## Python, dynamic_programming, minimum_coin_change.py

``````"""
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, n):
"""
>>> dp_count([1, 2, 3], 4)
4
>>> dp_count([1, 2, 3], 7)
8
>>> dp_count([2, 5, 3, 6], 10)
5
>>> dp_count([10], 99)
0
>>> dp_count([4, 5, 6], 0)
1
>>> dp_count([1, 2, 3], -5)
0
"""
if n < 0:
return 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()
``````