Lecture4

# Lecture4 - IE 495 Lecture 4 September 7 2000 Reading for...

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Unformatted text preview: IE 495 Lecture 4 September 7, 2000 Reading for this lecture Primary Â¡ Miller and Boxer, Chapters 2 and 3 Â¡ Aho, Hopcroft, and Ullman, Sections 2.5-2.9 Induction and Recursion Mathematical Induction Induction is a technique for proving statements about consecutive integers. Principle of Mathematical Induction Â¡ Let P(n) be a predicate that we want to prove TRUE for all positive n. Â¡ Method: 1. Prove P (1). 2. Prove P(k) â‡’ P(k+1) 2200 k â‰¥ 1. Example: Prove What does induction have to do with programming? Â¢ i Â£ 1 n i Â¤ n n Â¥ 1 2 Recursion Definition (Mathematics) : An expression, each term of which is determined by application of a formula to the preceding terms. In CS, a function that calls itself is called recursive . Recursion allows us to process large data sets based on our knowledge of smaller ones. The correctness and complexity of recursive algorithms can be proven by induction....
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Lecture4 - IE 495 Lecture 4 September 7 2000 Reading for...

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