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This Test will cover complete Algorithms with very important questions, starting off from basics to advanced level.

Q. In an Unweighted, Undirected connected Graph, the shortest path from a node

`S`

to every other node is computed most efficiently, in terms of time complexity, by?Q. The most efficient algorithm for finding the number of connected components in an undirected graph on

`n`

vertices and `m`

edges has time complexity __________ ?Q. The minimum number of comparisons required to determine, if an integer appears more than

`n/2`

times in a sorted array of `n`

integers?Q. A B-tree of order

`4`

is built from scratch by `10`

successive insertions. What is the maximum number of node splitting operations that may take place?Q. G is a graph on

`n`

vertices and `2n-2`

edges. The edges of G can be partitioned into two edge-disjoint spanning trees. Which of the following is NOT true for G?Q. We have a binary heap on

`n`

elements and wish to insert `n`

more elements(not necessarily one after another) into this heap. Total time required for this is?Q. What is the number of swaps required to sort

`n`

elements using selection sort, in the worst case?Q. In quick sort, for sorting

`n`

elements, the `(n/4)th`

smallest element is selected as Pivot using an `O(n)`

time algorithm. What is the worst case time complexity of the Quick Sort?Q. Two alternative package A and B are available for processing a database having

`10^k`

records. Package A requires `0.00001 n^2`

time units and package B requires `10nlog(n)`

[Base of log is 10] time units to process `n`

records. What is the smallest value of `k`

for which B will be preferred over A?Q. Let

`W(n)`

and `A(n)`

denote respectively, the worst case and average case running time of an algorithm executed on an input of size `n`

. Which of the following is ALWAYS TRUE?Q. The recurrence relation capturing the optimal execution time of the Tower of Hanoi problem with

`n`

discs is?Q. The worst case running to search for an element in a balanced binary search tree with

`n2^n`

elements is?Q. Assuming P not equal to NP, which of the following is TRUE?

Q. A list of

`n`

strings, each of length `n`

, is sorted into lexicographic order using the Merge-Sort algorithm. The worst case running time of this computation is?Q. You are given the Postorder traversal, P, of a binary search tree on the n elements 1,2,...,n. You have to determine the unique Binary Search Tree that has P as its Postorder traversal. What is the Time Complexity of the most efficient algorithm for doing this?

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