change/making_change.py
+++ b/Sprint-2/improve_with_caches/making_change/making_change.py
@@ -1,33 +1,37 @@
 from typing import List
 
 
-cache = {}
-coins = [200, 100, 50, 20, 10, 5, 2, 1]
+CACHE = {}
+COINS = [200, 100, 50, 20, 10, 5, 2, 1]
 
 
 def ways_to_make_change(total: int) -> int:
 
-    cache.clear()
+    CACHE.clear()
     return ways_to_make_change_helper(total, 0)
 
 
 def ways_to_make_change_helper(total: int, coin_index: int) -> int:
-    key = (total, coin_index)
-    if key in cache:
-        return cache[key]
-    
     if total == 0:
         return 1
-    if coin_index >= len(coins) or total < 0:
+    if coin_index >= len(COINS) or total < 0:
         return 0
+    
+    # Optimization: if this is the last coin, check if total is divisible by it
+    if coin_index == len(COINS) - 1:
+        return 1 if total % COINS[coin_index] == 0 else 0
+    
+    key = (total, coin_index)
+    if key in CACHE:
+        return CACHE[key]
 
     ways = 0
-    coin = coins[coin_index]
+    coin = COINS[coin_index]
     count_of_coin = 0
     
     while coin * count_of_coin <= total:
         ways += ways_to_make_change_helper(total - (coin * count_of_coin), coin_index + 1)
         count_of_coin += 1
     
-    cache[key] = ways
+    CACHE[key] = ways
     return ways