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Finding the Largest Profit or Loss with R

David Robinson takes us through a brainteaser:

I recently came across an interview problem from A Cool SQL Problem: Avoiding For-Loops . Avoiding loops is a topic I always enjoy reading about, and the blog post didn’t disappoint. I’ll quote that post’s description of the problem:

You have a table of trading days (with no gaps) and close prices for a stock.

Find the highest and lowest profits (or losses) you could have made if you bought the stock at one close price and sold it at another close price, i.e. a total of exactly two transactions.

You cannot sell a stock before it has been purchased. Your solution can allow buying and selling on the same trading_date (i.e. profit or loss of $0 is always, by definition, an available option); however, for some bonus points, you may write a more general solution for this problem that requires you to hold the stock for at least N days.

The SQL solution is another scenario where window functions save the day. In R, there are a couple straightforward options (if you happen to know about the functions!) which have radically different performance profiles.