Q. At which of the following stage(s), the degeneracy do not occur in transportation problem?
(m, n represents number of sources and destinations respectively)

(a) While the values of dual variables ui and vj cannot be computed.
(b) While obtaining an initial solution, we may have less than m + n -1 allocations.
(c) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously.
(d) At a stage when the no. of +ve allocation is exactly m + n - 1.

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Q. Consider an implementation of unsorted single linked list. Suppose it has its representation with a head and a tail pointer (i.e. pointers to the first and last nodes of the linked list). Given the representation, which of the following operation cannot be implemented in O(1) time ?

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Q. Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i, j) | 1 ≤ i ≤ 12, 1 ≤ j ≤ 12}. There is an edge between (a, b) and (c, d) if |a – c| ≤ 1 or |b–d| ≤ 1. The number of edges in this graph is

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Q. The runtime for traversing all the nodes of a binary search tree with n nodes and printing them in an order is

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Q. Consider the following statements :

S1: A queue can be implemented using two stacks.
S2: A stack can be implemented using two queues.

Which of the following is correct ?

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Q. Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

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Q. A priority queue is implemented as a max-heap. Initially, it has five elements. The level-order traversal of the heap is as follows:

20, 18, 15, 13, 12

Two new elements ‘10’ and ‘17’ are inserted in the heap in that order. The level-order traversal of the heap after the insertion of the element is:

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Q. If there are n integers to sort, each integer has d digits, and each digit is in the set  {1, 2, …, k}, radix sort can sort the numbers in:

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Q. Match the following:

a. Prim’s algorithm                  i. O(V^2E)
b. Bellman-Ford algorithm     ii. O(VE lgV)
c. Floyd-Warshall algorithm   iii. O(E lgV)
d. Johnson’s algorithm           iv. O(V^3)

Where V is the set of nodes and E is the set of edges in the graph.

Codes :
     a    b   c   d

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Q. Constructors have ............. return type.

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Q. Method over-riding can be prevented by using final as a modifier at ...............

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Q. Which of the following is a correct statement?

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Q. Which of the following is not a correct statement?

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Q. Given the following statements:

(a) To implement Abstract Data Type, a programming language require a syntactic unit to encapsulate type definition.
(b) To implement ADT, a programming language requires some primitive operations that are built in the language processor.
(c) C++, Ada, Java 5.0, C#2005 provide support for parameterised ADT.

Which one of the following options is correct?

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Q. Match the following types of variables with the corresponding programming languages:

(a) Static variables                   (i) Local variables in Pascal
(b) Stack dynamic                    (ii) All variables in APL
(c) Explicit heap dynamic       (iii) Fortran 77
(d) Implicit heap dynamic       (iv) All objects in JAVA

Codes:
      (a)   (b)   (c)   (d)

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Q. The number of different binary trees with 6 nodes is .............

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Q. Let A[1...n] be an array of n distinct numbers. If i < j and A[i] > A[j], then the pair (i,j) is called an inversion of A. What is the expected number of inversions in any permutation on n elements?

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Q. Which one of the following array represents a binary max-heap?

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Q. Match the following:

(a) Huffman codes                              (i) O(n2)
(b) Optimal polygon triangulation     (ii) θ(n3)
(c) Activity selection problem             (iii) O(nlgn)
(d) Quicksort                                         (iv) θ(n)

Codes:
      (a)   (b)   (c)   (d)

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Q. Suppose that we have numbers between 1 and 1000 in a binary search tree and want to search for the number 364. Which of the following sequences could not be the sequence of nodes examined?

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