It is Halloween again, and trick or treat is around the corner. You have the following problem to solve: There are a total of numHouses you want to visit, labeled from 0 to numHouses - 1. You are given an array of the ways you can visit them where Visit[i] = [ai, bi] indicates that you must visit house ai first if you want to visit house bi. Return true if you can visit all houses. Otherwise, return false (deadlock). Examples: If numHouses is 2 and Visit={[0,1]} return true If numHouses is 3 and Visit=[[0,1],[1,2], [2,1]} return false (deadlock to visit 2 you have to go first to 1 and to visit 1 you have to go to 2 first). a. Describe using pseudocode an efficient algorithm. How can you model the problem? How do you model the houses, and the (ordered) pairs of Visit? b. Give the time and space complexity. Hint: How would you model the problem? Can you use a graph? 1.)

Consider the two versions of Quicksort that are based on the following: (i) Median selection algorithm using the linear-time select method; (ii) The randomized pivot selection algorithm   Which of the two algorithms has a faster worst-case asymptotic behavior? Which of the two algorithms has a faster average-case performance? Provide empirical evidence of your answer by writing the corresponding programs for each and conducting experimental evaluation. Your experimental results should provide evidence of your answer. For this you need to run an adequate number of experiments on a variety of array/list sizes (use large randomly generated lists of integers).

Consider the 8-puzzle problem. Trace out the A* algorithm given the initial and goal states below. You are supposed to show the generated search tree until the search generates the goal state. For each state show the value of the evaluation function f(n) = g(n) + h(n). Recall that g(n) gives the path cost from the initial state to node n. Moreover, for this problem the step cost is 1 for any action (moving the empty tile). As a heuristic let h(n) be the number of misplaced tiles. Hence f(initial-state) = 0 + 3 = 3. The # symbol denotes the empty tile. Initial State Goal State 1 2 3 1 2 3 # 4 6 4 5 6 7 5 8 7 8 #

Given a set of jobs {J1, ... , Jn}, each job Ji = < ti, wi > has a required processing time ti and aweight wi. Design an efficient algorithm (pseudo code) to minimize the weighted sum of overall completion times ∑ni=1wiCi, where Ci  is the completion time of job i. What is the time complexityof your algorithm? Note: You first need to briefly explain your ideas to solve the problem, e.g. what data structures are used, how the intermediate results are saved, which sorting strategy is used, and why the final results are correct;

1. Prepare an excel table to compute the runtime for four different algorithms for solving the same problem, for value of N ranging from N= 10 to 100 in steps of 10 and then determine the best and worst algorithm. The runtimes of the algorithms are given as below: T₁(N) = (1.2) T₂(N) = 3N³ + 200 T₂(N) = NIgN T4(N) = 100N Make sure to attach the excel spread sheet. Also, may be worth to plot the function on excel chart (line plot) and you can show the functions growth.

Four criteria were defined for comparing search strategies: completeness, optimality, time complexity, and space complexity. Choose ONE of these criteria to explain why Iterative deepening search might be preferred over hill climbing (plain hill climbing, not random restart).

Four criteria were defined for comparing search strategies: completeness, optimality, time complexity, and space complexity. Choose ONE of these criteria to explain why Hill climbing (plain hill climbing, not random restart) might be preferred over iterative deepening search.

The time complexity equation of merger-sort is T(n) = 2* T(n/2) + n, where T(1) = C and C is a constant. Solve this equation by giving detailed steps.  2. The time complexity equation of merger-sort T(n) = 3* T(n/3) + n, where T(1)=T(2)=C, what would be T(n)?   Please do the 2 question only, thanks

Determine the cost and structure of an optimal binary search tree for a set of n = 4 keys with the following probabilities: i 1 3 4 Pi 0.12 0.18 0.18 0.17 0.05 0.05 0.10 0.08 0.07

Don't submit an AI generated response. I need the correct answer without any plagiarism otherwise I'll give you multiple downvotes for sure.