CS301- Data Structures Spring 2010 FINALTERM EXAMINATION

FINALTERM  EXAMINATION

Spring 2010

CS301- Data Structures

Time: 90 min

Marks: 58

Question No: 1      ( Marks: 1 ) - Please choose o

Which one of the following operations returns top value of the stack?

       ► Push

       ► Pop

       ► Top

       ► First

Question No: 2      ( Marks: 1 ) - Please choose one

Compiler uses which one of the following in Function calls,

       ► Stack

       ► Queue

       ► Binary Search Tree

       ► AVL Tree

Question No: 3      ( Marks: 1 ) - Please choose one

Every AVL is _________________

       ► Binary Tree

       ► Complete Binary Tree

       ► None of these

       ► Binary Search Tree  

Question No: 4      ( Marks: 1 ) - Please choose one

If there are 56 internal nodes in a binary tree then how many external nodes this binary tree will have?

       ► 54

       ► 55

       ► 56

       ► 57

Question No: 5      ( Marks: 1 ) - Please choose one

If there are 23 external nodes in a binary tree then what will be the no. of internal nodes in this binary tree?

       ► 23

       ► 24

       ► 21

       ► 22

Question No: 6      ( Marks: 1 ) - Please choose one

Which one of the following is not an example of equivalence relation? 

       ► Electrical connectivity 

       ► Set of people

       ► <= relation 

       ► Set of pixels 

Question No: 7      ( Marks: 1 ) - Please choose one

Binary Search is an algorithm of searching, used with the ______ data.

      ► Sorted

      ► Unsorted

       ► Heterogeneous

      ► Random

Question No: 8      ( Marks: 1 ) - Please choose one

Which one of the following is NOT true regarding the skip list?

       ► Each list S_i contains the special keys + infinity and - infinity.

       ► List S₀ contains the keys of S in non-decreasing order. 

       ► Each list is a subsequence of the previous one.

       ► List S_h contains only the n special keys.

Question No: 9      ( Marks: 1 ) - Please choose one

A simple sorting algorithm like selection sort or bubble sort has a worst-case of

       ► O(1) time because all lists take the same amount of time to sort

       ► O(n) time because it has to perform n swaps to order the list.

       ► O(n²) time because sorting 1 element takes O(n) time - After 1 pass through the list,

either of these algorithms can guarantee that 1 element is sorted.

       ► O(n³) time, because the worst case has really random input which takes longer to

sort.

Question No: 10      ( Marks: 1 ) - Please choose one

Which of the following is a property of binary tree?

       ► A binary tree of N external nodes has N internal node.

       ► A binary tree of N internal nodes has N+ 1 external node.

       ► A binary tree of N external nodes has N+ 1 internal node.

       ► A binary tree of N internal nodes has N- 1 external node.

Question No: 11      ( Marks: 1 ) - Please choose one

By using __________we avoid the recursive method of traversing a Tree, which makes use of stacks and consumes a lot of memory and time.

       ► Binary tree only

       ► Threaded binary tree

       ► Heap data structure

       ► Huffman encoding

Question No: 12      ( Marks: 1 ) - Please choose one

Which of the following statement is true about dummy node of threaded binary tree?

       ► This dummy node never has a value.

       ► This dummy node has always some dummy value.

       ► This dummy node has either no value or some dummy value.

       ► This dummy node has always some integer value.

Question No: 13      ( Marks: 1 ) - Please choose one

For a perfect binary tree of height h, having N nodes, the sum of heights of nodes is 

       ► N – (h – 1) 

       ► N – (h + 1) 

       ► N – 1 

       ► N – 1 + h 

Question No: 14      ( Marks: 1 ) - Please choose one

What is the best definition of a collision in a hash table?

► Two entries are identical except for their keys.

  ►   Two entries with different data have the exact same key

► Two entries with different keys have the same exact hash value.

►   Two entries with the exact same key have different hash values.

Question No: 15      ( Marks: 1 ) - Please choose one

Which formula is the best approximation for the depth of a heap with n nodes?

       ► log (base 2) of n

       ► The number of digits in n (base 10), e.g., 145 has three digits

       ► The square root of n

      ► n

Question No: 16      ( Marks: 1 ) - Please choose one

Which of the following statement is NOT correct about find operation: 

       ►    It is not a requirement that a find operation returns any specific name, just that finds on two elements return the same answer if and only if they are in the same set. 

       ► One idea might be to use a tree to represent each set, since each element in a tree has the same root, thus the root can be used to name the set. 

       ►  Initially each set contains one element. 

       ►  Initially each set contains one element and it does not make sense to make a tree of one node only. 

Question No: 17      ( Marks: 1 ) - Please choose one

Which of the following is not true regarding the maze generation?

► Randomly remove walls until the entrance and exit cells are in the same set. 

► Removing a wall is the same as doing a union operation. 

► Remove a randomly chosen wall if the cells it separates are already in the same set. 

►  Do not remove a randomly chosen wall if the cells it separates are already in the same set. 

Question No: 18      ( Marks: 1 ) - Please choose one

In threaded binary tree the NULL pointers are replaced by ,

       ► preorder successor or predecessor

       ► inorder successor or predecessor

       ► postorder successor or predecessor

       ► NULL pointers are not replaced

Question No: 19      ( Marks: 1 ) - Please choose one

Which of the given option is NOT a factor in Union by Size: 

       ► Maintain sizes (number of nodes) of all trees, and during union.

