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"You are given a DAG called G that is the prerequisite graph for a set of courses required for a degree. Each vertex corresponds to a course, and there is an edge from vertex C1 to vertex C2 if and only if C1 is a prerequisite for C2.
Give a high-level description of an algorithm that labels each vertex in G with the minimum number of semesters required to complete the course. (Assume that any course may be taken in any semester, but only if all the prerequisite courses have been taken in prior semesters.)
Your algorithm should run in linear time (i.e., O(E+V) for an adjacency list and O(V2) for an adjacency matrix.)
Compute the entropy of the plaintext message?
Write an algorithm or code segment for locating the nth successor of an item in a circlar linked list (the nth item that follows the given item in the list).
Write a recursive function to determine if a binary tree is a binary search tree.
Assume we tried to simplify RSA cryptosystem using just prime p instead of composite modulus N = pq. As in RSA, we would have encryption exponent.
Devise an algorithm that generates an access control matrix A for any given history matrix H of the Chinese Wall model. A significant portion of the grade for this problem involves your justification of your algorithm.
A group of ten people need to decide which one flavor of ice cream they will all order, out of three options. The algorithm can question and re-question the participants, and present the answers to the participants.
So that every house is within four miles of one of the base stations. Write efficient algorithm that achieves this goal, using as few base stations as possible.
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.
Explain the following sorting techniques using appropriate algorithms- (i) selection sort (ii) bubble sort
Describe a FAIRCOIN algorithm that returns either 0 or 1 with equal probability, using ONEINTHREE as your only source of randomness.
Suppose now there are three users. Find the probability that at a given time, all three users are transmitting simultaneously. Find the fraction of time during which the queue grows.
Design an algorithm based on BFS that either colors a graph with 2 colors or determines that two colors are not sufficient.
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