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Unformatted text preview: 16.41013: Principles of Autonomy and Decision Making Sample Final Exam December 3 rd , 2004 Name Email 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 – Dijkstra’s Algorithm (6 points) Consider the following graph, with node 1 as the start, and node 9 as the goal. 1 Part A1 – (2 points) How many times does the value at node 11 change? Part A2 – (2 points) What is the length of the shortest route from start to goal? Part A3 – (2 points) In what order are the nodes expanded? 3 – Once for each of node 11’s parents  nodes 5, 6 and 7. 8, following along the path 14789. 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. Let’s 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 B1 – (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 B2 – (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 C1 – (1 point) How can A* be made to behave just like breadthfirst search? Set h = 0 Part C2 – (1 point) How can depthfirst search be made to behave just like breadthfirst search? Use iterative deepening Part C3 – (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 C4 – (2 points) Is depth first always slower than breadth first search? Explain your answer....
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This note was uploaded on 11/07/2011 for the course AERO 16.410 taught by Professor Brianwilliams during the Fall '05 term at MIT.
 Fall '05
 BrianWilliams

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