Python/dynamic_programming/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, m, n):

    # 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__':
    print(dp_count([1, 2, 3], 3, 4))  # answer 4
    print(dp_count([2, 5, 3, 6], 4, 10))  # answer 5