From c90481b571dc632d8a419fb3346da48f006b7418 Mon Sep 17 00:00:00 2001 From: pathywang Date: Sun, 4 Oct 2026 05:35:24 +0100 Subject: [PATCH 1/4] improve fibonacci --- Sprint-2/improve_with_caches/fibonacci/fibonacci.py | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..61e26c2f 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,3 +1,8 @@ +cache = { + 0: 0, + 1: 1 +} + def fibonacci(n): if n <= 1: return n From 9e40a33d88efe8ed0ecf6db00a8b309addc17c73 Mon Sep 17 00:00:00 2001 From: pathywang Date: Sun, 4 Oct 2026 05:37:48 +0100 Subject: [PATCH 2/4] make changes --- .../improve_with_caches/making_change/making_change.py | 9 +++++++++ 1 file changed, 9 insertions(+) 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..e64d9696 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -1,4 +1,5 @@ from typing import List +cache = {} def ways_to_make_change(total: int) -> int: @@ -14,6 +15,11 @@ 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. """ + key = (total, tuple(coins)) + + if key in cache: + return cache[key] + if total == 0 or len(coins) == 0: return 0 @@ -29,4 +35,7 @@ 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 + + cache[key] = ways return ways + From 9f5699d5615987e8b59b7d655aba91ac501fc061 Mon Sep 17 00:00:00 2001 From: pathywang Date: Sat, 10 Oct 2026 12:59:31 +0100 Subject: [PATCH 3/4] correction --- .../fibonacci/fibonacci.py | 5 --- .../making_change/making_change.py | 34 +++++++++---------- 2 files changed, 16 insertions(+), 23 deletions(-) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 61e26c2f..60cc6671 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,8 +1,3 @@ -cache = { - 0: 0, - 1: 1 -} - def fibonacci(n): if n <= 1: return 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 e64d9696..32c075bb 100644 --- a/Sprint-2/improve_with_caches/making_change/making_change.py +++ b/Sprint-2/improve_with_caches/making_change/making_change.py @@ -1,4 +1,4 @@ -from typing import List +COINS = (200, 100, 50, 20, 10, 5, 2, 1) cache = {} @@ -8,34 +8,32 @@ 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: +def ways_to_make_change_helper(total: int, coin_index: int) -> int: """ Helper function for ways_to_make_change to avoid exposing the coins parameter to callers. """ - key = (total, tuple(coins)) + key = (total, coin_index) if key in cache: return cache[key] - if total == 0 or len(coins) == 0: + if total == 0: + return 1 + + if total < 0 or coin_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 + coin = COINS[coin_index] + + # Option 1: Skip this coin and move to the next denomination. + ways = ways_to_make_change_helper(total, coin_index + 1) + + # Option 2: Use this coin and consider it again. + if coin <= total: + ways += ways_to_make_change_helper(total - coin, coin_index) cache[key] = ways return ways - From 4a3e15cee22da84d0353a768547ff3607843c55e Mon Sep 17 00:00:00 2001 From: pathywang Date: Sat, 10 Oct 2026 13:13:17 +0100 Subject: [PATCH 4/4] correction --- Sprint-2/improve_with_caches/fibonacci/fibonacci.py | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc6671..8fdd80f7 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,11 @@ +cache = { + 0: 0, + 1: 1 +} + def fibonacci(n): - if n <= 1: - return n - return fibonacci(n - 1) + fibonacci(n - 2) + if n in cache: + return cache[n] + + cache[n] = fibonacci(n - 1) + fibonacci(n - 2) + return cache[n] \ No newline at end of file