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You are given a set U of n objects labeled p1, p2, . . . , pn. A distance function d(pi, pj) provides a numeric value measuring the "closeness" of two objects pi, pj, where 1 i, j n. You are asked to make use of this distance function to divide the n objects into k clusters, where k is a given parameter. You can think of a cluster as a subset of U, where objects in a cluster are "closer" to one another than to objects in another cluster. Propose an algorithm that divides the n objects of U into k clusters, making use of the MST of a graph. Provide a simple argument of correctness and a bound on the running time of the algorithm you are proposing.
Give a linear-time algorithm to find an odd-length cycle in a directed graph. You may not suppose that graph is strongly connected.
Write a pseudocode for a divide-and-conquer algorithm for finding the position of the largest element in an array of n numbers.
Study feasibility analysis for jobs of LRT algorithm when preemption is allowed. Which scheduling algorithm is best suited for high speed networks and why? Distinguish between static and dynamic systems.
Assume you have one machine and a set of n jobs a1, a2, ..., an to process on that machine. Determine the schedule that obtains the maximum amount of profit. Compute the running time of your algorithm?
The recent discovery of the following fragment of uncommented procedural C code in the Sunlab has caused a big scandal. What is the worst-case time complexity of foo(a,1,N,k), and for which inputsdoes it occur?
Design an algorithm to solve the Spectral Assembly problem under the above conditions. Does the problem have a unique solution?
Create a divide and conquer algorithm to solve problem. The time complexity of your algorithm must be O(nlgn) or better.
Make a list of some of the common data structures provided by C#. You should have a minimum of 4 different data types.
What is the time complexity of the procedure? If A[l .. r] = [24, 30, 09, 46, 15, 19, 29, 86,78], what is the output?
Describe the distinction between an ambiguity in a proposed algorithm and an ambiguity in the representation of an algorithm. Describe how the use of primitives helps remove ambiguities in an algorithm's representation.
WSDL service that receives a request for a stock market quote and returns the quote
Consider the following graph representing the state space and operators of a navigation problem: What is the minimum number of nodes expanded and the storage needed for BFS and DFS?
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