human
I am working on the file "DynamicProgramming/Dynamic Programming.ipynb".
The first task is:
DP Top Down Implementation ($\mathcal{O}(nc)$)
Can you write Python code for it?

What is a the Python code you requested?
assistant
#Here is the Python code you requested.

def coin_change_top_down(n, coins): 
    change = [0 for x in range(n + 1)]
    sol = [0 for x in range(n + 1)]
    
    def coin_change_helper(n, coins):
        # n is 0, basecase. We need no coins
        if n == 0:
            return 0, change

        # We have already computed the solution, just return it 
        if sol[n] != 0:
            return sol[n], change

        # Try every possible coin and recursively compute the best solution
        for c in reversed(coins):
            if n - c >= 0:
                sol_t, _ = coin_change_helper(n - c, coins)
                sol_t = sol_t + 1
                if sol_t < sol[n] or sol[n] == 0:
                    sol[n] = sol_t
                    change[n] = c

        return sol[n], change
    
    return coin_change_helper(n, coins)