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CS 240 Computer Science II Exam 3
Page 1
Spring ‘03
April 2, 2003
Name_____________________________
1. Linked lists.
a) Fill in the Java inner class below to support the implementation of a linked list in which each node holds
one String and a next reference.
[5 pts]
private class Node {
private _______ info;
private _______ next;
private Node(String s){
info = _______;
_________ = ________;
}
}
b) Indicate how the head pointer instance variable of the linked list is declared and start as the empty list.
The linked list starts with a dummy head node.
[4 pts]
___________ head = new _______________________;
c) Draw a box and pointer diagram to represent the ordered list (“cat”, “dog”, “fish”) as pointed to by
head. The linked list starts with a dummy head node.
[5 pts]
d) Fill in the blanks so that Java code that would add the value “ant” as a new first node of this ordered list.
[5 pts]
Node temp = new Node (“ant”);
temp. _______ = _______ . ________;
head.______ = ______ ;
2. Fill in the code below to complete the enqueue operation using a singly linked list implementation (no dummy
head node).
[5 pts]
public void enqueue(Object item){
if (item == null)
throw new IllegalArgumentException
("Trying to insert null onto the queue");
Node node = new Node (______);
if (size == 0){
head = _________;
} else {
tail._______ = _______;
}
tail = node;
size_____;
}
CS 240 Computer Science II Exam 3
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3. Give the time complexities, O(1) or O(n) for each of the operations of the implied data structure that are
implemented as a linked list.
_________ pop()
[8 pts]
_________ insert(item) //into a sorted list
_________ dequeue()
_________ insert(item) //unsorted list
_________ enqueue(item)
_________ getNextItem()
_________ push(item)
_________ isThere(item)
4. Fill in the blanks to implement a recursive binary search algorithm. Assume there is a public helper function that
calls the recursive function:
public int binarySearch(Comparable key){
return binarySearch(key, 0, vec.length – 1);
}
[10 pts]
private int binarySearch(Comparable key, int lo, int hi){
if( ____ > ____ ) {
return -1; //not found
} else {
int mid = ____________;
int comp = vec[mid].compareTo(key);
if(comp > 0){
return binarySearch(key, ________,________);
} else if(comp ____ 0){
return binarySearch(key, ________,________);
} else { // found it
return ________ ;
}
}
}
5. A recursive definition for determining the greatest common denominator is credited to Euclid. For example,
the GCD of 16 and 12 is 4.
If b==0 then the GCD(a,b) = a,
otherwise the GCD (a,b) = GCD (b, a%b) //% is modulus
[10 pts]
Write this recursive Java function to implement the calculation of the greatest common denomionator.
public static int GCD(int a, int b){
}
CS 240 Computer Science II Exam 3
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6. Trees.
[10 pts]
a) Assume the root is at level 0. What is the level of node F? ____
b) Circle the largest subtree that is a binary tree.
c) How many leaves are there in the whole tree? _____
d) If each node could have at most three children, how many nodes total
could be stored in this tree without adding any more levels? ______
e) List the ancestors of node H ______________________
A
/ \
B
C
/ \
\
D
E
F
/ \
/|\
G
H
I J K
f) List the descendants of node C. _______________________
g) Draw the conversion of this general tree as a binary tree (left child as
first child of the general tree and right child as a sibling in the general tree)
7. Assume nodes in a binary tree are defined in an inner class having the following instance variables.
Comparable info;
BSTNode left;
BSTNode right;
a) Finish the recursive Java function to count the number of nodes in a binary tree. The algorithm works as
follows. If the root (of tree or subtree) is null then return 0; otherwise return the sum of the nodes
on the left and the nodes on the right, plus one for the root.
[7 pts]
public int Counter( _________ curNode)
{
if(curNode _____________ ) return ____ ;
return Counter ( _________________ )
+ __________ ( _________________ )
+ ____ ;
}
b) Finish the recursive Java function to return if the item exists in the binary search tree.
[8 pts]
public boolean isThere( BSTNode root, Comparable item)
{
if (_______ == null) return false;
int comp = item.compareTo( _________ . ___________)
if(comp == 0) return ___________ ;
if(comp < 0) return isThere ( ______ . ______ , item )
else
}
return isThere (_______ . _______, item);
CS 240 Computer Science II Exam 3
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8. Create a binary search tree from the following character data entered into the bst left to right.
[4 pts]
DTWABQMN
a) List the nodes of your tree above from an inorder traversal.
[3 pts]
b) List the nodes of your tree above from a preorder traversal.
[3 pts]
9. Draw the following infix arithmetic expression as an expression tree. Represent precedence properly.
[4 pts]
(a+b)-c*(d+e)
a) Show a postorder traversal of your expression tree.
[3 pts]
10. True/False
[6 pts]
______ A doubly linked list permits traversal in both forward and backward directions
______ A doubly linked list doubles the algorithm complexity of the operations over a singly linked list.
______ Most operations on a binary tree depends on the depth of the tree which is logarithmic to its
capacity.
______ A binary search tree always generates the same inorder traversal regardless of the sequence the
nodes were entered into the tree.
______ A postorder traversal is the same as a reversed preorder travsersal.
______ The maximum number of nodes in a binary tree at level N is 2N