CSE 131 Module 7: Recursion

Studio


if necessary, review studio procedures before starting.

Warmup


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:

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:
    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.
sumDownBy2
harmonicSum
NB: The result of this computation should be a double. Be careful about integer divsion!
mult

Submitting your work (read carefully)



Last modified 11:55:48 CDT 13 May 2014
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