n1 n 1 2 3 n 1 recursion selfreference n n n

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Unformatted text preview: 1); Now evaluates to 4 * 6 20 Factorial  ­ Non ­recursive version • We can solve this problem using itera5on as well… # factorial function using iteration instead of recursion def factorial(an_int): product_so_far = 1 for index in range(an_int,0,-1): product_so_far = index*product_so_far return product_so_far • For some problems, loops are be`er. For others, recursion. Some5mes both work easily. 21 7 13 ­11 ­04 Recursive Func,ons  ­ Sum of the first N numbers Example 1 + 2 + 3 . . . N ­1 + N ∑1 ∑2 ∑3 ∑N-1 recursion = selfreference ∑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 22 Recursion is a form of repe,,on 1 + 2 + 3 . . . N ­1 + N ∑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 23 When does the recursion stop? • Just like with loops, we need a way to stop   While loop: stop when the Bool...
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This document was uploaded on 03/02/2014.

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