QUIZ 2

QUESTIONS

1. About Abstract Data Types (ADT):
   • Name an example of a ADT and name the operations that characterize this ADT. No need to explain if you know the right terminology.
   • How is the concept of an ADT expressed in Java?
2. Consider the pseudo code:

   X = 0;
   for i = 1 to N do

   for j = i to N do

   for k = j to N do

   X++;

   What is its running time in big-Oh notation?
3. Give the big-Oh value of the following geometric sums:
   • S₁ = 1 + 3 + 9 + 27 + ... + 3^n-1 (sum to n terms).
   • S₂ = 1 + (1/3) + (1/3²) + (1/3³) + ... + (1/3ⁱ) + ... (infinite sum).
4. Write a complete Java program which simply prints the string "Hello World!" on the screen.
   NOTE: "complete" means this program would compile and run. Make as short a program as possible, without any comments. It is possible to only use 3 lines of code.
5. Assume you have a reference H to the first node (or "head") in a singly linked list:

   H --> (a) --> (b) --> (c) --> (d) --> (e) --> null.

   Write a Java method called LastButOne to return a reference to the last but one node (this is node (d) in the figure above). In case the list has only one node, then return H itself. Here is the header for your method:

   public Node LastButOne(Node H);

   Note: the class Node has a public method called getNode() that returns a reference to the next node in the list.
6. Here is the pre- and post-order traveral listing of nodes in a binary tree:

   pre: (e, c, a, b, d)
   post: (a, b, c, d, e)

   Draw the binary tree. HINT: looking at the pre-order list, you know where to place node e and node c. But node a has two possible places.

ANSWERS

1. ADT:
   • ADT Stack. Characteristic operations are Push and Pop.
   • In Java, ADT's are represented by interfaces.
2. Each iteration does at most n operations. Hence, the running time is O(n³)
3. Sums:
   • The infinite sum (1+x+x²+x³+...) has value 1/(1-x) provided |x|<1. Hence answer is O(1).
   • The second sum is O(3ⁿ).
4. Hello Java Program:

   	class Hello {
   	  public static void main(String[] args){
   		System.out.println("Hello World!");
   	  }
   	}

5. List Java Program:

   	public Node LastButOne(Node H){
   	   Node Prev = H;
   	   H = H.getNext();
   	   if (H == null) {
   		return Prev;
   	   };
   	   while (H.getNext() != null){
   		Prev = H;
   		H = H.getNext();
   	   }
   	}

6. Tree Traversal: The tree is e(c(a,b),a).
   NOTATION: x(E1,E2) where E1,E2 are recursively expressions for the left and right subtrees rooted at x. A singleton tree with node x is simply denoted "x".