CSE 131 Module 6: Recursion

Studio

if necessary, review studio procedures before starting.

Warmup

• First, form a group:
• If you are at a table with a large, wall-mounted screens, a group of 3-4 people is fine.
• If you are seated at a table without a large screen, a group of 2 people is better.
• All but one member of your group should have this web page open so you can follow along and see the instructions as you work.
• All members of the group should update their repositories:
• Open your repository in eclipse
• Right-click (control-click on a mac) on your repository name
• Drag down to Team...
• Choose Update
• Plan to have one computer at which your team does its work. Initially, one of you will be in charge of typing at that computer.
• Throughout the studio, you should trade who is in charge of the keyboard. Before doing so, commit your work to make sure your work is saved.

Note for Fall 2015: Update your repos from the topmost level. There was a missing test case in the code I originally sent you. Thanks!

Note! It is very important to the pedagogical goals of this studio that you follow the directions below carefully. The object of studio is not to arrive at a solution, but rather to understand the processes involved in developing solutions.

For example, at times, you may be asked to sketch a solution using pencil and paper.

To be blunt, this means you must have pencil and paper out, and you must use said paper and pencil to sketch solutions. These sketches are very helpful both for your own understanding of recursive computations but also these sketches help us understand how you think about recursion.

Overview

In this studio you will learn two styles of developing recursive code:
• A recursive specification or formula may be provided for a computation. In such cases, the recursive code is often a direct transcription of the formula into Java.
• Examples or instances of the computation may be provided. In such cases, you must identify the recursive structure of the computation to obtain code.

Recursive Formulae

1. For each of the following recursive formulae, write the corresponding code in Java and test your solution using the provided JUnit test.
The functions defined below are partial, in the sense that they do not work on all inputs. Let's assume that inputs to all functions below are restructed to the nonnegative integers (0, 1, 2, …).

Do not worry about errors that may occur if improper inputs are presented.

factorial
This was done in front of you during lecture.
 fact(n) = { n × fact(n-1) n > 0 1 otherwise
Fibonacci
 fib(n) = { fib(n-1) + fib(n-2) n > 1 n otherwise
isOdd
 isOdd(n) = { ! isOdd(n-1) n > 0 false otherwise
sum
 sum(a,b) = { sum(a+1, b-1) b > 0 a otherwise
2. Using the substitution model, show (using pencil an paper) the evaluation of:
• isOdd(3)
• sum(100,3)
At this piont, show your work to a TA before proceeding!

Recursive Substructure

Below are some computations you have seen before, but we will now conceive of them recursively. Using pencil and paper, identify the recursive substructure as shown in lecture. This means circling the compuation that is smaller than the larger one, and identifying by name as a function call.

After identifying the substructure, implement the function recursively in Java and run the unit test.

Show your recursive structure diagrams to a TA for each problem below before coding it or before proceeding to the next problem.
factorial
This was done in front of you during lecture.
• fact(n) = n × (n-1) × (n-2) × … × 1
• fact(0) = 1
sumDownBy2
• sumDownBy2(n) = n + (n-2) + (n-4) + …
• sumDownBy2(1) = 1
• sumDownBy2(0) = 0
harmonicSum
• harmonicSum(n) = 1 + 1/2 + 1/3 + … + 1/(n-1) + 1/n
• harmonicSum(1) = 1
NB: The result of this computation should be a double. Be careful about integer divsion!
mult
•  mult(a,b) = a + a + … a + a | Added together b times | mult(a,0) = 0

• If your studio contains a feedback.txt file, respond to the questions and supply any requested information.
• You must commit all of your work to your repository. It's best to do this from the top-most level of your repository, which bears your name and student ID.

When you done with this studio, you must be cleared by the TA to receive credit.
• Fill in the form below with the relevant information
• Have a TA check your work
• The TA should check your work and then fill in his or her name
• Click OK while the TA watches
• If you request propagation, it does not happen immediately, but should be posted in the next day or so

This demo box is for studio 6
 Last name WUSTL Key Propagate? (or your numeric ID) Do not propagate e.g. Smith j.smith 1 Copy from 1 to all others 2 Copy from 2 to all others 3 Copy from 3 to all others 4 Copy from 4 to all others