Coin Change 2

You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

Example 1:

Input: amount = 5, coins = [1, 2, 5]
Output: 4
Explanation: there are four ways to make up the amount:
5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1

Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.

Example 3:

Input: amount = 10, coins = [10] 
Output: 1

Note:

You can assume that

• 0 <= amount <= 5000

• 1 <= coin <= 5000

• the number of coins is less than 500

• the answer is guaranteed to fit into signed 32-bit integer

分析

完全背包

这里注意coin外层，amount内层，是为了防止221 he 212这样重复出现

https://leetcode.com/problems/coin-change-2/discuss/141076/Logical-Thinking-with-Clear-Java-Code

class Solution:
    def change(self, amount: int, coins: List[int]) -> int:
        
        dp = [0] * (amount+1)
        dp [0] = 1
        for c in coins:
            for i in range(c,amount+1):            
                
                dp[i] += dp[i-c]
        return dp[amount]