7.cpp

/*

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

*/

class Solution {
public:
    int change(int amount, vector<int>& coins) {
        int values[amount+1];
        memset(values, 0, sizeof(values));
        values[0] = 1;
        for(int i=0; i<coins.size(); i++) {
            for(int j=coins[i]; j<=amount; j++) {
                values[j] += values[j - coins[i]];
            }
        }
        return values[amount];
    }
};