Introduction to Programming II Recursion - Lecture Slides | CS 112, Study notes of Computer Science

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Intro to Programming II

Recursion

Chris Brooks Department of Computer Science University of San Francisco Department of Computer Science — University of San Francisco – p.1/

Recursion

Recursion is a fundamental problem-solving technique Involves decomposing a problem into: A base case that can be solved directly A recursive step that indicates how to handle morecomplex cases. A common recursive example is factorial: long factorial(int input) if (input ==

return 1; else return input

factorial(input

1); Department of Computer Science — University of San Francisco – p.2/

Infinite recursion

A common error in recursion is forgetting the base case. This can lead to infinite recursion double factorial(int input) return input

factorial(input

1); This eill eventually have a stack overflow. Department of Computer Science — University of San Francisco – p.4/

Exercise: Fibonacci numbers

The Fibonacci numbers are defined as follows: f

f

f

n

f

n

f

n

The first few numbers are 1,1,2,3,5,8,13,21,... Write a class called Fibonacci. It should have a methodcalled getFib(int n) that calculates the nth Fibonaccinumber, plus a main method to test it. Department of Computer Science — University of San Francisco – p.5/

Recursion: Traversing a Maze

Solving a maze is the sort of problem that requirestrial-and-error. When you’re stuck, back up and undo the last thing youdid. This sort of approach works well with recursion. We’ll represent the maze as a two-dimensional array. 1 = clear, 0 = blocked. Start in the upper left, get to the lower right. Department of Computer Science — University of San Francisco – p.7/

Exercise: Solving a maze

Change the rules so that you always try to go left, thenright, then up, then down. Write a Maze constructor that takes two arguments: rowand col and generates a random maze of that size. Department of Computer Science — University of San Francisco – p.8/

Recursion in graphics: Exercise

Add your own pictures to the applet. Change the applet so that the recursive part of the pictureis in the lower right. Department of Computer Science — University of San Francisco – p.10/

Fractals

We can also use recursion to draw fractals Example: Koch snowflake Rule: Each line segment is replaced by a “wedge” withsides that are the same length as the replaced piece. As we increase the depth, it begins to look like asnowflake. Department of Computer Science — University of San Francisco – p.11/