### Problem

- Given a set of infinite coins
- Find the minimum number of coins 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 minimum number of coins of making change for 3
- Expected output: 1
- Explanation: there're 3 ways to making change for 3: {3}, {1, 1, 1}, {1, 2}, minimum is {3}

### Approach

To making change for a value

`i`

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

For each coin in the set

`c[j]`

, calculate the minimum number of coins to making change`m[i] = Math.min(m[i], m[i - c[j]]) + 1`

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

,`m[0] = 0`

is base case,`m[target]`

is the final result

### Implementation

```
```

### Complexity

- Time complexity: O(nm) with n is the change target, m is the number of coins
- Space complexity: O(n) with n is the change target