Computer Science 112a
Fall 2004
Ileana Streinu

Name:

112a-ax account:

The exam is open book: you may consult your notes, books. But all the work should be yours.

Show all your work: you may get partial credit. Add extra sheets if necessary.

1. (10 points) Allocation of memory for variables. Given the following Java program, specify where each variable will be allocated, and when. Write the answers next to each variable in the program.
   
   class Test{
   
   static int x,y,z;
   
   public static void main()
   
   int a,b;
   a=func(x,y,z,b);
   }
   int func(int a,b,c,d)
   {
   int x,y;
   ...
   }
   }
   

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2. (5 points) Stacks and Queues. Give a convincing but short argument for or against using stacks to store:
   
   • The requests sent to the printer.
     
     
     
     
     
   • The orders received by an on-line business.
     
     
     
     
     
   • The paper sheets as they are fed into a (real) printer.
     
     
     
     
     

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3. (20 points) Definition, allocation and access of variables in Java.
   • (5 points) Given the class definition (class variables only) for the Node of an arbitrary tree (no restriction on the number of children, String information, with parents):
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   • (5 points) Then, give basic Java code to create the tree structure below. I.e. define and allocate nodes, and give code to link them into the tree structure. Put the code into a default constructor.
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
   • (3 points) Write a Java statement to set to Alice the value of the info field of the grand-parent of node G.
     
     
     
     
     
     
     
     
     
     
   • (3 points) Write a Java statement to change the parent of the node H to be the node C. You should program this according to the specifications, i.e. do not make use of the fact that you happen to know who is the parent of the node H.
     
     
     
     
     
     
     
     
     
     
   • (4 points) Write Java statements to make all the descendents of node C to aquire a new child each.
     
     
     
     
     
     
     
     
     
     

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4. (37 points) Java and C++ pointers.
   Given the following C++ class definition:
   
   class BNode{
   int x;
   BNode* y;
   BNode* z;
   };
   
   and the following definitions of variables:

   BNode a1, *a2, a3[5];
   BNode* b4[10];

   • (1 point each) Which of the following is a valid C++ expression? Cross the invalid expressions.
     
     1. a2-> y . z
     2. a3[2].x ->x
     3. a2->z
     4. a4[2]->z->y->y.z
     5. a1.y
     6. a2.z
     7. a3[2].x
     8. a1.y.z
     9. a1.y -> z
     10. a1 -> z
     11. a2.y -> z
     12. a2->y ->y
     13. a3[2].x.z
     14. b4[5].y->z
     15. b4[5]->y->z->z
     16. b4[5]->y->z->z->x
     17. a3[2]->z->y
     
     
     
     
     
     
   • (10 points) Java pointers Redefine the class in Java and rewrite all the correct statements above in Java.
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

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5. (8 points) Recursion. Write a short recursive Java function (NOT a whole program!!!) to compute the minimum element in a binary search tree.

The program should use the representation of a binary (search) tree as a pointer to the root node, where a tree node is a Java structure defined as:

class TreeNode{
int data;
TreeNode left;
TreeNode right;
}

Name your function minTree. It should take as argument the root and return an integer (the minimum value). Design the function as a separate entity, not as part of some binary tree class.

If the recursive definition seems elusive but you have other ideas for solving this problem, I also accept other solutions. Warning: an iterative solution may not be easy to produce.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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6. (5 points) Stacks and recursion. Trace the stack behavior for the following recursive function call. What is the value printed in the main function?
   
   main()
   {
   int a = func(2,2);
   System.out.println(a);
   }
   
   
   int func(int a, int b)
   { if (a==0 || b== 0) return 1;
   return func(a, b-1)*func(a-1, b);
   }
   
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    

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7. (6 points) Graphs. Given the graph:

• (2 points)Write the adjacency list representation for the graph, with each adjacency list sorted increasingly by the vertex number.





















• (2 points) Starting from vertex A, list the vertices of the graph in the order in which they are visited by a depth-first search algorithm.

 

 
 
 
 
 
 
 

• (2 points) Starting at vertex A, list the vertices in the order in which they are visited by a breadth-first search algorithm.

 
 
 
 
 
 
8. (3 points) Tree Traversal. Given the following binary tree:


Write down the vertices of the tree in prefix, infix and postfix order.
 
 
 
 
 
 
 
 
 
 

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9. (6 points) Binary Search Trees and Sorting. Sort the list of numbers {15, 3, 12, 5, 1, 14, 2, 9, 7} using binary search trees.
• Step 1:construct the binary search tree.
• Step 2: traverse the tree in the appropriate order (and specify which one).

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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Enjoy your winter break :-) Ileana