Q. Consider the following conditions :

(a) The solution must be feasible, i.e. it must satisfy all the supply and demand constraints.
(b) The number of positive allocations must be equal to m+n-1, where m is the number
of rows and n is the number of columns.
(c) All the positive allocations must be in independent positions.

The initial solution of a transportation problem is said to be non-degenerate basic feasible solution if it satisfies :

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Q. Big-O estimates for the factorial function and the logarithm of the factorial function i.e. n! and log n! is given by

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Q. Match the following:

List-I                                       List-II
a. Classification           i. Principal Component Analysis
b. Clustering                 ii. Branch and Bound
c. Feature Extraction   iii. K-nearest neighbour
d. Feature Selection   iv. K-means

Codes:
      a    b    c    d

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Q. Merge sort makes two recursive calls. Which statement is true after these two recursive calls finish, but before the merge step?

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Q. Searching for an element in the hash table requires O(1) time for the ............... time, whereas for direct addressing it holds for the ............. time.

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Q. An algorithm is made up of 2 modules M1 and M2. If time complexity of  modules M1 and M2 are h(n) and g(n) respectively, the time complexity of the algorithm is

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Q. What is the maximum number of parenthesis that will appear on the stack at any one time for parenthesis expression given by

( ()     (())         (()) )

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Q. Suppose that the splits at every level of Quicksort are in proportion 1-β to β, where 0<β≤0.5 is a constant. The number of elements in an array is n. The maximum depth is approximately

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Q. The minimum number of nodes in a binary tree of depth d (root is at level 0) is

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Q. The efficient data structure to insert/delete a number in a stored set of numbers is

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Q. Consider the following statements:

(i) A graph in which there is a unique path between every pair of vertices is a tree.
(ii) A connected graph with e = v – 1 is a tree.
(iii) A graph with e = v – 1 that has no circuit is a tree.

Which of the above statements is/are true?

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Q. Consider the In-order and Post-order traversals of a tree as given below:

In-order: j e n k o p b f a c l g m d h i
Post-order: j n o p k e f b c l m g h i d a
The Pre-order traversal of the tree shall be

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Q. A simple graph G with n-vertices is connected if the graph has

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Q. Linked Lists are not suitable for ...................

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Q. The decision tree classifier is a widely used technique for ...............

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Q. Match the following :

(a) Dangling pointer    (i) Buffer replacement policy
(b) Page fault               (ii) Variable-length records
(c) List representation (iii) Object identifier
(d) Toss-immediate      (iv) Pointer-swizzling

Codes :
      (a)   (b)  (c)  (d)

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Q. The time complexity of recurrence relation

T(n) = T(n/3) + T(2n/3) + O(n)

is

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Q. The time complexity of an efficient algorithm to find the longest monotonically increasing subsequence of n numbers is

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Q. Given 0-1 knapsack problem and fractional knapsack problem and the following statements :

S1 : 0-1 knapsack is efficiently solved using Greedy algorithm.
S2 : Fractional knapsack is efficiently solved using Dynamic programming.

Which of the following is true ?

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Q. Consider the following sequence of operations :

(i) Pointer p1 is set to point at a new heap-dynamic variable.
(ii) Pointer p2 is assigned p1’s value.
(iii) The heap dynamic variable pointed to by p1 is explicitly de-allocated, but p2 is not changed by the operation.

This situation leads to which of the following :

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