CS 320 n Visual Programming Advanced Recursion Slides

CS 320 n –Visual Programming Advanced Recursion (Slides 8 -2) Thanks to Wanda Dann, Steve Cooper, and Susan Rodger for. Visual slide. Programming ideas. Advanced Recursion

What We Will Do Today • Look at using recursion to solve other forms of problems Visual Programming Advanced Recursion 2

A second form of recursion • A second form of recursion is used when the solution to a problem depends on the ability to break a problem down into smaller and smaller sub-problems. • Example – Files are stored on computers in directories. – Directories can store files and other directories (sub directories) – How do you find all the files in a directory? Visual Programming Advanced Recursion 3

Directory Structure Directories Files Visual Programming Advanced Recursion How deep can this go? 4

Finding all the Files • Break the big problem up into smaller problems • Find the “immediate” files in this directory • then go to each sub directory and find the files in it • To solve the big problem (find all the files in a directory) we solve smaller problems (find all the files in the sub directories) – The smaller problems are solved the same way as the big problem! Visual Programming Advanced Recursion 5

Another Example • Towers of Hanoi • A classic puzzle Visual Programming Advanced Recursion 6

A Towers Problem Source Spare Target (cone. From) (cone. Spare) (cone. To) • The challenge is to move all the disks from the source cone to the target cone. • RULES: – Move 1 disk at a time – A larger disk may never be on top of a smaller disk Visual Programming Advanced Recursion 7

Initial world • The disks are instances of the Torus class. (A torus is a doughnut shaped object. ) • Each cone is positioned exactly 1 meter from its nearest neighbor. • Each disk is positioned exactly 0. 1 meter above the disk below it. Visual Programming Advanced Recursion 8

Identifying the disks • To make it easier to describe our solution, we give each disk an id number and a name. id number 1 2 3 4 Visual Programming Advanced Recursion name disk 1 disk 2 disk 3 disk 4 9

Solving the problem • Our solution will use the – Principle of “wishful thinking” • assume we could solve a smaller version of the same problem • if we could solve the smaller version, it would make it easier to solve this problem. – Base case – the simplest possible version of this problem, one that can obviously be solved. Visual Programming Advanced Recursion 10

Wishful thinking in practice Assume I could move 3 of the disks to the spare cone. Then I could move the 4 th disk (base case) to the target cone. Visual Programming Advanced Recursion 11

Storyboard • To solve the towers problem, we need to know howmany disks we have and which cone is the source, the target, and the spare: World. towers: Parameters: howmany, source, target, spare If howmany is equal to 1 move it (the smallest disk) from the source to the target Else (1) call towers to move howmany-1 disks from source to spare (using target as spare) (2) move it (disk # howmany) from the source to the target base case – move 1 disk a smaller problem -recursively move the rest of the disks (3) call towers to move howmany-1 disks from the spare to the target (using the source as the spare) Visual Programming Advanced Recursion 12

towers • The base case occurs when howmany equals 1, just move the disk. • Two recursive calls are used to solve the smaller problem (moving howmany-1 disks), which helps us solve the bigger problem (moving howmany disks). Visual Programming Advanced Recursion 13

Moving a disk • A challenge in this animation is how to move a disk from one tower to another. • In the towers method, we assumed that we had a method named move. It that would accomplish the task. To write the move. It method, we need to know: – What are the parameters to send in to our method? – What steps need to occur? • • How high to raise the disk object? How far (forward/back) to move it? Visual Programming Advanced Recursion 14

move. It Storyboard • The parameters are: – whichdisk – the disk id number – fromcone – the source cone – tocone – the target cone • A storyboard describing the steps is: move. It: Parameters: whichdisk, fromcone, tocone Do in order Lift the disk up above the top of the fromcone Move it (forward or back) to a location above the tocone Lower the disk down onto the tocone Visual Programming Advanced Recursion 15

Nested Ifs • The disk id number is used to determine which disk to – move up – move over – move down • This means that nested Ifs must be used three times! (The code on this slide is for just one move. ) Visual Programming Advanced Recursion 16

Using an expression • We noticed that the distance each disk has to move up (and then back down) is 0. 3 meters more than 0. 1 * the id number (whichdisk). • We could use an expression to compute the distance for the move up and move down instructions. move the appropriate disk 0. 3 + 0. 1 *whichdisk Visual Programming Advanced Recursion 17

Problem • The problem with this nifty math expression is that we need to have the disk's name to write a move instruction. • For example, disk 1 move up … must be an object, cannot use the id number here Visual Programming Advanced Recursion 18

Using a Function • We decided to write a function to convert the disk id number (i) to the disk name. Visual Programming Advanced Recursion 19

move. It Visual Programming Advanced Recursion 20

Demo! Visual Programming Advanced Recursion 21