recursive thinking
Post on 31-Dec-2015
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Chapter 8 introduces the technique of recursive programming.
As you have seen, recursive programming involves spotting smaller occurrences of a problem within the problem itself.
This presentation gives an additional example, which is not in the book.
Recursive ThinkingRecursive Thinking
Data StructuresData Structuresand Other Objectsand Other ObjectsUsing JavaUsing Java
First ExampleFirst Example
Task to write a non-negative integer to Task to write a non-negative integer to screen with decimal digits stackedscreen with decimal digits stacked
Number 7895Number 7895 OutputOutput
77
88
99
55
One digit solutionOne digit solution
Print that digit!Print that digit! Number 7Number 7 Output Output
77
Many digit solutionMany digit solution
Print all digits except the last, stacked Print all digits except the last, stacked verticallyvertically
Then print the last digitThen print the last digit
77
88
99 Now print the 5 which is 7895%10Now print the 5 which is 7895%10
PseudocodePseudocode
//printing the digits of a non-negative number stacked vertically
if (the number has only one digit)
write that digit.
else
write the digits of the number/10 stacked vertically
Write the single digit of number %10.
Recursive solutionRecursive solution
Always has a stopping case (base case)Always has a stopping case (base case)if (number < 10)if (number < 10)
System.out.println(number);System.out.println(number); Always has a recursive callAlways has a recursive callelseelse
{{
writeVertical(number/10);writeVertical(number/10);
system.out.println(number%10);system.out.println(number%10);
}}
Recursively callRecursively call
Number is 7895
Call 17895
Call 17895
Call 2789
Call 17895
Call 2789
Call 17895
Call 2789
Call 378
Call 17895
Call 2789
Call 378
Call47
Now come backNow come back
Call 17895
Call 2789
Call 378
Call47
Call 4 with a 7 is a one digit numberTherefore, print out that single digit and that call is complete
7Call 17895
Call 2789
Call 378
Now return from 4th callNow return from 4th call
Call 17895
Call 2789
Call 378
Returning from that 4th call the next statement if System.out.println(number%10)
Since that number is 78 : print out 78%10 or 8
78
Call 17895
Call 2789
Now return from third callNow return from third call
Call 17895
Call 2789
Returning from that 3rd call the next statement if System.out.println(number%10)
Since that number is 789 : print out 789%10 or 9
789
Call 17895
Returning from 2nd callReturning from 2nd call
Returning from that 2nd call the next statement if System.out.println(number%10)
Since that number is 7895 : print out 789%10 or 5
7895
Call 17895
Return from first callReturn from first call
We’re Done!!!!
A Car ObjectA Car Object
To start the example, think about your favorite family car
A Car ObjectA Car Object
To start the example, think about your favorite family car
A Car ObjectA Car Object
To start the example, think about your favorite family car
A Car ObjectA Car Object
To start the example, think about your favorite family car
A Car ObjectA Car Object
To start the example, think about your favorite family car
Imagine that the car is controlled by a radio signal from a computer
A Car ClassA Car Class
public class Car { . . .}
To start the example, think about your favorite family car
Imagine that the car is controlled by a radio signal from a computer
The radio signals are generated by activating methods of a Car object
public class Car{ public Car(int carNumber); public public void move( ); public void turnAround( ); public boolean isBlocked( );
... We don't need to know the private fields! ...}
methods for the Car Classmethods for the Car Class
public static void main(...){ Car racer = new Car(7);
. . .
The ConstructorThe Constructor
When we declare a Car
and activate the constructor, the computer makes a radio link with a car that has a particular number.
public static void main(...){ Car racer = new Car(7);
racer.turnAround( ); . . .
The turnAround methodThe turnAround method
When we activate turnAround, the computer signals the car to turn 180 degrees.
public static void main(...){ Car racer = new Car(7);
racer.turnAround( ); racer.move( ); . . .
