There's a tricky greedy algorithm to solve this problem, but using recursion is 10x easier.

In this problem, you can own or not own the stock, or you can sell it, in which case you can't do anything else. You can describe this with 3 states, Not Own, Own, and Sold:

0. Problem

We want the max profit in the Bought and Sold state on day n. We'll sove for these:

1. Recursion

We can look at the arrows that point to each state to get the recursion:

2. Base case

We start out in the Not Own state with 0 profit. The profits in all the other states don't exist yet. We'll set them to -infinity so they don't count towards any computations and get overwritten as soon as possible.

3. Code

We can use Dynamic Programming and "Tabulation+":

Time Complexity $O(n)$. We loop through an array.

Space Complexity $O(1)$. We store 3 variables.

This is the optimal solution. Here are some minor optimizations, if you're curious.