I’m changing up the format. I’m going to be going through a so-called “Leetcode Study Plan”, in particular the one on dynamic programming, and see how it compares to what I’d do for teaching this topic. I will “just” be solving the problems as with my other posts here, but I’ll hopefully be finding good notes to fulfill a larger write-up of how one might, or might not, use this to help their students.

Findings

To be honest, I don’t think this is off to a great start with Fibonacci. I suppose it’s nice to use arrays to compute intermediate values, but the recurrence here is meaningfully simpler than what comes up in “real” (or at least the hard) dynamic programming problems. In particular, we don’t choose from a collection of solved subproblems, we always know we’ll use the n-1 and n-2 solutions to create the n solution.

Speaking of solutions… I playfully made one without any arrays. Presumably if I had to use this to teach dynamic programming, I would use the “array based” method even though it’s not needed, as demonstrated:

class Solution:
    def fib(self, n: int) -> int:
        if n == 0: return 0
        if n == 1: return 1
        prevprev = 0
        prev = 1
        for i in range(2, n+1):
            tmp = prev + prevprev
            prevprev = prev
            prev = tmp
        return prev

So if I want to play along more, we have:

class Solution:
    def fib(self, n: int) -> int:
        if n == 0: return 0
        if n == 1: return 1
        a = [0, 1]
        for i in range(2, n+1):
            a.append(a[i-1]+a[i-2])
        return a[-1]

I will admit it looks prettier.

This and more dynamic programming problems will be listed here.