In this article, we will learn to resolve the Coin Change problem in Java by using a dynamic programming algorithm

## Problem

Given a set of infinite coins

Find the number of ways to making change for a specific amount of money, without considering the order of the coins

## Example

Input: given a set of infinite coins {2, 3, 1}. Find the number of ways to making change for 4

Expected output: 4

Explanation: those 4 ways are {1, 1, 1, 1}, {1, 1, 2}, {1, 3} and {2, 2}

## Dynamic Programming Approach

To making change for a value

`j`

, need to use coins with a value less than or equal to`j`

For each coin in the set

`c[i]`

, calculate the ways of making change`w[j] = w[j] + w[j - c[i]]`

with`c[i] <= j <= target`

,`w[0] = 1`

is base case,`w[target]`

is the final result

```
import java.util.Arrays;
public class DP_CoinChange {
static int countWays(int[] coins, int targetCoinChange) {
int[] wayOfCoinChanges = new int[targetCoinChange+1];
wayOfCoinChanges[0] = 1;
for (int i = 0; i < coins.length; i++) {
for (int j = coins[i]; j <= targetCoinChange; j++) {
wayOfCoinChanges[j] += wayOfCoinChanges[j - coins[i]];
}
System.out.println(Arrays.toString(wayOfCoinChanges));
}
return wayOfCoinChanges[targetCoinChange];
}
public static void main(String[] args) {
System.out.println(countWays(new int[]{2, 3, 1}, 4));
}
}
```

- Time complexity is O(nm) and space complexity is O(n) where n is the change target, m is the number of coins