Making Change Making Change

Nicola is taking a much needed vacation. He'll be backpacking around some lesser-known countries. Each has its own unique currency.

When making purchases, Nicola would like to use the minumum number of coins possible. For example, Outer Leftopia has coins with denomination 1, 3, and 5 shillings. He wants to buy a souvenir that costs 13 shillings. He can do that using two 5 shilling coins and one 3 shilling coin.

You can assume Nicola has access to an infinite number of coins of each denomination. (He has a large bank account and access to an ATM).

Input: Two arguments. The first argument is an int: the price of the purchase. The second is a list of ints: the denominations of available coins.

Output: int. The minimum number of coins Nicola can use to make the purchase. If the price cannot be made with the available denominations, return None.


How it is used: Besides helping Nicola make change, this is an example of a problem in combinatorial optimization.

Precondition: Inputs are all positive integers.