From 2da2744fb9f6c516ba5040af8482839ed2fd3b5c Mon Sep 17 00:00:00 2001
From: Nataliia Volkova <volkov.nataliia@gmail.com>
Date: Sun, 15 Feb 2026 17:37:53 +0000
Subject: [PATCH 1/3] fibonacci

---
 Sprint-2/improve_with_caches/fibonacci/fibonacci.py | 12 ++++++++++--
 1 file changed, 10 insertions(+), 2 deletions(-)

diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
index 60cc667..7e92d1a 100644
--- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
+++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py
@@ -1,4 +1,12 @@
+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

From 62e1e7170856df37d818498192f02cec27ec9864 Mon Sep 17 00:00:00 2001
From: Nataliia Volkova <volkov.nataliia@gmail.com>
Date: Sun, 15 Feb 2026 18:32:59 +0000
Subject: [PATCH 2/3] making_change

---
 .../making_change/making_change.py             | 18 ++++++++++++++++--
 1 file changed, 16 insertions(+), 2 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 255612e..482a515 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:
     """
@@ -8,14 +9,25 @@ 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])
+    
 
 
 def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+    key = (total, tuple(coins))
+    if key in cache:
+        return cache[key]
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
     """
     if total == 0 or len(coins) == 0:
-        return 0
+        result = 0
+        cache[key] = result
+        return result
+
+    if total == 1 or len(coins) == 1:
+        result = 1
+        cache[key] = result
+        return result
 
     ways = 0
     for coin_index in range(len(coins)):
@@ -29,4 +41,6 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
                 intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
                 ways += intermediate
             count_of_coin += 1
-    return ways
+
+    cache[key] = ways
+    return ways
\ No newline at end of file

From 403c9019c4b5c60bce4b74f93b29d119a8934fa3 Mon Sep 17 00:00:00 2001
From: Nataliia Volkova <volkov.nataliia@gmail.com>
Date: Tue, 21 Apr 2026 18:59:37 +0100
Subject: [PATCH 3/3] simplify complexity, math instead recursion on 0 total,
 and 0  number coins teps

---
 .../making_change/making_change.py            | 40 ++++++++-----------
 1 file changed, 16 insertions(+), 24 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 482a515..e675b49 100644
--- a/Sprint-2/improve_with_caches/making_change/making_change.py
+++ b/Sprint-2/improve_with_caches/making_change/making_change.py
@@ -1,6 +1,7 @@
 from typing import List
 
 cache = {}
+coins = [1, 2, 5, 10, 20, 50, 100, 200]
 
 def ways_to_make_change(total: int) -> int:
     """
@@ -8,39 +9,30 @@ 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])
+    return ways_to_make_change_helper(total, 0)
     
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
-    key = (total, tuple(coins))
+def ways_to_make_change_helper(total: int, index: int) -> int:
+    key = (total, index)
     if key in cache:
         return cache[key]
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
     """
-    if total == 0 or len(coins) == 0:
-        result = 0
-        cache[key] = result
-        return result
-
-    if total == 1 or len(coins) == 1:
-        result = 1
-        cache[key] = result
-        return result
+    if total == 0:
+        cache[key] = 1
+        return 1
+    
+    if index == len(coins):
+        cache[key] = 0
+        return 0
 
+    coin=coins[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 coin * count <= total:
+        ways += ways_to_make_change_helper(total - coin * count, index + 1)
+        count +=1
     cache[key] = ways
     return ways
\ No newline at end of file