From 57900a73fdb39cdaafc6eeb3f129ae3cf134420e Mon Sep 17 00:00:00 2001
From: shaghayeghfar <146011477+shaghayeghfar@users.noreply.github.com>
Date: Wed, 14 Oct 2026 20:56:06 +0100
Subject: [PATCH 1/2] improve_with_caches task id completed

---
 .../fibonacci/fibonacci.py                    | 13 ++++++-
 .../making_change/making_change.py            | 39 +++++++++++++------
 2 files changed, 39 insertions(+), 13 deletions(-)

diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
index 60cc6671..b25b936c 100644
--- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
+++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
@@ -1,4 +1,15 @@
+
+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 255612e5..de42d91e 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 +1,47 @@
+
 from typing import List
 
 
 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.
+    cache = {}
+    coins = [200, 100, 50, 20, 10, 5, 2, 1]
+
+    return ways_to_make_change_helper(total, coins, cache)
 
-    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], cache: dict
+) -> int:
+    if total == 0:
+        return 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:
+    if len(coins) == 0:
         return 0
 
+    key = (total, tuple(coins))
+
+    if key in cache:
+        return cache[key]
+
     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
+                ways += ways_to_make_change_helper(
+                    total - total_from_coins,
+                    coins[coin_index + 1:],
+                    cache,
+                )
+
             count_of_coin += 1
+
+    cache[key] = ways
     return ways

From 5956424d7bf7394fcbea1c9083a51e1e2a4906ad Mon Sep 17 00:00:00 2001
From: shaghayeghfar <146011477+shaghayeghfar@users.noreply.github.com>
Date: Wed, 21 Oct 2026 17:38:04 +0100
Subject: [PATCH 2/2] the changes were done

---
 .../making_change/making_change.py               | 16 +++++++---------
 1 file changed, 7 insertions(+), 9 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 de42d91e..591f0096 100644
--- a/Sprint-2/improve_with_caches/making_change/making_change.py
+++ b/Sprint-2/improve_with_caches/making_change/making_change.py
@@ -1,31 +1,28 @@
 
-from typing import List
-
-
 def ways_to_make_change(total: int) -> int:
     cache = {}
     coins = [200, 100, 50, 20, 10, 5, 2, 1]
 
-    return ways_to_make_change_helper(total, coins, cache)
+    return ways_to_make_change_helper(total, coins, 0, cache)
 
 
 def ways_to_make_change_helper(
-    total: int, coins: List[int], cache: dict
+    total: int, coins: list[int], start_index: int, cache: dict
 ) -> int:
     if total == 0:
         return 1
 
-    if len(coins) == 0:
+    if start_index == len(coins):
         return 0
 
-    key = (total, tuple(coins))
+    key = (total, start_index)
 
     if key in cache:
         return cache[key]
 
     ways = 0
 
-    for coin_index in range(len(coins)):
+    for coin_index in range(start_index, len(coins)):
         coin = coins[coin_index]
         count_of_coin = 1
 
@@ -37,7 +34,8 @@ def ways_to_make_change_helper(
             else:
                 ways += ways_to_make_change_helper(
                     total - total_from_coins,
-                    coins[coin_index + 1:],
+                    coins,
+                    coin_index + 1,
                     cache,
                 )