LeetCode 518 Coin Change II - Medium

518. Coin Change II — Medium

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Problem

518. Coin Change 2 -- Medium

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

Solution

# DP:
class Solution:
    def change(self, amount: int, coins: List[int]) -> int:
        #O(N x amount)
        dp = [0] * (amount + 1)
        dp[0] = 1 # take 0 amount, only 1 combination 
        #For each amount x, compute the number of combinations: dp[x] += dp[x - coin].
        for i in coins:
            for j in range(i, amount + 1):
                dp[j] += dp[j - i]
        return dp[amount]