Recursion

1
Recursion

• similar to iteration in that you repeatedly do a
  little bit of the task and then loop again and
  work on a smaller piece - eventually reaching
  your goal
• accomplished by a method invoking itself!
• so, if it invokes itself - then lets think about
  that - how do you think its going to stop???

2
Recursion

• Iteration
• public void pickAll()
• while (nextToABeeper())
• pickBeeper()

Recursion public void pickAll() if (!
nextToABeeper() return pickBeeper()
pickAll()
This recursive definition goes like this Are
there any beepers left on this corner? No - then
were done. Yes - then pick one beeper and then
pickAll.
3
Recursion

• The key to recursion
• we dont define a problem in terms of exactly
  itself - we define the problem in terms of a
  smaller/simpler (yet very closely related)
  problem - also, we define the simplest/smallest
  situation separately.
• in the previous problem we define the simplest
  situation to be there are no beepers on the
  corner - this becomes our base case
• otherwise, we have more work to do - so we solve
  a tiny part of the problem (pickBeeper) and then
  invoke ourself to finish the smaller (yet
  related) problem - this becomes our
  general/recursive case.

4
You Try!

• write a recursive method called goToSouthWall
• precondition bot is already facing south - there
  are no walls in the way
• postcondition bot is at the south wall still
  facing south - it is still on the same avenue
• What are preconditions postconditions?

the things that need to be true in order for the
method to perform its task - the contract between
the client and the method
what will be true after the method has finished
executing - only guaranteed if the preconditions
are met
5
Writing Recursive Methods - the Process

• The process for writing recursive robot
  instructions is very similar to that for writing
  loops
• Step 1 Consider the stopping condition (also
  called the base case)--what is the simplest case
  of the problem that can be solved? In the pickAll
  problem, the simplest, or base, case is when the
  robot is already on an empty corner.

6
the Process - contd

• Step 2 What does the robot have to do in the
  base case? In this example there's nothing to do.
  
• Step 3 Find a way to solve a small piece of the
  larger problem if not in the base case. This is
  called "reducing the problem in the general
  case." In the pickAll problem, the general case
  is when the robot is on a corner with one or more
  beepers and the reduction is to pick up a beeper.

7
the Process - contd

• Step 4 Make sure the reduction leads to the base
  case. Again, in the above example of pickAll, by
  picking up one beeper at a time, the robot must
  eventually clear the corner of beepers,
  regardless of the original number present.

8
Iteration vs. Recursion

• An iterative loop must complete each iteration
  before beginning the next one.
• A recursive method typically begins a new
  instance before completing the current one. When
  that happens, the current instance is temporarily
  suspended, pending the completion of the new
  instance. Of course, this new instance might not
  complete before generating another one. Each
  successive instance must be completed in turn,
  last to first.

9
Iteration vs. Recursion

• Since EACH recursive instance is supposed to make
  some (often minimal) progress toward the base
  case, we should not use loops to control
  recursive calls. Thus, we will usually see an IF
  or an IF/ELSE in the body of a recursive method,
  but not a WHILE.

10
Follow the steps and write the method

• Use recursion to move a robot named Karel to a
  beeper. Follow the steps presented earlier
• Step 1 What is the base case?
• Karel is on the beeper.
• Step 2 What does the robot do in the base case?
• Nothing.
• Step 3 What is the general case?
• The robot is not on the beeper.

11
writing the recursive method - contd

• Step 4 What is the reduction (what do we do in
  the general case)?
• Move toward the beeper and make the recursive
  call.
• Does the reduction lead to termination? Yes,
  assuming the beeper is directly in front of the
  robot, the distance will get shorter by one block
  for each recursive call. By the way, this
  assumption becomes the precondition(i.e., there
  is a beeper somewhere in front of the bot).

12
Why Recursion?

• there are problems which are much easier to solve
  using recursion
• Problem the Lost Beeper Mine
• Karel is facing East and there is a beeper
  somewhere in front of her. Directly North of that
  beeper there is a Beeper Mine (a corner with a
  large number of beepers on it). The Beeper Mine
  is exactly the same number of corners North of
  the single beeper as Karel is away from the
  single beeper at the beginning. Get Karel to the
  Beeper Mine! Try this without recursion.

13
lets write it

• Step 1 What is the base case?
• Karel is on the beeper
• Step 2 What does Karel have to do in the base
  case?
• turnLeft (this will face Karel north)
• Step 3 What is the general case?
• Karel is not on the beeper

14
lets write it

• Step 4 What is the reduction?
• Move one block forward, make the recursive call
  and have Karel execute a second move after the
  recursive call. This second move will be executed
  in all instances but the base case, causing Karel
  to make as many moves north after the base case
  as it did in getting to the base case.
• Now, code it before we go on

15
Lost Beeper Mine solution

• public void findMine()

lets trace the execution