ESC101: Fundamentals of Computing End-Semester Exam

Transcription

1 ESC101: Fundamentals of Computing End-Semester Exam Time:3 hours, MM:120 marks May INSTRUCTIONS: 1. Write all answers ON THE QUESTION PAPER ITSELF either in the blanks provided or in the space next to/after the question. If you really need more space then write on the reverse side (but avoid as far as possible). 2. The paper has EIGHT questions 1. Consider the classes: /** defines imaginary numbers a+ib */ class Imaginary double a, b; /** defines a pair of imaginary numbers */ class ImaginaryPair Imaginary x1, x2; ImaginaryPair (Imaginary x, Imaginary y) x1 = x; x2 = y; public static void test() Imaginary x = new Imaginary (); x.a += 12; ImaginaryPair q = new ImaginaryPair(x,x); q.x1.a += 5; System.out.println(q.x2.a); // A // B // C a. Does the code give an error at line B? If so, is it at compile time or run time? [2] Page 1 of 14

2 b. What is the value printed at line C? [2] c. What would be printed if line C reads [1] System.out.println(x.a); d. what improvements can you suggest around line A? [2] e. What happens in test() when this constructor is added to class Imaginary Imaginary (double a,double b) this.a = a; this.b = b; [1] f. Given the addition of part (e), fill in the missing lines in this code: [7] public static ImaginaryPair solvequadratic (double a, double b, double c) double real = -b/(2*a); double D = b*b- 4*a*c; Imaginary q1,q2; if( D 1 0 ) double a1= real + Math.sqrt(D)/2*a; double a2= real - Math.sqrt(D)/2*a; q1 = 2 ; q2 = 3 ; Page 2 of 14

3 else double img= 4 ; q1 = 5 ; q2 = 6 ; return 7 ; Fill in the following: 1 : 2 : 3 : 4 : 5 : 6 : 7 : 2. Estimate the running times for each code segment. Use the big-o notation in terms of n. Assume "a" is a variable of suitable type. [ ] a) for (i=1; i<=n; i++) for(j=1; j<=10; j++) for(k=1; k<=n; k++) a += i + j + k; b) int i = 2; while(i<n) for(j=i; j<=n; j++) a[i][j]++; i = 2*i; Page 3 of 14

4 c) void comp(int[] a) int n= a.length; while( n > 1) for(int i=0 ; i<n/2; i++) if(i+n/2 < a.length ) a[i] += a[i+n/2]; n=n/2; d) static int[] f = new int[max]; int test(int n) // n less than MAX if(n==0 n==1) f[n]=1; else if(f[n] == 0) f[n]= test(n-1) + test(n-2); return f[n]; e) What does the function test() do? [1] f) Given f(n) = 2n 6 + n , find the simplest g(n) such that f(n)= O(g(n)) and the bound is tight. [2] Page 4 of 14

5 3. The class below defines a doubly linked list. The figure below shows how a doubly linked list looks (list with only two elements). Basically, a node in the list points to the next node, as well as the previous node. NIL is the special null element for this class. The predecessor of the first node is NIL, similarly the successor of the last filled node is NIL. [4 x ] NIL DATA DATA NIL public class DLL public static final DLL NIL=new DLL(); private DLL next; private DLL prev; private Object data; private DLL() //part a : write this part here public DLL(Object o) data=o; prev=nil; next=nil; public DLL insert(object o, int n) /* Assume n is 0 or more. if n==0 then inserts o at the beginning. if n>=length of list, inserts o at the end. Otherwise inserts o after the nth element, where the first element is counted as 1 (not 0). */ DLL newdll=new DLL(o); if (n==0) //part b : write this part here else if (n>=this.length()) DLL last=this.getlast();//gets last non NIL element last.next=newdll; //part c : write this part here else DLL temp=this; for (int i=1;i<n;i++) temp=temp.next; newdll.next=temp.next; //part d : write this part here Page 5 of 14

6 return(newdll); a) Assuming that both length() and getlast() have been defined in the class, fill in code for the locations marked by comments part a, part b, part c, part d so that everything works correctly. [4x3] b) Why is the constructor without any arguments defined as private? [1] c) Assuming the class has a print() function which prints out the doubly linked list starting from the beginning of this what would be the output if the following code fragment is executed? [2] DLL a=new DLL(new Integer(1)); DLL b=new DLL(new Integer(10)); a.insert(new Integer(2),4); a.print(); a.insert(new Integer(3),0); a.print(); b.insert(new Integer(9),3); b=b.insert(new Integer(8),0); b.print(); Page 6 of 14

7 4. Consider the following class/interface definitions: public interface I1 void f1(int i); public abstract class A implements I1 public void f(int j) System.out.println("f In A "+j); a) Assuming I1 has compiled will A compile. If your answer is No, give the reason. [2] b) The following classes and interfaces are added public interface I2 void f1(int i); public class B extends A implements I2 public void f1(int k) System.out.println("f1 in B "+k); public static void test() B b = new B(); I1 a = new C(); I1 a1 = new B(); b.f1(10); ((A)a1).f1(11); a.f1(12); a.f(13); ((A)a).f(14); public class C implements I1 public void f1(int g) System.out.println("f1 in C "+g); Assuming I1, A have compiled, will I2, B, C compile? If no, give all the errors and reasons for those errors. [2] c) Assuming everything has been compiled (after commenting out erroneous lines, if needed) function test is executed. What happens? [4] Page 7 of 14

