1. 1 Survey of Computer Science CSCI 110, Spring 2011 Lecture 14 Recursion

2. 2 Recall Divide and Conquer Draw City Draw Building Draw Streets Draw Park Draw Outline Draw Doors Draw Windows Repeat Buildings

3. 3 Recursion Count 10000 votes Count 5000 votes Count 2500 votes When the subproblems are smaller versions of the original problem, we can use recursion to solve the problem.

4. 4 Example Draw stars How to draw n stars using recursion: 1) Draw 1 star 2) Draw (n - 1) stars The first step is trivial, and we can simply write a line of code to do it. The second step is a smaller version of the original problem. A function that can draw n stars can also draw n-1 stars.

5. 5 Diagramming drawStars Draw n stars Draw 1 starDraw n-1 stars Draw 1 starDraw n-2 stars... Draw 0 stars

6. 6 DrawStars in Python #program drawing.py import sys def drawStars( n ): if n < = 0: sys.stdout.write("") #do nothing else: sys.stdout.write("*") drawStars( n - 1) #Begin main program here drawStars(2) Base Case General Case

7. 7 Execution of drawStars dS(2) n if n <=0:... else: sys.stdout.write("*") drawStars(n-1) n if n <=0:... else: sys.stdout.write("*") drawStars(n-1) n if n <=0: sys.stdout.write("") #do nothing else:...

8. 8 Recursive function calls A recursive call is a function call in which the called function is the same as the one making the call. In other words, recursion occurs when a function calls itself! But we need to avoid making an infinite sequence of function calls (infinite recursion).

9. 9 Finding a recursive solution A recursive solution to a problem must be written carefully. The idea is for each successive recursive call to bring you one step closer to a situation in which the problem can easily be solved. This easily solved situation is called the base case. Each recursive algorithm must have at least one base case, as well as the general case.

10. 10 General form for recursion if some easily-solved condition: # base case solution statement(s) else: # general case recursive function call

11. 11 Example: Factorial Definition of Factorial n! = 1 * 2 * 3 * 4 *... * (n-1) * n; 0! = 1 In other words: fact(n) = 1, n = 0 n * fact( n-1), n > 0 fact( n - 1) {

12. 12 Writing Factorial in Python def factorial (n): #we will write this code in class.

13. 13 Execution of factorial fact(2) n if n <= 0: return 1 else: return n * fact(n - 1) n if n <= 0: return 1 else: return n * fact(n - 1) n if n <= 0: return 1 else: return n * fact(n - 1)

14. 14 Invocation tree for factorial Fact( 3) : Fact( 2) : Fact( 1) : Fact( 0) : Trace of Factorial (we will do in class) nFact(n - 1)Fact( n )

15. 15 Rabbit populations: Fibonacci

16. 16 Fibonacci in Python def fib (n): #we will write this code in class.

17. 17 Fibonacci Execution tree

18. 18 How long will this take? For large numbers, each time you increment by 1, it takes about twice as long to compute the Fibonacci result: Fib(32) Fib(31)Fib(30) Suppose our computer can process 10 9 operations per second. How long will it take to compute Fib(100)? (Approximate answer will be given in class).

19. 19 Classes and Objects Python is an object oriented programming language. All items of data are objects. Objects have properties: Things that describe the objects Objects have methods: Things an object can do. A class describes a group of objects that have the same methods and set of properties. Example: A car class Properties: color, number of doors, body type Methods: accelerate, brake, steer My car is an object that is a member of the car class.

20. 20 Using Pre-defined classes Python has many libraries with pre-defined classes that we can use in our programs. Example: The Turtle( ) class. A turtle in python is an object from the Turtle class. Properties: x position, y position, direction, pen position, etc. Methods: forward(distance), backward(distance), left(angle), etc. yertle = Turtle( )#Create a turtle object, identified as yertle yertle.forward(150)#Call the forward( ) method for yertle.

21. 21 Writing a Class definition class Critter: color = "red"#color is a property mood = "happy"#mood is another property def talk(self):#talk is a method print "I am a critter!" def sing(self):#sing is another method print "Tra la la" #main program starts here crit = Critter( ) print crit.color crit.talk( ) crit.sing( )

22. 22 Using self in a class method class Critter: color = "red" mood = "happy" def talk(self): print "I am a " + self.mood + " critter!" crit = Critter( ) crit.talk( ) We can use self to refer to a given object in a class method. Example:

23. 23 The docstring The docstring is used to describe the objects in a class. Example: class Critter: """A virtual pet"""... crit = Critter( ): print crit.__doc__

24. 24 The constructor function We can use a constructor function to initialize properties. Example: class Critter: """A virtual pet""" def __init__(self, clr, md): self.color = clr self.mood = md def talk(self): print "I am a " + self.mood + " critter!" crit = Critter("green", "sad") print crit.color crit.talk( )