CS320n –Visual Programming Introduction to Recursion (Slides 8-1) Thanks to Wanda Dann, Steve Cooper, and Susan Rodger for slide ideas

CS320n –Visual Programming

Introduction to Recursion(Slides 8-1)

Thanks to Wanda Dann, Steve Cooper, and Susan Rodger for slide ideas.

Visual Programming Introduction to Recursion 2

What We Will Do Today• Look at the programming technique known

as recursion


Repetition• repetition

– definite, counted -> loop– indefinite, as long as some condition is true -> while

• In some situations, we don’t know exactly how many times a block of instructions should be repeated.– repeat until some condition is true– the repetition of step may help get closer to the

condition being true• Games with decisions such as checkers or

chess. – don’t know how many moves it will take to reach the

end of the game or a stalemate


Indefinite Repetition• In programs where a count of repetitions is not

known (indefinite), we can use one of two repetition control mechanisms:– While statement, last time– Recursion, today


Recursion• Many of the pieces we use to create a program

are identified by using special words. For example,– Do in order– Do together– If/Else – Loop

• Recursion is not a program statement with a special word that identifies it as part of the programming language.

• Recursion means that a method (or a function) calls itself.


Example – horse race• Horse race• In repeated moves,

one horse is randomly selected to move forward.

• The selected horse moves straight ahead to the finish line.

• First horse to the finish line wins


• "do everything again" means that the entire method should be repeated

• this is recursion• could this be done with a while loop?

Storyboardrace

If one of the horses has won the winner says, “I won!!!”Else randomly choose one horse and move it forward a small amount do everything again


Do everything again?• How do we implement “do everything

again” ?– Create a call to the race method itself.

– Recursion means that a method calls a copy of itself.

race

If one of the horses has won the winner says, “I won!!!”Else randomly choose one horse and move it forward a small amount call the race method


Stepwise Refinement

isGameOver?

whichHorseWon?

moveRandomHorseForward

race

If one of the horses has won the winner says, “I won!!!” Else randomly choose one horse and move it forward a small amount call the race method


function is Game Over• world level function

• returns a boolean

• is the finish line < 0.5 meters in front of any horse?– remember, center point not at the front

• if so, game is over

• return true


which Horse Won• world level function

• returns an object

• which horse is within 0.5 meters of finish line? – or which horse is closest to finish line– or which horse is within winning distance

• return that horse object


move Random Horse Forward• world level method

• pick one of the horses at random and move it forward between 0.05 and 0.15 meters

• how to pick a horse at random?– use the world level function


First Attempt


race Method• uses recursion

• where is the “way out?”


Testing• Testing a program that used random

numbers requires extra caution. • In this example, we ran the program 20

times and found that – racehorse1 won 3 times– racehorse2 won 0 times– racehorse3 won 17 times

• Something is wrong! Each horse should win approximately 1/3 of the time.


Removing the bug• The bug in this code is that we have

– nested If statements, and– we used a 33% probability for each If

statement

• What we didn't consider is that if racehorse1 was not selected, then we have a 50% probability of selecting either racehorse2 or racehorse3.


Probability Tree

1/3 of the timeSelect race horse 1

2/3 s of the timeDon’t select race horse 1

1/3 of the timeSelect race horse 2

2/3s of the timeSelect race horse 11/3 of time

race horse 1moves

2/9 s of timerace horse 2moves

4/9 s of timerace horse 2moves


Correct Version of move Random Horse Forward


Retest• Run Program 20 times

– racehorse1 won 6 times– racehorse2 won 6 times– racehorse3 won 11 times

• Appears problem is fixed

• Each horse should win approximately 1/3 of the time

• more than 20 tests to really check program


Modifying the Horse Race• Change the race so that all three horses

move a random distance at the same time

• easy to change with a Do Together block, but what else needs to change?

Documents

CS320n –Visual Programming Introduction to Recursion (Slides 8-1) Thanks to Wanda Dann, Steve Cooper, and Susan Rodger for slide ideas