# Vending Machine

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We're writing code for a vending machine and want to manage how we're handling change returned from payments. We want to calculate the minimum number of coins to add up to a customer's change.

This vending machine could be used anywhere in the world with any currency, so as an input, we'll also provide the denominations of coins available for change.

**Write a function minCoinsForChange that returns an integer for the smallest number of coins required to make change. If a combination is not possible, return -1.**

Assume you have as much of any available denomination needed to solve the problem.

```
const denominations = [1, 5, 10];
const targetChange = 12;
minCoinsForChange(denominations, targetChange);
// Output: 3 --> 1x10 + 2x1
const denominations = [5, 10, 25];
const targetChange = 53;
minCoinsForChange(denominations, targetChange);
// Output: -1
```

### Validate My Answer

This can be solved either bottom-up or top-down. In either case, the solutions are reasonable so go with what you're most comfortable with.

This can be solved using dynamic programming. You can solve subproblems and use memoization to build up your solution.

This can be solved in

*O(d x target)*, where`d = denominations.length`

and`target`

is the actual value of the target.