8 d) Suppose class C now in addition extends A, what will be the output on executing test, assuming once again the erroneous lines are commented out, if needed. [4] e) Will the following interface definition compile, if your answer is no give the error(s): [3] public interface I void f1(); int f2(string s); static void f3(int i); 5. Here is a variant of the Regula-falsi method to solve an equation in one variable, refer to the figure below. f(x) 2 4 x 1 3 It starts with two initial guesses (x-coordinates of points 1 and 2 in the figure above). The point of intersection of the secant (dashed line) joining points 1 and 2 with the x-axis, is determined (say x'). The next point on the curve which is used for drawing the secant will be (x', f(x')). This is point 3 in the figure above. Now the secant will be drawn between points 2 and 3 to give point 4. Unlike regula-falsi the two y values need not have opposite signs. This process is continued till the stopping criterion is met. This method is not guaranteed to find the root if one exists. It can diverge. Below assume that class F is defined and F.f(double x) calculates the function. a) Write the formula for x n+1 assuming the previous two points are (x n-1, y n-1 ) and (x n, y n ). b) Define the exception class that you will use to handle cases when it does not converge. Page 8 of 14

9 c) Assuming that the stopping criterion is x n+1 - x n / x n+1 < EPSILON (a constant defined in the class), write the main loop for the formula in a). You need not handle exceptions here. d) Briefly, say how you will determine that the method is diverging, so that the exception can be raised. [3, 4, 4, 4] 6. Here is an implementation of a binary tree: public class BinaryTree public static final BinaryTree NULL= new BinaryTree(); private Object data; private BinaryTree left, right; private BinaryTree() data=null; left=this; right=this; public BinaryTree(Object o) data=o; left=null; right=null; public boolean isempty() return(this==null); Page 9 of 14

10 public boolean isleaf() return(left==null && right==null); a. Sketch the tree resulting from this code: [3] BinaryTree l,r,t; t=new BinaryTree(new Integer(4)); // A l=new BinaryTree(new Integer(2)); r=new BinaryTree(new Integer(7)); t.left= l; t.right = r; l=t; t=new BinaryTree(new Integer(5)); t.left = l; t.right = NULL; [NOTE: This code cuts corners; in practice you should define methods like getlefttree() and insertlefttree() etc.] b. Explain the argument "new Integer(7)" in line A. [1] c. Consider this function for finding the height of the tree. (height of a single node tree = 0) [3] public int height() if (isleaf()) return( 1 ); else return(1+math.max( 2, 3 ); Fill in the following: 1 : 2 : 3 : d. Using the three following statements: [4] ll = left.preorder(); rr = right.preorder(); pp = System.out.print(((Integer)data).intValue()+" "); Page 10 of 14

11 define the traversal function: public void preorder () if ( 4 ) // statements pp, ll and rr come here. e. Define this function which returns true if the tree is a sorted binary tree (i.e. left.data <= root.data <= right.data) for all nodes. Assume that compare(d1,d2) returns -1,0,+1 if d1 is less, equal or greater respectively. [4] public boolean issorted () if ( ) // fill this code // insert code here: return true; Page 11 of 14

12 7. a) How many lines of output will be generated by the Java program segment: [6x1.5 = 9] for (index = 0; index < 4; index++) for (count = 0; count < index; count++) System.out.println(index); What if anything, is wrong with the following: b) interface Taxable double taxrate = 0.06; double calculatetax(); c) Vector v = new vector(); v.add(0.0); // the first element in the vector is 0.0 d) Is it alright if a class implements two interfaces, each of which has the same definition for the constant PI? e) Here is a method definition: int compute( int a, double y).... Which of the following has a different signature? a. int compute( int sum, double value).... b. double compute( int a, double y).... c. double compute( int sum, double y).... d. int compute( int a, int y).... f) Assume that a recursive method has made several recursive calls to itself. Which of the following is TRUE? a. There are many copies of the local variables of the recursive method. b. There must be a single return statement in the recursive method. c. The recursive method must have at least one argument. d. The recursive method must call itself again. Page 12 of 14

13 h) In each of the following cases, explain the effect of the keyword "final", and provide an example where its use would be appropriate. [3x2] a. final int a = 3; b. final void a()... c. final class A a. When invoked from the command line, what does class A do? [2] class A public static void main (String[] args) for (int i = 0; i < args.length; i++) System.out.print (args[i] + " "); System.out.println(); b. Consider this code fragment: [2] import java.util.date; class joindate public static int findage(date birthday) Date today = new Date(); System.out.println(today);... other code follows. How can you re-write the same class without an "import" statement? c. Suppose we have a comparison function [2] int compare(object o1, Object o2) which returns -1, 0, 1 depending on whether o1 is less, equal to or greater than o2. Write the expression which uses the compare function to compare two int variables x and y. Page 13 of 14

14 d. Will the following class definition compile, if your answer is no give the error(s): [2] private class P Marks Tally e. Write the expression which will convert f defined by String f = "7.532"; to a float number. [2] g. What is the output of test(5) in class A below? [4] class A int x; void test(int x) System.out.println("x="+x); int y=2*x; int z=this.x; int u=3*y; int w=4; TOTAL: System.out.println("y="+y); System.out.println("z="+z); System.out.println("u="+u); int w=20; System.out.println("w="+w); System.out.println("w="+w); //A h. What happens when you add this line just after line A? [1] double y = 3; Page 14 of 14