Memoizing Coin Change

Question

I want to convert my coin change function to memoized function
to do that, I decided to use dictionary so that a key in my dict will be the coin and the value will be a

Answer 1

It doesn't answer your question as asked, but if r[0] to r[i] are the number of ways of making change with the first k of your denominations, then r[i+1] is the number of ways of making change with the first k-1 denominations plus r[i-k]. This leads to an elegant solution to the problem you're solving:

def change(total, denominations):
    r = [1] + [0] * total
    for k in denominations:
        for i in xrange(k, len(r)):
            r[i] += r[i - k]
    return r[total]

print change(100, (50, 20, 10, 5, 1))

This approach is discussed in Polya's book "How to solve it". In general, using memoisation to ameliorate recursive solutions is a simple way to code dynamic programming solutions in Python, but my personal opinion is that it's an important skill to be able to drop down a level and figure out exactly how to build the intermediate results in a table in a dynamic programming solution. Often (and exemplified here), the result is faster and way simpler to read (although harder to code in the first place).