Tags: "leetcode", "dynamic-programming", access_time 2-min read

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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 1. 0 <= amount <= 5000 2. 1 <= coin <= 5000 3. the number of coins is less than 500 4. the answer is guaranteed to fit into signed 32-bit integer

Solution

class Solution {
    public int change(int amount, int[] coins) {
        int[] combos = new int[amount + 1];
        combos[0] = 1;

        for (int i = 0; i < coins.length; i++) {
            int coin = coins[i];
            for (int j = 1; j <= amount; j++) {
                if (j >= coin) {
                    //NEW combo = combo WITH coin + combo WITHOUT coin
                    combos[j] += combos[j - coin];
                    // System.out.println(Arrays.toString(combos));
                }
            }
        }

        return combos[amount];
    }
}

Hint

https://youtu.be/jaNZ83Q3QGc