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Unformatted text preview: Caltech CS 1 -- Fall 2008 CS1: Introduction to Computation Day 4: October 8, 2008 Dynamic Evolution of Computations Caltech CS 1 -- Fall 2008 Before we begin... • Let's select house ombudspeople! • Meet at noon on Thursday at the Athenaeum (olive walk entrace) • Starting tomorrow! Caltech CS 1 -- Fall 2008 Today, let’s think about: • How do our computations unfold? – in space – in time • This will lead us to consider: • efficiency of program execution (first look at a huge subject) Caltech CS 1 -- Fall 2008 Design and analysis (again) • Last time saw how to design recursive procedures • There are many ways to design a procedure that solves the same problem • Analysis will help us to distinguish "good" solutions from "bad" ones – based on some criterion for "good" and "bad" • Design and analysis always interact! Caltech CS 1 -- Fall 2008 Example • Recall from last time: (define (sum-integers n) (if (= n 0) (+ n (sum-integers (- n 1))))) Caltech CS 1 -- Fall 2008 Revisited (summarizing steps) • Evaluate: (sum-integers 3) • (if (= 3 0) 0 (+ 3 (sum-integers (- 3 1)))) • (if #f 0 (+ 3 (sum-integers (- 3 1)))) • (+ 3 (sum-integers (- 3 1))) • (+ 3 (sum-integers 2)) • (+ 3 (if (= 2 0) 0 (+ 2 (sum-integers (- 2 1))))) • (+ 3 (+ 2 (sum-integers 1))) • (+ 3 (+ 2 (if (= 1 0) 0 (+ 1 (sum-integer (- 1 1)))))) Caltech CS 1 -- Fall 2008 Revisited (summarizing steps) • (+ 3 (+ 2 (+ 1 (sum-integers 0)))) • (+ 3 (+ 2 (+ 1 (if (= 0 0) 0 …)))) • (+ 3 (+ 2 (+ 1 (if #t 0 …)))) • (+ 3 (+ 2 ( + 1 0))) • … • 6 Caltech CS 1 -- Fall 2008 Evolution of computation • (sum-integers 3) • (+ 3 (sum-integers 2)) • (+ 3 (+ 2 (sum-integers 1))) • (+ 3 (+ 2 (+ 1 (sum-integers 0)))) • (+ 3 (+ 2 (+ 1 0))) Caltech CS 1 -- Fall 2008 What can we say about the computation? On input N : • How many calls to sum-integers ? N+1 • How much work per call? (sum-integers 3) (+ 3 (sum-integers 2)) (+ 3 (+ 2 (sum-integers 1))) (+ 3 (+ 2 (+ 1 (sum-integers 0)))) (+ 3 (+ 2 (+ 1 0))) Caltech CS 1 -- Fall 2008 Work per call? • (+ 3 (sum-integers 2)) • (+ 3 (if (= 2 0) 0 (+ 2 (sum-integers (- 2 1))))) • (+ 3 (+ 2 (sum-integers 1))) compare if add * add call *(subtract costs same as add) Caltech CS 1 -- Fall 2008 What can we say about the computation? on input N : • How many calls to sum-integers ? N+1 • How much work per call? constant • one comparison, one if , two additions, one function call (at most) • How many deferred operations at end? (sum-integers 3) (+ 3 (sum-integers 2)) (+ 3 (+ 2 (sum-integers 1))) (+ 3 (+ 2 (+ 1 (sum-integers 0)))) (+ 3 (+ 2 (+ 1 0))) Caltech CS 1 -- Fall 2008 Deferred operations? • (+ 3 (+ 2 (+ 1 0))) • Last call to sum-integers gives the result – base case • but have to use this result to "finish up" computations that were previously started to get final result • We call those incomplete computations deferred operations or pending operations Caltech CS 1 -- Fall 2008 What can we say about the...
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This note was uploaded on 09/25/2010 for the course CS 1 taught by Professor Chang during the Spring '08 term at UMBC.
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- chang
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