       ► Make smaller tree, the subtree of the larger one. 

       ►  Make the larger tree, the subtree of the smaller one. 

       ► Implementation: for each root node i, instead of setting parent[i] to -1, set it to -k if tree rooted at i has k nodes.

Question No: 20      ( Marks: 1 ) - Please choose one

Suppose we had a hash table whose hash function is “n % 12”, if the number 35 is already in the hash table, which of the following numbers would cause a collision?

       ► 144

      ► 145

   ► 143

       ► 148

Question No: 21      ( Marks: 1 ) - Please choose o

What requirement is placed on an array, so that binary search may be used to locate an entry?

       ► The array elements must form a heap.

       ► The array must have at least 2 entries.

       ► The array must be sorted.

       ► The array’s size must be a power of two

Question No: 22      ( Marks: 1 ) - Please choose one

A binary tree with 24 internal nodes has ______ external nodes.

       ► 22

       ► 23

       ► 48

       ► 25

Question No: 23      ( Marks: 1 ) - Please choose on

In case of deleting a node from AVL tree, rotation could be prolong to the root node.

       ► Yes

       ► No

Question No: 24      ( Marks: 1 ) - Please choose one

when we have declared the size of the array, it is not possible to increase or decrease it during the ________of the program.

       ► Declaration

       ► Execution

       ► Defining

       ► None of the abov

Question No: 25      ( Marks: 1 ) - Please choose one

it will be efficient to place stack elements at the start of the list because insertion and removal take _______time.

       ► Variable

       ► Constant

       ► Inconsistent

       ► None of the above

Question No: 26      ( Marks: 1 ) - Please choose one

   _______ is the stack characteristic but _______was implemented because of the size limitation of the array.

       ► isFull(),isEmpty()

       ► pop(), push()

       ► isEmpty() , isFull()

       ► push(),pop()

Question No: 27      ( Marks: 2 )

Give the difference between strict and complete binary tree.

Ans:

A tree is a strictly binary tree if its each leaf node has non-empty left and right sub trees, and

If there are left and right sub-trees for each node in a binary tree is known as complete binary tree.

Question No: 28      ( Marks: 2 )

A complete binary tree can be stored in an array. While storing the tree in an array

we leave the first position (0th index )of the array empty. Why?

Ans

Because we need a pointer in an array to point a position of node of tree. parent node and the children nodes. In case of having  a  node with  left  and  right children, stored at position  i in the array, the left 2i and the right child will be at 2i+1 position. If the value of i  2, the parent will be at position 2 and the left child will be at position 2i i.e. 4 .The right child will be at position 2i+1 i.e. 5. we have not started  the 0^th  position. It is simply due to the fact if the position is 0,  2i will also

become 0.  So we will start from the 1^st  position, ignoring the 0^th.

Question No: 29      ( Marks: 2 )

Give the name of two Divide and Conquer algorithms.

Ans:

1.   Merge sort

2.   Quick sort

3.   Heap sort

Question No: 30      ( Marks: 2 )

Give the effect of sorted data on Binary Search.

Question No: 31      ( Marks: 3

Give any three characteristics of Union by Weight method.

Ans:

1.   This is also calles union by size.

2.   Maintain sizes (number of nodes) of all trees, and during union.

3.   Make smaller tree, the subtree of the larger one.

4.   for each root node i, instead of setting parent[i] to -1, set it

to -k if tree rooted at i has k nodes.

Question No: 32      ( Marks: 3 )

Here is an array of ten integers:

            5   3   8   9   1   7   0   2   6   4

Draw this array after the FIRST iteration of the large loop in an insertion sort (sorting from smallest to largest). This iteration has shifted at least one item in the array!

Question No: 33      ( Marks: 3 )

Give your comment on the statement that heap uses least memory in array representation of binary trees. Justify your answer in either case.

Question No: 34      ( Marks: 5 )

Suppose we have the following representation for a complete Binary Search Tree, tell the Left and Right child nodes and Parent node of the node D

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	…
0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	…

Question No: 35      ( Marks: 5 )

Explain the following terms:

1.   Collision

2.   Linear Probing

3.   Quadratic Probing

Ans:

Collision:

it takes place when two or more keys (data items) produce the same index.

Linear Probing

when there is a collision, some other location in the array is found. This is known as linear probing. In linear probing, at the time of collisions, we add one to the index and check that location. If it is also not empty, we add 2 and check that position. Suppose we keep on incrementing the array index and reach at the end of the table. We were unable to find the space and reached the last location of  the array.

Quadratic Probing

In the quadratic probing when a collision happens we try to find the empty location at

index + 12. If it is filled then we add 22  and so on.

Quadratic probing uses different formula:

1.   Use F(i) = i² (square of i) to resolve collisions

2.   If hash function resolves to H and a search in cell H is inconclusive, try

H + 1², H + 22, H + 32

Question No: 36      ( Marks: 5 )

Here is an array with exactly 15 elements:

1   2   3   4   5   6   7   8   9   10   11   12   13   14   15.

Suppose that we are doing a binary search for an element. Indicate any elements that will be found by examining two or fewer numbers from the array.