Computer Science 112a
Fall 2000
Ileana Streinu

Name:

112a-ax account:

The exam is open book: you may consult your notes, books, even computer programs that you have written before. But all the work should be yours.

Show all your work: you may get partial credit. Write legibly in the space allocated to each question, or, if necessary, on the back of the preceeding page. If necessary, you can use extra sheets. Answer all 9 questions (summing up to 100 points).

1. (3 points) Write the arithmetic expression tree for the following arithmetic expression: (((2+3)-(2*5))/(3-(4+5)))
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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2. (3 points) What type of traversal of an arithmetic expression tree would you perform to get the following expression: 2244+*-32+* ? Draw the arithmetic expression tree corresponding to this expression.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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3. (9 points)
   • (3 points) Draw the double linked list structure, using the box notation, for the following list: {a, d, e, g,h}, and give the struct definition for a node of this list.
   
   
   
   
   
   
   
   
   
   
   
   
   
   • (3 points) Show the modification of the links when the new item f is inserted in alphabetical order in this list (i.e. after the element e). Assuming that you have access to the list through a variable head pointing to the first node, write the C++ instructions that would perform this insertion. I mean: do not write a class function and do not call a class function from the list class - just write the few C++ instructions that would insert this particular element in this particular list, using well known ways to access fields of a struct (i.e. using dot and/or arrow notation). Try to use additional temporary variables (besides head) only if strictly necessary.
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
   • (3 points) Show the modification of the links when the item e is removed from the list, and write the C++ instructions that perform this deletion. Just like in the previous case, do not use additional variables unless really necessary and rely only on elementary dot and/or arrow notation.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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4. (15 points) Given the following code:


struct SNode{
int info;
SNodePtr parent;
};
typedef SNode* SNodePtr;

main()
{
SNode a1, a2, a3, a4;
SNodePtr b;
b = &a1;
a1.info = 1; a2.info = 2; a3.info = 3; a4.info = 4;
a1.parent = new SNode;
a2.parent = &a1;
a3.parent = &a2;
a4.parent = &a1;
b->parent->parent = NULL;
b->parent->info = 0;
}
 

• (5 points) Draw a "box and arrow" structure corresponding to the set of SNode's created by this program and fill in all the information and pointers as done by the program.

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• (2 points) Write a C++ statement to set to 10 the value of the info field of the parent of a1.

 

 
 
 
 
 
 

• (3 points) Write a C++ statement to change the parent of a3 to be a4.











• (5 points) If you remove the node created with new in the previous program, what will you create (circle all that apply)?
  • a memory leak
  • a dangling pointer
    
    

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5. (34 points) Given the following structure definition:


struct BNode{
int a;
BNodePtr b;
BNodePtr c;
};
typedef BNode* BNodePtr;
and the following definitions of variables:

BNode n1, *n2, n3[5];
BNodePtr n4[10];

Which of the following is a valid C expression? (2 points each) Cross the invalid expressions.
 

1. n1 -> a
2. n1.a
3. n2.a
4. n2->a
5. n1.b.b
6. n1.b -> b
7. n2.b -> b
8. n2->b ->b
9. n2-> b . b
10. n3[2].c
11. n3[2].c ->a
12. n3[2].c.a
13. n3[2]->c->a
14. n4[5].b->a
15. n4[5]->b->a
16. n4[5]->b->c->a
17. n4[2]->c->b->b.a

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6. (12 points) Write a short recursive C++ function (NOT a whole program!!!) to compute the length of a list. Call it Length. The list is given by a pointer to its first element, i.e. your function has one argument, which you may head). Do NOT write this function as a class function in some List class.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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7. (10 points) Given the graph:
   
   
   
   • (2 points)Write the adjacency list representation for the graph. Assume that the nodes are inserted in the vertex array in alphabetical order, that the information stored with each vertex is its one-letter "name", and that the adjacency lists are stored in sorted order (increasing) of the vertex number.
      

      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      

   • (2 points) Write the adjacency list representation for the underlying undirected graph. Assume that the nodes are inserted in the vertex array in alphabetical order, that the information stored with each vertex is its one-letter "name", and that the adjacency lists are stored in sorted order (increasing) of the vertex number.
      

      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      

   • (3 points) Starting from vertex A, list the vertices of the original directed graph in the postfix order in which they are visited by a depth-first search algorithm. Assume that the visit function lists the data in each node (not the index of the vertex) as it visits it.
      

      
      
      
      
      
      
      

   • (3 points) Starting at vertex A, list the vertices of the underlying undirected graph in the order in which they are visited by a breadth-first search algorithm. Assume that the visit function lists the data in each node, as it visits it.
   
    
    
    
    
    
    

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8. (8 points) What is the following recursive function computing? You can answer with a mathematical formula or explain in English (in no more than two lines) what it is doing.
   
   int funct(int a[], int n)
   { if (n == 1) return(a[0]);
   else return ( a[n-1] + funct(a,n-1));
   }
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   Now trace the stack behavior for the following function call:
   funct(b, 3) , where the array b contains the numbers 2,5,3 stored in this order.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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9. (6 points) Sort the list of numbers {5, 7, 2, 6, 8, 4, 1, 3, 9} 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 the winter break :-) Ileana