package q322

// Note: The cache size only needs to be min(max(coins), amount).

func coinChange(coins []int, amount int) int {
	if amount == 0 {
		return 0
	}

	cache := make([]int, amount+1)
	cache[0] = amount + 1
	for p := 1; p < len(cache); p *= 2 {
		copy(cache[p:], cache[:p]) // fill with MAX+1
	}
	cache[0] = 0

	for i := 1; i < len(cache); i++ {
		for _, c := range coins {
			if (i - c) < 0 {
				continue
			}
			cache[i] = min(cache[i], cache[i-c]+1)
		}
	}
	if cache[amount] > amount {
		return -1
	}
	return cache[amount]
}

var _ = coinChange