Algorithmic problems form the heart of computer science, but they rarely arrive as cleanly packaged, mathematically precise questions. Rather, they tend to come bundled together with lots of messy, application-specific detail, some of it essential, some of it extraneous. As a result, the algorithmic enterprise consists of two fundamental components: the task of getting to the mathematically clean core of a problem, and then the task of identifying the appropriate algorithm design techniques, based on the structure of the problem. These two components interact: the more comfortable one is with the full array of possible design techniques, the more one starts to recognize the clean formulations that lie within messy problems out in the world. At their most effective, then, algorithmic ideas do not just provide solutions to well-posed problems; they form the language that lets you cleanly express the underlying questions.
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