518 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.

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

Solution)

This problem can be solved by Dynamic Programming.

We have to reuse the history calculation.

First, we have to create one dimensional array which length is amount+1.

Then, we have to repeat to find all combination for the given coins based on the following rule.

if amount >= coin:

combination\[amount\] += combination\[amount-coin\]

class Solution {
    public int change(int amount, int[] coins) {
        // using dynamic programming
        // basic idea
        // if amount >= coin:
        //      combination[amount] += combination[amount-coin]
        int[] combination = new int[amount+1];
        combination[0] = 1;
        for (int coin: coins) {
            if (coin > amount) continue;
            for (int i = coin; i <= amount; i++)
                if (i >= coin) combination[i] += combination[i-coin];
        }
        return combination[amount];
    }
}