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16410f04safinsol - 16.410-13: Principles of Autonomy and...

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Unformatted text preview: 16.410-13: Principles of Autonomy and Decision Making Sample Final Exam December 3 rd , 2004 Name E-mail Note: Budget your time wisely. Some parts of this exam could take you much longer than others. Move on if you are stuck and return to the problem later. Problem Number Max Score Grader Problem 1 20 Problem 2 20 Problem 3 20 Problem 4 27 Problem 5 30 Problem 6 30 Problem 7 14 Total 161 Problem 1 Search (20 points) Part A Dijkstras Algorithm (6 points) Consider the following graph, with node 1 as the start, and node 9 as the goal. 1 Part A-1 (2 points) How many times does the value at node 11 change? Part A-2 (2 points) What is the length of the shortest route from start to goal? Part A-3 (2 points) In what order are the nodes expanded? 3 Once for each of node 11s parents - nodes 5, 6 and 7. 8, following along the path 1-4-7-8-9. 1, 2, 3, 5, 6, 4, 7, 8, and then 9. 2 3 4 5 6 7 8 1 1 1 1 9 10 11 12 13 14 1 1 1 1 1 1 1 1 5 1 12 3 1 1 1 1 1 1 1 1 9 1 8 7 1 1 1 1 1 1 1 1 1 2 Part B A* Search (8 points) Consider the following maze. Actions are moves to the 8 neighboring squares. Each such move involves a move over a distance, which is the cost of the move. Lets say that the distance to the left and right neighbors, and to the upper and lower neighbors is 1, and that the distance to the corner neighbors is 2 . Part B-1 (4 points) Is Euclidean distance an admissible heuristic? Why or why not? (The Euclidean distance between two points <x1,y1> and <x2,y2> is [(x2 x1} 2 + (y2 y1) 2 ] 1/2 ). Yes. Euclidean distance is the straight line distance between two points, which is the shortest distance between those points. Hence Euclidean distance is always less than or equal to the true distance of any path between those two points within the maze. Part B-2 (4 points) Is Manhattan distance an admissible heuristic? Why or why not? (Manhattan distance between two points <x1,y1> and <x2,y2> is (|x2 x1| + |y2 y1|) ). No. The Manhattan distance may be greater than the true distance. For example, the Manhattan distance to the corner neighbors will be greater than the true distance. 3 Part C Properties of Search (6 points) Part C-1 (1 point) How can A* be made to behave just like breadth-first search? Set h = 0 Part C-2 (1 point) How can depth-first search be made to behave just like breadth-first search? Use iterative deepening Part C-3 (2 points) Is A* always the fastest search method? Explain your answer. No. Hill climbing w/o backtracking, for example, could find a solution much faster (if it is lucky). Part C-4 (2 points) Is depth first always slower than breadth first search? Explain your answer....
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16410f04safinsol - 16.410-13: Principles of Autonomy and...

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