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"""

You have m types of coins available in infinite quantities

where the value of each coins is given in the array S=[S0,... Sm-1]

Can you determine number of ways of making change for n units using

the given types of coins?

https://www.hackerrank.com/challenges/coin-change/problem

"""

def dp_count(S, m, n):

"""

>>> dp_count([1, 2, 3], 3, 4)

>>> dp_count([1, 2, 3], 3, 7)

>>> dp_count([2, 5, 3, 6], 4, 10)

>>> dp_count([10], 1, 99)

>>> dp_count([4, 5, 6], 3, 0)

"""

# table[i] represents the number of ways to get to amount i

table = [0] * (n + 1)

# There is exactly 1 way to get to zero(You pick no coins).

table[0] = 1

# Pick all coins one by one and update table[] values

# after the index greater than or equal to the value of the

# picked coin

for coin_val in S:

for j in range(coin_val, n + 1):

table[j] += table[j - coin_val]

return table[n]

if __name__ == "__main__":

import doctest

doctest.testmod()

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