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## Answers for Quiz on Chapter 9

This page contains sample answers to the quiz on Chapter 9 of Introduction to Programming Using Java. Note that generally, there are lots of correct answers to a given question.

Question 1: | Explain what is meant by a recursive subroutine.
Answer: | A recursive subroutine is simply one that calls itself either directly or through a chain of calls involving other subroutines.
Question 2: | Consider the following subroutine:
    static void printStuff(int level) {
        if (level == 0) {
           System.out.print("*");
        }
        else {
           System.out.print("[");
           printStuff(level - 1);
           System.out.print(",");
           printStuff(level - 1);
           System.out.println("]");
        }
    }
Show the output that would be produced by the subroutine calls printStuff(0), printStuff(1), printStuff(2), and printStuff(3).
Answer: | The outputs are:
    printStuff(0) outputs:   *
    printStuff(1) outputs:   [*,*]
    printStuff(2) outputs:   [[*,*],[*,*]]
    printStuff(3) outputs:   [[[*,*],[*,*]],[[*,*],[*,*]]]
(Explanation: For printStuff(0), the value of the parameter is 0, so the first clause of the if is executed, and the output is just *. For printStuff(1), the else clause is executed. This else clause contains two recursive calls to printStuff(level-1). Since level is 1, level-1 is 0, so each call to printStuff outputs a *. The overall output from printStuff(1) is [*,*]. In a similar way, printStuff(2) includes two recursive calls to printStuff(1). Each call to printStuff(1) outputs [*,*]. And printStuff(2) just takes two copies of this and puts them between [ and ] separated by a comma: [[*,*],[*,*]]. Finally, the output from printStuff(3) outputs two copies of [[*,*],[*,*]] separated by a comma and enclosed between brackets. Once you recognize the pattern, you can do printStuff(N) for any N without trying to follow the execution of the subroutine in detail.)
Question 3: | Suppose that a linked list is formed from objects that belong to the class
    class ListNode {
       int item;       // An item in the list.
       ListNode next;  // Pointer to next item in the list.
    }
Write a subroutine that will count the number of zeros that occur in a given linked list of ints. The subroutine should have a parameter of type ListNode and should return a value of type int.
Answer: | I'll give both a non-recursive solution and a recursive solution. For a linked list, the recursion is not really necessary, but it does nicely reflect the recursive definition of ListNode
    static int countZeros( ListNode head ) {
       int count;        // The number of zeros in the list.
       ListNode runner;  // For running along the list.
       count = 0;
       runner = head;    // Start at the beginning of the list.
       while (runner != null) {
          if ( runner.item == 0)
             count++;  // Count the zero found in the current node.
          runner = runner.next;  // Advance to the next node.
       }
       return count;
    }

    static int countZerosRecursively( ListNode head ) {
       if ( head == null) {
              // An empty list does not contain any zeros.
           return 0;
       }
       else {
           int count = countZerosRecursively( head.next );  // Count zeros in tail.
           if ( head.item == 0 )
               count++;  // Add 1 to account for the zero in the head node.
           return count;
       }
    }
Question 4: | What are the three operations on a stack?
Answer: | The three stack operations are push, pop, and isEmpty. The definitions of these operations are: push(item) adds the specified item to the top of the stack; pop() removes the top item of the stack and returns it; and isEmpty() is a boolean-valued function that returns true if there are no items on the stack.
Question 5: | What is the basic difference between a stack and a queue?
Answer: | In a stack, items are added to the stack and removed from the stack on the same end (called the "top" of the stack). In a queue, items are added at one end (the "back") and removed at the other end (the "front"). Because of this difference, a queue is a FIFO structure (items are removed in the same order in which they were added), and a stack is a LIFO structure (the item that is popped from a stack is the one that was added most recently).
Question 6: | What is an activation record? What role does a stack of activation records play in a computer?
Answer: | When a subroutine is called, an activation record is created to hold the information that is needed for the execution of the subroutine, such as the values of the parameters and local variables. This activation record is stored on a stack of activation records. A stack is used since one subroutine can call another, which can then call a third, and so on. Because of this, many activation records can be in use at the same time. The data structure is a stack because an activation record has to continue to exist while all the subroutines that are called by the subroutine are executed. While they are being executed, the stack of activation records can grow and shrink as subroutines are called and return.
Question 7: | Suppose that a binary tree of integers is formed from objects belonging to the class
    class TreeNode {
       int item;       // One item in the tree.
       TreeNode left;  // Pointer to the left subtree.
       TreeNode right; // Pointer to the right subtree.
    }
Write a recursive subroutine that will find the sum of all the nodes in the tree. Your subroutine should have a parameter of type TreeNode, and it should return a value of type int.
Answer: |
    static int treeSum( TreeNode root ) {
           // Find the sum of all the nodes in the tree to which root points.
        if ( root == null ) {
              // The sum of the nodes in an empty tree is zero.
           return 0;
        }
        else {
              // Add the item in the root to the sum of the
              // items in the left subtree and the sum of the
              // items in the right subtree.
           int total = root.item;
           total += treeSum( root.left );
           total += treeSum( root.right );
           return total;
        }
     }
Question 8: | What is a postorder traversal of a binary tree?
Answer: | In a traversal of a binary tree, all the nodes are processed in some way. (For example, they might be printed.) In a postorder traversal, the order of processing is defined by the rule: For each node, the nodes in the left subtree of that node are processed first. Then the nodes in the right subtree are processed. Finally, the node itself is processed. This rule is applied at all levels of the tree.
Question 9: | Suppose that a <multilist> is defined by the BNF rule
    <multilist>  ::=  <word>  |  "(" [ <multilist> ]... ")"
where a <word> can be any sequence of letters. Give five different <multilist>'s that can be generated by this rule. (This rule, by the way, is almost the entire syntax of the programming language LISP! LISP is known for its simple syntax and its elegant and powerful semantics.)
Answer: | Here are five possibilities (out of an infinite number of possibilities), with some explanation:
    fred  --  A <multilist> can just be a word, such as "fred".

    ( )   --  The [ ]... around <multilist> means that there can be
              any number of nested <multilist>'s, including zero.  If
              there are zero, then all that's left is the empty
              parentheses.

    ( fred mary chicago ) -- A <multilist> consisting of three
                             <multilist>'s -- "fred", "mary", and
                             "chicago" -- inside parentheses

    ( ( able ) ( baker charlie ) ) -- A <multilist> containing two
                                      <multilist>'s.

    ( ( a ( b ) ) ( c ( d e ) g ) )  -- Even more nesting.
Question 10: | Explain what is meant by parsing a computer program.
Answer: | To parse a computer program means to determine its syntactic structure, that is, to figure out how it can be constructed using the rules of a grammar (such as a BNF grammar).

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