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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.)
Solve the following recurrence relations by the method of your choiceT(n) = 1 for n = 4 and T(n) =pnT(pn) + n for n > 4. Argue that the solution to the recurrence T(n) = T(n=3) + T(2n=3) + cn is (n lg n) by appealing to the recursion tree.
Create algorithm which concatenates T1 and T2 into single binary search tree. Worst case running time must be O(h).
Using dynamic programming, write an algorithm to find the maximum sum of contiguous sublist of a given list of n real values.
Given the probabilities r1, · · · , rn, the costs c1, · · · , cn, and the budget B, ?nd the redundancies m1, · · · , mn that are within the available budget and that maximize the probability that the system works correctly. Devise an ef?cient algo..
Provides learners with an understanding of how data structures are used in algorithms and enables them to design and implement data structures
Explain the FIFO structure of the queue Explain how you would implement the queue data structure in its simplest form. Illustrate your answer fully with the necessary sample code
Write a method singleParent, which returns number of nodes in a binary tree that have only one child.
In this programming assignment you will implement an open hash table and compare the performance of four hash functions using various prime table sizes.
Katt wishes you to create an algorithm that, given a string X, determines efficiently how many ways X can be broken up into sequence of words.
How does he calculate the signature on each of m1j mod n (for positive integer j), m1-1 mod n, m1*m2 mod n, and in general m1j*m2k mod n (for arbitrary integers j and k)?
Their priorities are 2, 3, 1, 5 and 4, respectively, with 1 being the highest priority. Specify the order in which processes execute and determine the mean process turnaround time for each of the scheduling algorithms.
Write an implementation of a data structure S that supports the following operations: Insert(S, x): insert the key x into S only if it is not already there.
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