The move methodThe move method
When we activate move, the computer signals the car to move forward one foot.
public static void main(...){ Car racer = new Car(7);
racer.turnAround( ); racer.move( ); . . .
The move methodThe move method
When we activate move, the computer signals the car to move forward one foot.
public static void main(...){ Car racer = new Car(7);
racer.turnAround( ); racer.move( ); if (racer.isBlocked( ) ) System.out.println (“Cannot move!”); . . .
The isBlocked( ) methodThe isBlocked( ) method
The isBlocked method detects barriers.
Your MissionYour Mission
Write a method which will move a Car forward until it reaches a barrier...
Your MissionYour Mission
Write a method which will move a Car forward until it reaches a barrier...
Your MissionYour Mission
Write a method which will move a Car forward until it reaches a barrier...
Your MissionYour Mission
Write a method which will move a Car forward until it reaches a barrier...
...then the car is turned around...
Your MissionYour Mission
Write a method which will move a Car forward until it reaches a barrier...
...then the car is turned around... ...and returned to its original location, facing the
opposite way.
Your MissionYour Mission
Write a method which will move a Car forward until it reaches a barrier...
...then the car is turned around... ...and returned to its original location, facing the
opposite way.
Your MissionYour Mission
Write a method which will move a Car forward until it reaches a barrier...
...then the car is turned around... ...and returned to its original location, facing the
opposite way.
public void ricochet(Car movingCar)
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
public void ricochet(Car movingCar)
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar)
movingCar.move( );. . .
movingCar.move( );. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);This makes the problem a bit smaller. For example, if the car started 100 feet from the barrier...
100 ft.
movingCar.move( );. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);This makes the problem a bit smaller. For example, if the car started 100 feet from the barrier... then after activating move once, the distance is only 99 feet.
99 ft.
movingCar.move( );. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
We now have a smaller version of the same problem that we started with.
99 ft.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
Make a recursive call to solve the smaller problem.
99 ft.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
99 ft.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
The recursive call will solve the smaller problem.
99 ft.
movingCar.move( );ricochet(movingCar);. . .
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
What is the last step that's needed to return to our original location ?
99 ft.
movingCar.move( );ricochet(movingCar);movingCar.move( );
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar);
What is the last step that's needed to return to our original location ?
100 ft.
movingCar.move( );ricochet(movingCar);movingCar.move( );
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar)
This recursive method follows a common pattern that you should recognize.
movingCar.move( );ricochet(movingCar);movingCar.move( );
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar)
When the problem is simple, solve it with no recursive call. This is the base case.
movingCar.move( );ricochet(movingCar);movingCar.move( );
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar)
When the problem is more complex, start by doing work to create a smaller version of the same problem...
movingCar.move( );ricochet(movingCar);movingCar.move( );
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar)
...use a recursive call to completely solve the smaller problem...
movingCar.move( );ricochet(movingCar);movingCar.move( );
Pseudocode for ricochetPseudocode for ricochet
if movingCar.isBlocked( ), then the car is already at the barrier. In this case, just turn the car around.
Otherwise, the car has not yet reached the barrier, so start with:
public void ricochet(Car movingCar)
...and finally do any work that's needed to complete the solution of the original problem..
Implementation of ricochetImplementation of ricochet
public void ricochet(Car movingCar){ if (movingCar.isBlocked( )) movingCar.turnAround( ); // Base case else { // Recursive pattern movingCar.move( ); ricochet(movingCar); movingCar.move( ); }}
Look for this pattern in the other examples of Chapter 8.
An ExerciseAn Exercise
Can you write Can you write ricochet as a new ricochet as a new method of the Car method of the Car class, instead of a class, instead of a separate method?separate method?
You have 2 minutes towrite the implementation.
public void ricochet( ){ . . .
An ExerciseAn Exercise
public void ricochet( ){ if (isBlocked( )) turnAround( ); // Base case else { // Recursive pattern move( ); ricochet( ); move( ); }}
One solution:
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