Skip to content

London | November 25 | Donara Blanc | Sprint 2 | Improve with caches #132

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
donarbl wants to merge 1 commit into
base: main
Choose a base branch
from
+19 −17
Open

London | November 25 | Donara Blanc | Sprint 2 | Improve with caches #132

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
8 changes: 6 additions & 2 deletions Sprint-2/improve_with_caches/fibonacci/fibonacci.py
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,4 +1,8 @@
def fibonacci(n):
def fibonacci(n, cache={}):
if n <= 1:
return n
return fibonacci(n - 1) + fibonacci(n - 2)
if n in cache:
return cache[n]
result = fibonacci(n - 1) + fibonacci(n - 2)
cache[n] = result
return result
28 changes: 13 additions & 15 deletions Sprint-2/improve_with_caches/making_change/making_change.py
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,22 +1,15 @@
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.

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 = {}
return ways_to_make_change_helper(total, (200, 100, 50, 20, 10, 5, 2, 1), cache)


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.
"""
def ways_to_make_change_helper(total: int, coins: tuple, cache: dict) -> int:
if total == 0 or len(coins) == 0:
return 0

cache_key = (total, coins)
if cache_key in cache:
return cache[cache_key]
ways = 0
for coin_index in range(len(coins)):
coin = coins[coin_index]
Expand All @@ -26,7 +19,12 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
if total_from_coins == total:
ways += 1
else:
intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
intermediate = ways_to_make_change_helper(
total - total_from_coins,
coins=coins[coin_index + 1:],
cache=cache
)
Comment on lines 10 to 26
Copy link

@cjyuan cjyuan Mar 2, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Tuple or array creation are relatively costly operations.

From lines 5 and 24, we know coins can only be one of the following 9 tuples:

(200, 100, 50, 20, 10, 5, 2, 1)
(100, 50, 20, 10, 5, 2, 1)
(50, 20, 10, 5, 2, 1)
...
(1)
()

We could further improve the performance if we can

  • avoid repeatedly creating the same sub-tuples at line 24 (e.g. use another cache), and
  • create key as (total, a_unique_integer_identifying_the_subtuple) instead of as (total, tuple of coins)
    • There are only a small number of different sub-tuples. We can easily assign each sub-tuple a unique integer.

ways += intermediate
count_of_coin += 1
return ways
cache[cache_key] = ways
return ways