Sample Data Structures Questions

Sample Data Structures Questions
Chapter 7
Stacks

Data Structures and Other Objects Using C++
by Michael Main and Walter Savitch
Second Edition ISBN 0-201-70297-5, Softcover, 816 pages, 2000

The Purpose of These Questions

These are typical exam questions from Chapter 7 of the textbook. These exact questions might not be on your exam, but if you research and find the right answers to these questions, that should be good preparation for a real exam. (It's also possible that some of this material was not covered in your class.) There are 6 short answer questions and 16 multiple choice questions in this file.

Short Answers

Short Answers
Sections 7.1 - 7.2
Stacks and Their
Applications

Explain what modifications would be needed to make the parenthesis matching algorithm check expressions with different kinds of parentheses such as (), [] and {}'s.

Complete the body of this function. You do not need to check the precondition. You may use the stack template class.


  bool balanced(const char p[ ], size_t n)
  // Precondition: p[0]...p[n-1] contains n characters, each of which
  // is '(', ')', '{' or '}'.
  // Postcondition: The function returns true if the characters form a
  // sequence of correctly balanced parentheses with each '(' matching
  // a ')' and each '{' matching a '}'. Note that a sequence such as
  // ( { ) } is NOT balanced because when we draw lines to match the
  // parentheses to their partners, the lines cross each other. On the
  // other hand, ( { } ) amd { ( ) } are both balanced.

Short Answers
Section 7.3
Implementations of
the stack ADT

I am going to execute this code with THREE pushes and ONE pop:


   stack<int> s;
   s.push(1);
   s.push(2);
   s.push(3);
   s.pop( );

Suppose that s is represented by a partially filled array. Draw the state of the private member variables of s after the above code:


           _______            __________________________________
      used|       |      data|      |      |      |      |      |
          |_______|          |______|______|______|______|______|
                               [0]    [1]    [2]    [3]    [4]

I am going to execute this code with THREE pushes and ONE pop:
```
   stack<int> s;
   s.push(1);
   s.push(2);
   s.push(3);
   cout << s.pop( );
```
Suppose that s is represented by a linked list. Draw the state of the private member variables of s after the above code:
_______ head_ptr| | |_______|

Short Answers
Section 7.4
More Complex
Stack Applications

Implement the following function. You may use the stack template class and the stack operations of push, pop, peek, is_empty, and size. You may also use cin.peek( ) and use "cin>>i" to read an integer.


   int evaluate_postfix_from_cin( )
   // Precondition (Which is not checked): The next input line of cin is a
   // properly formed postfix expression consisting of integers, 
   // the binary operations + and -, and spaces. 
   // Postcondition: The function has read the next input line (including
   // the newline) and returned the value of the postfix expression.
   {
      int i;
      stack<int> s;

Consider the usual algorithm to convert an infix expression to a postfix expression. Suppose that you have read 10 input characters during a conversion and that the stack now contains these symbols:
```
              |       |  
              |   +   |  
              |   (   |  
       bottom |___*___|     
```
Now, suppose that you read and process the 11th symbol of the input. Draw the stack for the case where the 11th symbol is:
A. A number:
B. A left parenthesis:
C. A right parenthesis:
D. A minus sign:
E. A division sign:

Multiple Choice

Multiple Choice
Sections 7.1-7.2
Stacks and Their
Applications

Entries in a stack are "ordered". What is the meaning of this statement?

A. A collection of stacks can be sorted.

B. Stack entries may be compared with the '<' operation.

C. The entries must be stored in a linked list.

D. There is a first entry, a second entry, and so on.

The operation for adding an entry to a stack is traditionally called:

A. add

B. append

C. insert

D. push

The operation for removing an entry from a stack is traditionally called:

A. delete

B. peek

C. pop

D. remove

Which of the following stack operations could result in stack underflow?

A. is_empty

B. pop

C. push

D. Two or more of the above answers

Which of the following applications may use a stack?

A. A parentheses balancing program.

B. Keeping track of local variables at run time.

C. Syntax analyzer for a compiler.

D. All of the above.

Consider the following pseudocode:


   declare a stack of characters
   while ( there are more characters in the word to read )
   {
      read a character
      push the character on the stack
   }
   while ( the stack is not empty )
   {
      write the stack's top character to the screen
      pop a character off the stack
   }

What is written to the screen for the input "carpets"?

A. serc

B. carpets

C. steprac

D. ccaarrppeettss

Here is an INCORRECT pseudocode for the algorithm which is supposed to determine whether a sequence of parentheses is balanced:


   declare a character stack 
   while ( more input is available)
   {
      read a character
      if ( the character is a '(' ) 
         push it on the stack
      else if ( the character is a ')' and the stack is not empty )
         pop a character off the stack
      else
         print "unbalanced" and exit
    }
    print "balanced"

Which of these unbalanced sequences does the above code think is balanced?

A. ((())

B. ())(()

C. (()()))

D. (()))()

Consider the usual algorithm for determining whether a sequence of parentheses is balanced. What is the maximum number of parentheses that will appear on the stack AT ANY ONE TIME when the algorithm analyzes: (()(())(()))?

A. 1

B. 2

C. 3

D. 4

E. 5 or more

Consider the usual algorithm for determining whether a sequence of parentheses is balanced. Suppose that you run the algorithm on a sequence that contains 2 left parentheses and 3 right parentheses (in some order). What is the maximum number of parentheses that will ever appear on the stack AT ONE TIME during the computation?

A. 1

B. 2

C. 3

D. 4

E. 5 or more

Multiple Choice
Section 7.3
Implementations of
the stack ADT

Suppose we have an array implementation of the stack class, with ten items in the stack stored at data[0] through data[9]. The CAPACITY is 42. Where does the push member function place the new entry in the array?

A. data[0]

B. data[1]

C. data[9]

D. data[10]

Consider the implementation of the stack using a partially-filled array. What goes wrong if we try to store the top of the stack at location [0] and the bottom of the stack at the last used position of the array?

A. Both peek and pop would require linear time.

B. Both push and pop would require linear time.

C. The stack could not be used to check balanced parentheses.

D. The stack could not be used to evaluate postfix expressions.

In the linked list implementation of the stack class, where does the push member function place the new entry on the linked list?

A. At the head

B. At the tail

C. After all other entries that are greater than the new entry.

D. After all other entries that are smaller than the new entry.

In the array version of the stack class (with a fixed-sized array), which operations require linear time for their worst-case behavior?

A. is_empty

B. peek

C. pop

D. push

E. None of these operations require linear time.

In the linked-list version of the stack class, which operations require linear time for their worst-case behavior?

A. is_empty

B. peek

C. pop

D. push

E. None of these operations require linear time.

Multiple Choice
Section 7.4
More Complex
Stack Applications

What is the value of the postfix expression 6 3 2 4 + - *:

A. Something between -15 and -100

B. Something between -5 and -15

C. Something between 5 and -5

D. Something between 5 and 15

E. Something between 15 and 100

Here is an infix expression: 4+3*(6*3-12). Suppose that we are using the usual stack algorithm to convert the expression from infix to postfix notation. What is the maximum number of symbols that will appear on the stack AT ONE TIME during the conversion of this expression?

A. 1

B. 2

C. 3

D. 4

E. 5

Data Structures and Other Objects Using C++

Michael Main (main@colorado.edu)
and
Walter Savitch (wsavitch@ucsd.edu)