Project Euler Problem 031

Statement

In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).

It is possible to make £2 in the following way:

1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

How many different ways can £2 be made using any number of coins?

Solution

For this solution what is needed is dynamic programming, is one of the most popular of ways
of using dynamic programming.

if __name__ == '__main__':
    amounts = [0 for x in range(201)]
    notes = [1, 2, 5, 10, 20, 50, 100, 200]
    for note in notes:
        amounts[note] += 1
        index = note + 1
        while index < len(amounts):
            amounts[index] += amounts[index - note]
            index += 1
    print("The result is:", amounts[200])

The Python file is available for download here.

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