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- Boolean Satisfaction Problem Boolean Satisfiability Problem (SAT) (https://en.wikipedia.org/wiki/Boolean_satisfiability_problem) is one of the most important problems in Computer Science. SAT is a problem that has NP-Complete complexity, where the only way to solve the problem is to try all the possibilities and check which one is correct. [LO 1, LO 2, LO 3 & LO 4,] Briefly describe how you used Backtracking to solve the Boolean Satisfiability Problem. Note that your solution must have exponential complexity. [LO 1, LO 2, LO 3 & LO 4,] Briefly explain how you use Strongly Connected Component (SCC) to solve the special case of the Boolean Satisfiability Problem, namely 2-SAT (https://en.wikipedia. org/wiki/2-SAT) . This solution has linear complexity. Solve the Subparts A&B thank u NOTE LO1: Explain fundamental concept of analysis arithms. LO2: Apply algorithm techniques and methods. LO3: Solve a problem using specific algorithm. LO4: Compare several algorithm design…Group scheduling Scheduling tasks to actors (people, CPUs, machines etc) is a problem that one encounters very often in practice. In this small exercise, we practice how to solve such a problem by using recursive problem solving. More specifically, we solve the following problem: We are organizing a course and have n� tutorial groups. To run the groups, we are hiring m� teaching assistants. Due to other responsibilities, an assistant is not necessarily able to teach all possible tutorial groups but has a set of groups that s/he can teach. We call this set of possible groups the preferences of the assistant.Is it possible to assign each tutorial group one assistant in a way that (i) all the assistants' preferences are respected, and (ii) each assistant teaches at most one tutorial group?Needless to say, this a very simplified version of the problem; in real life, some groups need more assistants, some assistants can teach more groups, consecutive group times for an assistant should be…True or false according to the following statements: The complexity of time necessitates the inclusion of more CPU cycles. The complexity of space necessitates less storage space. Time complexity may be gauged by looking at the total number of operations. The most operations needed is the worst-case situation for an algorithm.
- Python question Analysis: Discussion of Theoretical Concepts (Q12-13) In this part you are required to utilise concepts from the unit to analyse algorithms, computational problems, and broadly algorithmic design questions. Question 12 (Application and differentiation of definitions) 12a) Out of Greedy approach, bruteforce approach and backtracking approach, which one generally is most suitable for the Knapsack problem? Explain why. 12b) Out of Greedy approach, bruteforce approach and backtracking approach, which one generally is most suitable for the minimum spanning tree (MST) problem? Explain why. Question 13 (Explanation of advanced derivation from the lecture) 13a) Can the following statement be true for a particular decision problem A? Explain. “The decision problem A belongs to class NP-complete but does NOT belong to class P” 13b) Can the following statement be true for a particular decision problem A? Explain. “The decision problem A belongs to class…(a) The Fibonacci sequence can also be seen in hurricanes prediction. The shape takes in the form of a spiral, it can be in a nesting process and repeated into infinity. It is called the logarithmic spiral, and it abounds in nature. The Fibonacci sequence of numbers, “Fn”, is defined using the recursive relation. Fibonacci sequence of numbers can be computed as follows: Fn = Fn-1+Fn-2 If the 12th and 13th terms in the hurricane prediction sequence are 89 km/hour and 144 km/hour, analyze the value of the 15th, 16th, and 17th hurricane speed by using the Fibonacci formula as stated above.Deadlock avoidance: Select all of the following statements that are true. Deadlock avoidance aims to ensure that a system of processes will never enter an unsafe state. Claim edges in resource allocation graphs indicate resource requests that a process may send out in the future. The banker's algorithm can only be applied when there are single units of each resource type only. In order for the banker's algorithm to be applicable, when a process starts up, it must state in advance the maximum number of resources it may request. After the execution of the banker's algorithm, if Finish[i] == false for all processes i, then the system is in a safe state. Unsafe system states can lead to deadlocks.
- 1. Big-O notation. We have learnt big-O notation to compare the growth rates of functions, this exercise helps you to better understand its definition and properties.(a) Suppose n is the input size, we have the following commonly seenfunctions in complexity analysis: f1(n) = 1, f2(n) = log n, f3(n) = n, f4(n) = n log n, f5(n) = n^2, f6(n) = 2^n, f7(n) = n!, f8(n) = n^n. Intuitively, the growth rate of the functions satisfy 1 < log n < n < n log n < n^2 < 2^n < n! < n^n. Provethis is true.[Hint: You are expected to prove the following asymptotics by using the definition of big-O notation: 1 = O(log n), log n = O(n), n = O(n log n), n log n = O(n^2), n^2 = O(2^n), 2^n = O(n!), n! = O(n^n). Note: Chap 3.2 of our textbook provides some math facts in case you need.]Instructions Suppose you are the TA for the FCP course in environmental engineering department. You are given the midsem and endsem marks for the N Students in the course. A student P is said to dominate a student Q, if the midsem and endsem marks of P are both greater than the respective midsem and endsem marks of Q. Design an efficient algorithm for finding all the students that are not dominated by any other student in the class. Analyze the time complexity as well. Implement the code in C++.a)(i). People often use recursive algorithms. Discuss the difference between direct recursion and indirect recursion. In which situations would a direct or indirect recursion be a better choice to use?(ii). Two Level 200 IT students, James and Morris, are discussing how to compare two algorithms for solving a given problem. James suggests that they should use the execution times of the algorithms as criterion; but Morris insists that they should use the number of statements the algorithms execute as criterion. (α)Explain the reasons why both criteria they are considering are not good for comparing algorithms. (β)Recommend an ideal solution/criterion that they should rather use for comparing algorithms. Give a practical example to illustrate your answer.
- Question 3 a) Iteration and recursion are two very fundamental concepts underlying things we do in computing. (i). Distinguish between the terms Iteration and Recursion in the context of solving problems in business, science or engineering. (ii). Using practical examples in business, science or engineering, explain reasons why people still use recursion to solve problems even-though iteration is more efficient. b) Describe how a Savings and Loans Company can use singly-linked lists to keep track of customers that its Susu collectors (or mobile bankers) have won for the company over the last 2 months; and draw a suitable diagram (with hypothetical data) to illustrate your answer. c) In many fields of human endeavour, we use stacks on daily basis. Provide and explain four practical examples where we use stacks in real life.Complete the following analysis of an algorithm such that the time complexity, T(n), of the given algorithm is determined. The analysis uses instruction count (i.e. number of times the statement is executed) as the measure for the analysis. The instruction count of each instruction in the algorithm is indicated at the right of the statement after the //. You should replace each of the question marks(?) by the corresponding instruction count in order to complete the analysis. The total instruction count is obtained by adding all the instruction counts. Note that in this exercise, the linear search algorithm is analyzed in a case where the item to be searched is assumed not found in the array (i.e.Worst Case Analysis) int linearSearch(item, array) { // worst case instruction countint index = 0; // ?while (index < array.length) { // ?if (array[index] == item) { // ?return index; // ?}index++; // ?}return -1; // ?} // ------// T(n) = ? where n is the array sizeHelp with Time/space complexity. Would the time complexity be O(n^2) or O(n*m) ?