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Unformatted text preview: computa,ons • Recursion is an elegant way of describing the computa5on of certain func5ons   Ex: the sum of the first N natural numbers 1 + 2 + 3 . . . N ­1 + N ∑N = N + ∑N-1 ∑N-1 = N - 1 + ∑N-2 ∑N-2 = N - 2 + ∑N-3 ... ∑3 = 3 + ∑2 ∑2 = 2 + ∑1 ∑1 = 1 ∑1 ∑2 ∑3 ∑N-1 ∑N 5 Recursive Func,on Example • Suppose we want to calculate 237. We know that 237 is 23*236. If we know the solu5on for 236 we would know the solu5on for 237. 148035889 237? 6436343 279841 12167 23*6436343 23*279841 23*12167 236? 235? 234? 233? 529 23*529 232? 23 23*23 1 1 23*1 231? 230? 23* 148035889 = 3,404,825,447 6 2 13 ­11 ­04 237 = 23 * 236 = 23 * (23* 235) = 23 * (23* (23* 234)) = 23 * (23*(23*(23* 233))) = 23 * (23*(23*(23*(23*232))))= 23 * (23*(23*(23*(23*(23*231)))))= 23 * (23 *(23*(23*(23*(23*(23*230))))))= 23 * (23 *(23*(23*(23*(23*(23*1))))))= 23 * (23 *(23*(23*(23*(23*(23))))))= 23...
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This document was uploaded on 03/02/2014.

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