Describe a greedy algorithm that chooses the proposed talk with the earliest end time among all those that do not clash with talks already planned at each stage to solve the issue of arranging a subgroup of a collection of proposed talks in a lecture hall.
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Describe a greedy
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- Text reading is an integral component in our counting algorithms, and it is also ubiquitous in daily applications. The following is a very bad algorithm for reading from a text file, although it is correct and straightforward. It reads from a file line by line, and concatenate them into text. Then we split it using a regular expression. The split part is fast in linear complexity (we will learn it in Comp-2140), hence that is not our concern. Note that trim() is needed to remove empty strings. static String [] readTextBAD (String PATH) throws Exception { BufferedRe ader br=new BufferedReader (new FileReader(PATH)); String text=""; String line=""; while ((line=br.readLine ())!=null) text=text+" "+line.trim(); String tokens []=text.trim().split("[^a-zA -Z]+"); return tokens; } 5.4.1 Time complexity of readTextBAD Write below the time complexity of readTextBAD in terms of the text word length n, and explain your answer. Refer to repeat1 example in the textbook for the cause of low speed…Describe a greedy algorithm for scheduling a subset of a collection of proposed talks in a lecture hall by choosing the proposed talk with the earliest end time among all those that do not clash with talks already planned at each stage.Suppose we have a group of proposed talks with preset start and end times. Students of CSE340 were asked to design an algorithm to schedule as many of these talks as possible in a lecture hall, under the assumptions that once a talk starts, it continues until it ends, no two talks can proceed at the same time, and a talk can begin at the same time another one ends. Assume that talk j begins at time sj (where s stands for start) and ends at time ej (where e stands for end). One student proposed the algorithm shown in Algorithm 1 on the next page, which simply adds talks in order of earliest start time (smallest sj ). (a) Prove, using a counter example, that the proposed algorithm does not always produce an optimal schedule (i.e., a schedule with most possible talks). (b) Another student proposed adding talks in order of shortest duration (ej - sj ). Prove, using a counter example, that even with this new criteria, the algorithm does not always produce an optimal schedule.
- Develop Pseudo-code (English-like) for: In the Find Largest pseudo-code algorithm of Figure 2.14, listed below, if the numbers in our list were not unique and therefore the largest number could occur more than once. Modify the algorithm below to find all the occurrences of the largest number and their position in the list.Devise an algorithm that matches the lower bound, i.e., sorts a list in which each paper is within k slots of its proper position in e (n log k) time. Hint: See Exercise 6.5-8 on page 166 of Introduction to Algorithms, Third Edition.Write for the following problem a recursive algorithm whose worst-case timecomplexity is not worse than Θ(n ln n). Given a list of n distinct positiveintegers, partition the list into two sublists, each of size n/2, such that thedifference between the sums of the integers in the two sublists is maximized.You may assume that n is a multiple of 2.
- Text reading is an integral component in our counting algorithms, and it is also ubiquitous in daily applications. Thefollowing is a very bad algorithm for reading from a text file, although it is correct and straightforward. It reads froma file line by line, and concatenate them into text. Then we split it using a regular expression. The split part isfast in linear complexity (we will learn it in Comp-2140), hence that is not our concern. Note that trim() is neededto remove empty strings.static String [] readTextBAD ( String PATH ) throws Exception {BufferedReader br =new BufferedReader (new FileReader ( PATH ) ) ;String text ="";String line ="";while (( line = br . readLine () ) != null )text = text +" "+ line . trim () ;String tokens []= text . trim () . split ("[^a-zA -Z]+") ;return tokens ;}5.4.1 Time complexity of readT extBADWrite below the time complexity of readTextBAD in terms of the text length n (number of lines), and explain youranswer. Refer to repeat1 example in the…In python, The Longest Subsequence Problem is a well-studied problem in Computer Science, where given a sequence of distinct positive integers, the goal is to output the longest subsequence whose elements appear from smallest to largest, or from largest to smallest. For example, consider the sequence S= [9,7,4,10,6,8,2,1,3,5]. The longest increasing subsequence of S has length three ([4,6,8] or [2,3,5]), and the longest decreasing subsequence of S has length five([9,7,4,2,1] or [9,7,6,2,1]). And if we have the sequence S = [531,339,298,247,246,195,104,73,52,31], then the length of the longest increasing subsequence is 1 and the length of the longest decreasing subsequence is 10. Question: Find a sequence with nine distinct integers for which the length of the longest increasing subsequence is 3, and the length of the longest decreasing subsequence is 3. Briefly explain how youconstructed your sequence.A graph is a collection of vertices and edges G(V, E). A weighted graph has weights (numbers, etc.) on every edge. A multigraph can have more than one edges between any vertices. Explain why a person should use a weighted graph instead of a multigraph. Give examples. An adjacency matrix might be a better choice for speeding up a program, however, it consumes huge memory for large graphs. How this situation can be improved? What programming constructs better suit graph representation? Explain with example
- Develop a brute-force algorithm that finds the longest common sequential elements of two given lists with the Java programming language. For example, the following two lists are given: S1 = [B,C,D,A,A,C,D] S2 = [A,C,D,B,A,C] Common lists are: [B,C], [C,D,A,C], [D,A,C], [A,A,C], [A,C], [C,D], … Note that although both lists have a common [C,D,A,C] (sub)list, both list items are skipped and the left-to-right order is intact. Apply the brute force algorithm. Explain Time Complexity?Pseudo-random numbers Randomly generating numbers is a crucial subroutine of many algorithms in computer sci- ence. Because computers execute deterministic code, it is not possible (without external influence) to generate truly random numbers. Hence, computers actually generate psuedo- random numbers. The linear congruential method is a simple method for generating pseudo-random numbers. Let m be a positive integer and a be an integer 2 < a <m, and c be an integer 0 ≤ c<m. A linear congruential method uses the following recurrence relation to define a sequence of pseudo-random numbers: In+1=a+c mod m (a) Use the linear congruence method with a = 8, c=5, and m = 14, to compute the first 15 pseudo-random numbers when co= 1. That is, compute zo,X1, X 14- (b) From part (a) we should notice that, with m = 14, the sequence does not contain all 14 numbers in the set Z14. In particular because the sequence is periodic. Using m = 8, determine the value of a which does give all 8…The Python implementation updates the cost of reaching from the start vertex to each of the explored vertexes. In addition, when it decides on a route, A* considers the shortest path from the start to the target, passing by the current vertex, because it sums the estimate from the heuristic with the cost of the path computed to the current vertex. This process allows the algorithm to perform more computations than BFS when the heuristic is a proper estimate and to determine the best path possible.