Level 5Exercise #119

Memoized coin change

Count ways to make amount with unlimited coins using a cached recursive state.

What you’ll practice

This Level 5 exercise focuses on cache decorator in the Algorithms curriculum. Solve the challenge prompt above using clear, idiomatic Python and the relevant language or standard-library tools.

Relevant Python reference: Python Standard Library — Algorithms.

Sample Test Cases

Example #1

Input:coin_ways(coins=(1,2), amount=4)

Output:3

Reference Solution

Reveal Reference Solution

def coin_ways(coins: tuple[int,...], amount: int) -> int:
    from functools import cache
    @cache
    def ways(i, remaining):
        if remaining == 0: return 1
        if remaining < 0 or i == len(coins): return 0
        return ways(i, remaining-coins[i]) + ways(i+1, remaining)
    return ways(0, amount)

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Memoized coin change

What you’ll practice

Sample Test Cases

Further Reading

Reference Solution