"""
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)
4
>>> dp_count([1, 2, 3], 3, 7)
8
>>> dp_count([2, 5, 3, 6], 4, 10)
5
>>> dp_count([10], 1, 99)
0
>>> dp_count([4, 5, 6], 3, 0)
1
"""
# 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()