22 - CMPSCI 187 Programming With Data Structures Lecture#22...

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CMPSCI 187: Programming With Data Structures Lecture #22: Introduction to Recursion 2 November 2011
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Introduction to Recursion • What is Recursion, and Why Recursion? • Ungrounded Recursion • The Factorial Function • Tracing Recursive Code: Computing Sums • Iterative Alternatives • Indirect Recursion
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What is Recursion, and Why Recursion? • A method is recursive if it calls itself. A method can call any other method, and its own execution is suspended until (or unless) the new method finishes. • When more than one version of the same method is on the stack, they have separate contexts -- separate copies of local variables and parameters. None of them affect any of the others, except by finishing their execution. • Recursive code is often the cleanest and simplest way to solve a problem. • Many mathematical and computing concepts have recursive definitions . For example, a stack is either empty, or is another stack with an element pushed onto it. A recursive algorithm can often be written directly from a recursive definition. This is a main theme of CMPSCI 250 -- the close connection between algorithm and definition makes it easier to prove correctness, often by mathematical induction.
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More Recursion Examples • “Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law.”
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