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Describe a polynomial time algorithm that solves the following decision problem: Given a graph G and an edge f in it, does G have a cycle containing f?
Design an O(V+E) time algorithm that computes the smallest number of batches required to complete all tasks. A task can be assigned to a batch i if and only if all tasks that are its prerequisites have already been assigned to batches 1 to (i-1).
A huge, well regarded supplier of key raw materials to your corporation's production process requires a year-end summary report of totals purchased from it.
Assume a flash storage device is used instead of disk, and it has seek time of 1 microsecond and transfer rate of 40 MB per second. Recompute the cost of sorting the relation in seconds.
Write down the algorithm for the program which prompts the user to enter five test scores, compute the total of the five tests and determine the weighted average of each test.
Provide a recurrence for worst case running time of recursive Binary Search function in terms of n, the size of the search array. Solve the recurrence.
How a vEB tree can be used to support these three operations and analyze the time/space complexity of your algorithms.
Create algorithm to calculate union of two input sets given as arrays, both of size O(n). The output must be array of distinct elements that form union of the sets.
Discuss the benefits of dynamic over-static arrays. Under what conditions will you choose dynamic arrays?
As queries are expensive, you would like to calculate median using as few queries as possible. Provide the algorithm which finds median value using at most O(log n) queries.
Create the algorithm which takes as inputs, matrices C, D, and vertex indices i and j, and returns minimum-cost path from vertex i to vertex j.
Given connected undirected graph G described by the adjacency list representation create the efficient algorithm to find the path in G which goes through exactly once in each direction.
Write an algorithm that takes a sequence of real numbers s and its length n and returns the absolute value of the average of these numbers.
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