cache.py

class Solution:
    def change(self, amount: int, coins: List[int]) -> int:
        return self.cc(amount, coins,0, {})
    
    def cc(self, amount, coins, i,cache):
        if amount == 0 or i >= len(coins):
            return 1
        if amount < 0:
            return 0        
        if (amount, i) not in cache:
            cache[(amount, i)] = self.cc(amount - coins[i], coins, i, cache) + self.cc(amount, coins, i + 1, cache)

        return cache[(amount,i)]