From dd903f9f6dbf2766a3affcf8ae9174801dd81bf6 Mon Sep 17 00:00:00 2001 From: ZabihollahNamazi Date: Wed, 24 Jun 2026 16:39:08 +0100 Subject: [PATCH 1/2] fibonacci --- .../improve_with_caches/fibonacci/fibonacci.py | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) diff --git a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py index 60cc667..76001ba 100644 --- a/Sprint-2/improve_with_caches/fibonacci/fibonacci.py +++ b/Sprint-2/improve_with_caches/fibonacci/fibonacci.py @@ -1,4 +1,17 @@ def fibonacci(n): + if n < 0: + raise ValueError("Fibonacci is not defined for negative integers.") if n <= 1: return n - return fibonacci(n - 1) + fibonacci(n - 2) + + # Track the last two numbers in the sequence + prev2 = 0 # fibonacci(0) + prev1 = 1 # fibonacci(1) + + # Calculate upward to n + for _ in range(2, n + 1): + current = prev1 + prev2 + prev2 = prev1 + prev1 = current + + return prev1 \ No newline at end of file From 6b14f4f505cadb2836becfa777dd0fc3d2e00f2d Mon Sep 17 00:00:00 2001 From: ZabihollahNamazi Date: Wed, 24 Jun 2026 16:44:43 +0100 Subject: [PATCH 2/2] making change --- .../making_change/making_change.py | 42 +++++-------------- 1 file changed, 11 insertions(+), 31 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..d0feed6 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 +1,12 @@ -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]) - - -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: - 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 - return ways + coins = [1, 2, 5, 10, 20, 50, 100, 200] + + dp = [0] * (total + 1) + + dp[0] = 1 + + for coin in coins: + for i in range(coin, total + 1): + dp[i] += dp[i - coin] + + return dp[total] \ No newline at end of file