This problem is same as asked in here.

Given a list of coins, their values (c1, c2, c3, ... cj, ...), and the total sum i. Find the minimum number of coins the sum of which is i (we can use as many coins of one type as we want), or report that it's not possible to select coins in such a way that they sum up to S.

I"m just introduced to dynamic programming yesterday and I tried to make a code for it.

# Optimal substructure: C[i] = 1 + min_j(C[i-cj])
cdict = {}
def C(i, coins):

    if i <= 0:
        return 0

    if i in cdict:
        return cdict[i]
    else:
        answer = 1 + min([C(i - cj, coins) for cj in coins])
        cdict[i] = answer
        return answer

Here, C[i] is the optimal solution for amount of money 'i'. And available coins are {c1, c2, ... , cj, ...} for the program, I've increased the recursion limit to avoid maximum recursion depth exceeded error. But, this program gives the right answer only someones and when a solution is not possible, it doesn't indicate that.

What is wrong with my code and how to correct it?