'Tis the season for interviews and career preparation. So without further ado, let's do a welcome back post! Problem. Given an input string $s$ of length $n$ containing only left and right parentheses, determine whether or not it is a valid parenthetical expression. By definition, a parenthetical expression is valid . . .

For this week's algorithm post, we'll examine a recent exam problem I had for my algorithms class! I couldn't come up with a story for this one, though, sorry. :( n.b. I present here my refined solution from the exam. It got full credit, but alternative solutions do exist! Problem. . . .

The king of Sikinia was very satisfied with your work documenting his kingdom's wealth distribution. As a result, he has put you in charge of improving the country's road system. Various portions of the country are well reachable from existing roads, while others are cut off from the transportation network. . . .

The king of the distant country Sikinia has tasked you to keep records of the individual wealth of his people. There are $n = 2^k$ people living in Sikinia. However, the king does not care about every individual's wealth, but the net-worth of every $2^i$'th wealthiest person. Your . . .

The class I TA for recently began examining recursive algorithms that follow the divide-and-conquer paradigm. These algorithms are a particularly interesting subset that can involve some tricky algebra when proving asymptotic bounds. This article is intended to help those students, as well as delve a lot deeper into the rigorous . . .