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# Vending Machine

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.

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### Validate My Answer

1. 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.

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

3. This can be solved in O(d x target), where `d = denominations.length` and `target` is the actual value of the target.

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### Vending Machine

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.

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