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New Mexico Computer Science For All Recursion Maureen Psaila-Dombrowski

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Recursion What is Recursion? ▫ It is a concept/method used in computer science and mathematics ▫ Recursive problem: The problem can be described as a reduced or smaller form of the same problem ▫ Sometimes the problem gets so small that the solution of the small problem is trivial can solved recursively or has a recursive implementation ▫ Recursion occurs in computer science when you use a recursive implementation ▫ ….WHAT?

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Recursion - Example Classic example is a factorial: n! 5! 5! = 5 * 4 * 3 * 2 * 1

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Recursion - Example 5! = 5 * 4 * 3 * 2 * 1 NON – recursive definition Recursive definition Maybe it can be solved recursively ! But 4! = 4 * 3 * 2 * 1 5! = 5 * 4! SO… The problem can be broken down into a smaller or reduced version of the same problem

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Recursion - Example Look for the smallest MOST TRIVIAL form of the problem: 5! = 5 * 4 * 3 * 2 * 1 5! = 5 * 4! but 4! = 4 * 3 * 2 * 1 and 4! = 4 * 3! since 3! = 3 * 2 * 1 but 3! = 3 * 2 * 1 and 3! = 3 * 2! since 2! = 2 * 1 but 2! = 2 * 1! since 1! = 1 TRIVIAL CASE

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Recursion - Example So 5! = 5 * 4 * 3 * 2 * 1 Or 5! = 5 * 4! Can be solved Recursively Or in general n! = n * n-1 * n-2 * …* 3 * 2 * 1 Or n! = n * (n-1)!

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Recursion in Computer Languages Implemented by calling a function or procedure in the body of that same function or procedure. ▫must be prevented from consuming excessive computing resources Factorial Psuedocode factorial N if N <=1 (then factorial = 1) (else factorial = N * factorial[N-1])

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Recursive Programming Pros ▫Recursive description --- simple, elegant, and easy to explain and understand. ▫Recursive implementation --- straightforward to build and verify. Cons ▫Can be difficult to understand at first. ▫In some programming languages not as efficient as iteratively ▫Can be difficult to program circularity infinite loop MUST PUT IN A STOP

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Why use Recursion? So if can be less efficient and difficult to understand and program, why use recursion? ▫The problem/program may be easier to understand, solve and program using recursion ▫When you have a recursive description recursive solution is the most direct solution path ▫Usually creating an easy to verify code is more important than creating the most efficient code

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Recursion in NetLogo Draw a spiral from the outside in:

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Recursion in NetLogo Iteratively ▫Specify initial line length Interative Draw ▫While (condition?), repeat Turtle draws a line Turtle turns right Reduce line length

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GO TO MODEL

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Recursion in NetLogo Recursively ▫Specify initial line length Recursive Draw ▫Turtle draws a line ▫Turtle turns right ▫Draw a new line with a reduced length But we forgot something! We Forgot The STOP!

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Recursion in NetLogo Recursively ▫Specify initial line length Recursive Draw ▫If (condition?) STOP ▫Turtle draws a line ▫Turtle turns right ▫draw a new live with a reduced length

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GO to Code

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Important Note For every recursive algorithm…… ….. There is an equivalent iterative (looping) algorithm!!

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Summary Recursion: CS method ▫The solution depends on the solution to smaller instances of the same problem ▫In most programming languages a function or procedure calling itself in the code Pros: shorter, easier to understand, more elegant Cons: often not as efficient as iterative and can be difficult to program Why use recursion? ▫The problem/program is easier to understand using recursion ▫The problem is easier to solve using recursion

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