Leetcode: Coin Change 2

Posted on February 27, 2018September 10, 2019 by braindenny

Coin Change 2

Similar Problems:

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.

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

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

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

## Blog link: https://code.dennyzhang.com/coin-change-2
class Solution(object):
    ## Basic Ideas: Dynamic programming
    ##   dp(i) = {coin1: count1, coin2: count2, coin3: count3, ...}
    ##           count_j is the combination with the maximum value as coin_j
    ##
    ## Complexity: Time O(k*n), Space O(n)
    def change(self, amount, coins):
        """
        :type amount: int
        :type coins: List[int]
        :rtype: int
        """
        if amount == 0: return 1
        if len(coins) == 0: return 0
        dp = [None]*(1+amount)
        for i in range(0, amount+1): dp[i] = collections.defaultdict(lambda: 0)
        for coin in coins: dp[0][coin] = 1
        coins.sort()
        for i in range(1, amount+1):
            for coin in coins:
                if i<coin: break
                v = i-coin
                dp[i][coin] = dp[v][coin]

            dp[i][0] = 1
            for j in range(1, len(coins)):
                dp[i][coins[j]] += dp[i][coins[j-1]]

        return dp[amount][coins[-1]]

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