Fingerprinting

by JT Cho

In today's blog, I'll introduce the concept of fingerprinting algorithms. The premise of fingerprinting is simple. Suppose that you have two objects, $x$ and $y$, and you want to quickly verify if $x = y$. If $x, y$ are drawn from some universe $U$, to determine whether $x = y$ one could . . .

A Variation on Flipping Lightbulb Switches, pt. 1

by JT Cho

##Introduction Problem. Suppose you are in a room with $n$ lightbulbs and $k$ switches, where $1 \leq n$ and $1 \leq k$. Suppose that any particular switch turns a subset of light bulbs on. Find the minimum number of switches such that flipping them on turns on all of the . . .

Enumerating Binary Strings Without K-Runs of Ones

by JT Cho

Despite having studied mathematics and computer science for quite some time now, I am still amazed to this day at how the two fields can intersect in profound and unexpected ways. This post expounds upon one such case, examining how solving a seemingly simple enumeration problem algorithmically convolves interesting mathematical . . .

Algorithms 4: Symmetry in Parentheses

by JT Cho

'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 . . .