# Consider a state space with branching factor 10 and a goal 5 steps away from the start state. If a breadth-first search uses 1MB of memory to find the goal, approximately how much memory will be used if the goal is 7 steps away from the goal? 100 GB 10 GB 10 MB 70 MP

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- Vertex S denotes the start state and vertices G1 and G2 denote the two goal states. Directed edges are labelled with the actual costs of traversing the edge. In what order would Breadth-First Search retrieve the states from the frontier when starting the search in S? If all else is equal, consider states in alphabetic order. There are two possible correct answers, depending on what variant of Breadth-First Search you are using. Select either one of them to receive full marks. options are S, A, B, C, D, E, F, G1 b. S, A, B, C, E, F, D, G1 c. S, A, B, C, E, F, G1 d. S, A, B, C e. S, A, C, G1 f. S, A, E, G1 g. S, B, A, C, E h. S, B, F, D, G2 i. S, C, B, F, A, D, E, G1 j. S, C, G1For problem 1, you should provide a list of numbers of states for each of the search methods. Problem 1 In the state space shown below ( refer to image ), write the order in which states are expanded if the initial state is 4 and there are two goal states: 5 and 8. For example, for breadth first search the answer would be: 4 2 7 1 3 6 8 using depth-first search using iterative deepening.2. Draw the state space that would be generated by the Breadth-First Search algorithm for theinitial state given in Table 2. You can stop when the first goal state is reached. Perform themoves strictly in the following sequence: Up; Down; Left; Right. Do not create more thanone copy of any particular state, and identify the goal state.
- Consider a state space where the start number is 2 and the successor function for state n returns two states, number 3n -2 and 3n-1. (a) Draw the portion of the state space for states 2 to 41. (b) Suppose the goal state is 37. List the order in which nodes will be visited for breadth first search, depth first search. (c) Suppose the goal state is 13. List the order in which nodes will be visited for depth first search with limit 2 and iterative depending search.A 2-dimensional Turing machine has an infinite 2-dimensional grid asits storage device (one cell for every address (i, j) ∈Z×Z). Instead ofL and R, there are 5 options for the head to move from (i, j): Left (to(i −1, j), Right (to (i + 1, j)), Up (to (i, j + 1)), Down (to (i, j −1)),and Stay (remain at (i, j)) .Let us assume, that our 2-dimensional TM M has an additional 1-dimensional tape where the input is located as in a 1-tape TM. The2-dimensional storage device contains a blank symbol in every cell atthe start of the computation.Show that a 2-dimensional TM is not more powerful, i.e., every lan-guage accepted by a 2-dimensional TM M is accepted by one of ourstandard 1-dimensional TMs. You don’t have to simulate directly witha 1-tape TM, as you are allowed to use what we know about k-tape(1-dimensional) TMs without proof.Describe the moves of a simulating TM M ′ in plain English. For everypossible move of M , you have to design a sequence of moves of M ′that simulates that move of…Consider a system with four page frames and a program that uses eight pages. Consider the reference string 0 1 7 2 0 3 1 7 0 1 7 and assume that all four page frames are initially empty. Consider the three following algorithms: a. Optimal page replacement b. FIFO page replacement c. LRU page replacement In each cases show a diagram (ASCII art recommended) that shows which pages are in which frames throughout time, and page faults at the bottom. For instance: would mean that at step 1 page 0 is referenced and loaded into frame 0, which is a page fault; then page 1 is referenced, and so on. The goal is to fill this table to see what in memory when and thus infer the number of page faults. The first 4 steps are ALWAYS the same, as above (i.e., just fill the four frames, with one page fault each time)
- Consider a state space where the start state is number 1 and the successor function for state n returns two states, numbers 2n and 2n + 1. a) Draw the portion of the state space for states 1 to 31. b) Suppose the goal state is 12. List the order in which nodes will be visited for depth first search if we start with the left side of the tree, depth first search if we start with the right side of the tree, and breadth first search.Vertex S denotes the start state and vertices G1 and G2 denote the two goal states. Directed edges are labelled with the actual costs of traversing the edge. What path from S to a goal would be found by Breadth-First Search (BFS)? If all else is equal, consider states in alphabetic order.Question 17. Sorting a data set is an important sub-problem in data science. Given the size n of a data set, which statements are correct? a) Bubble Sort has worst-case run-time complexity O(n).b) Bubble Sort has worst-case run-time complexity O(n log N).c) Bubble Sort has worst-case run-time complexity O(n2).d) Merge Sort has worst-case run-time complexity O(n).e) Merge Sort has worst-case run-time complexity O(n log N).f) Merge Sort has worst-case run-time complexity O(n2).g) Quick Sort has worst-case run-time complexity O(n).h) Quick Sort has worst-case run-time complexity O(n log N).i) Quick Sort has worst-case run-time complexity O(n2).
- Consider a state space where the start state is number 1 and the successor function for state n returns two states, numbers 2n and 2n + 1. a) Draw the portion of the state space for states 1 to 31. b) Suppose the goal state is 12. List the order in which nodes will be visited for depth first search if we start with the left side of the tree, depth first search if we start with the right side of the tree, and breadth first search. c) Calculate the total time in terms of number of nodes each algorithm will take to find the goal state 12.Consider the navigation problem shown in Figure 1. The number next to each edge is the cost of the performing the action corresponding to that edge. You start from A and your goal is to get to F. List the order in which nodes are expanded, which nodes are added to the fringe and which states are added to the closed set when performing Graph Search using: breadth-first search. depth-first search. iterative deepening search. uniform cost searchQuestion 1. Describe differences between breadth-first and depth-first searches and provide a sequence for each of the searches for the following graph: A / \ B C / / \ D E F Question 2. For the graphs shown below, provide at least 2 BFS and 2 DFS Traversal Paths for each. See starting nodes in bold below for each graph. Left Graph BFS 1: 1 BFS 2: 4 DFS 1: 1 DFS 2: 4 Right Graph BFS 1: 1 BFS 2: 10 DFS 1: 1 DFS 2: 10

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