Algorithms are a science of cleverness. A natural manifestation of logical reasoning—mathematical induction, in particular—a good algorithm is like a fleeting, damning snapshot into the very soul of a problem. A jungle of properties and relationships becomes a simple recurrence relation, a single-line recursive step producing boundless chaos and complexity. And to see through deep complexity, it takes cleverness.
It was the programming pioneer Edsger W. Dijkstra that really figured this out, and his namesake algorithm remains one of the cleverest things in computer science. A relentless advocate of simplicity and elegance in mathematics, he more or less believed that every complicated problem had an accessible ground floor, a way in, and math was a tool to find it and exploit it.
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