week-12-handout

week-12-handout - 1 COMP 202 Introduction to Computing 1...

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Unformatted text preview: 1 COMP 202 Introduction to Computing 1 COMP 202 - Week 12 1 COMP 202 Week 12 Recursion and Runtime Stack Learning outcomes Defining procedures recursively Writing recursive methods Know about the memory organization of a Java program COMP 202 Introduction to Computing 1 COMP 202 - Week 12 2 Recursion COMP 202 Introduction to Computing 1 COMP 202 - Week 12 3 Recursive definition Some concepts can be defined using the concept itself Example: Consider the following list of numbers: 24, 88, 40, 37 Such a list can be defined as A LIST is a: number or a: number comma LIST 2 COMP 202 Introduction to Computing 1 COMP 202 - Week 12 4 Recursive definition Sometimes, mathematical functions can be defined in terms of the same function Example n! = n * (n-1)! 0! = 1 How would you compute factorial, based on this definition? 5! = 5 * 4! = 5 * (4 * 3!) = 5 * (4 * (3 * 2!)) = 5 * (4 * (3 * 2 * (1!))) = 5 * (4 * (3 * 2 * (1 * (0!)))) Where would you stop! Yes, you have the definition of a special case. 0! = 1 5! = 5 * (4 * (3 * 2 * (1 * (1)))) The special case is called base case COMP 202 Introduction to Computing 1 COMP 202 - Week 12 5 Factorial.java public class Factorial { public static int factorial (int n ){ /* Basis condition */ if (n == 0) return 1; else return n * facotrial ( n-1); } public static int facotrial2 (int n){ /* calculate factorial in iterative manner */ int fact = 1; for (int i=1; i < n; i++){ fact = fact * i; } } public static void main (String args) { int X = 6; int factX = factorial (X); System.out.printf(Factorial of %d is %d\n, X, factX); factX = factorial2(X); System.out.printf(Factorial of %d is %d\n, X, factX); } } COMP 202 Introduction to Computing 1 COMP 202 - Week 12 6 Recursion Sometimes a procedure to solve a problem can be defined by applying the same procedure on parts of the problem Example: Reverse the String [0(L-1)] Reverse the String [1(L-1)] put the charAt(0) at the end 3 COMP 202 Introduction to Computing 1 COMP 202 - Week 12 7 StringReverse.java public class StringReverse { public static String reverse ( String s ){ if (s.length() <= 1) return s; else return reverse ( s . subString(1) )+s.charAt(0); } public static void main (String args) { Scanner kb = new Scanner(System.in); System.out.print(Enter String to reverese: ); String str = kb.next(); System.out.println( reverse ( str )); } } Sample output: $java StringReverese Enter String to reverse: Harry yrraH $ COMP 202 Introduction to Computing 1 COMP 202 - Week 12 8 Recursion Very often a recursive program is much simple than an iterative program Two things about a recursive function or method Recurrence relation Basis condition In the previous example: Recurrence relation: Reverese(string [0 to (L-1)]) is equivalent to Reverse(substring[1 to L-1]) appended with charAt(0) Basis condition: Reverse of a string with 1 letter is itself...
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This note was uploaded on 06/28/2008 for the course COMP 202 taught by Professor Verbrugge during the Fall '07 term at McGill.

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week-12-handout - 1 COMP 202 Introduction to Computing 1...

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