📗 Enter your ID (the wisc email ID without @wisc.edu) here: and click (or hit enter key) 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25m24
📗 If the questions are not generated correctly, try refresh the page using the button at the top left corner.
📗 The same ID should generate the same set of questions. Your answers are not saved when you close the browser. You could print the page: , solve the problems, then enter all your answers at the end.
📗 Please do not refresh the page: your answers will not be saved.
📗 [4 points] Consider A* search on the following grid, with initial state and goal state , and one can move left, right, up, or down one step at a time (no wrapping around). The cost g is the number of moves taken, and the heuristic h is the Manhattan distance to the goal state.
1
2
3
4
5
6
7
8
9
📗 Answer:
📗 [3 points] Suppose the initial state is \(S\) and goal state is \(G\). What is the smallest value of the heuristic at state \(1\) such that when A search (A* without the star) is used on the following graph and it does not find the optimal solution. In case of tie, expand the state with a smaller index (i.e. \(1\) before \(2\)).
📗 In case the diagram is not clear, the edge costs are
📗 Answer: .
📗 [3 points] The initial state and goal state of an 8-puzzle are given below. If the heuristic is the sum of Manhattan distances between the current position of each tile and the goal position, what is the heuristic of the initial state?
The goal state is:
\(1\)
\(2\)
\(3\)
\(4\)
\(5\)
\(6\)
\(7\)
\(8\)
\(0\)
The initial state is:
📗 Answer: .
📗 [4 points] Given the list of states in the priority queue (frontier) and the current cost \(g\) and heuristic cost \(h\), what is the largest value of \(x\) so that state \(0\) will be removed (expanded) from the priority queue next in all three informed search strategies: UCS (Uniform Cost Search), (Best First) Greedy Search, and A Search? Break ties by expanding the state with the smallest index.
State
0
1
2
3
4
5
g
h
\(x\)
📗 Answer: .
📗 [4 points] Given initial state \(S\) and goal state \(G\), write down the expansion path (list of expanded nodes) for . In case the diagram is not clear, the edge costs are (heuristic on the diagonal).
📗 Answer: .
📗 [3 points] Let \(h_{1}\) be an admissible heuristic from a state to the optimal goal, A* search with which ones of the following \(h\) will be admissible?
📗 Choices:
None of the above
📗 [3 points] Let \(h_{1}\) be an admissible heuristic from a state to the optimal goal, A* search with which ones of the following \(h\) will be admissible? Enter the correct choices as a list, comma separated, without parentheses, for example, "1, 2, 4".
📗 Choices:
(1)
(2)
(3)
(4)
(5)
(6)
(7) None of the above
📗 Answer (comma separated vector): .
📗 [3 points] Let \(h_{1}\) be an admissible heuristic from a state to the optimal goal, A* search with which ones of the following \(h\) will be admissible?
📗 Choices:
None of the above
📗 [3 points] Let \(h_{1}\) be an admissible heuristic from a state to the optimal goal, A* search with which ones of the following \(h\) will be admissible?
📗 Choices:
None of the above
📗 [3 points] If \(h_{1}\) and \(h_{2}\) are both admissible heuristic functions, which ones of following are also admissible heuristic functions? Enter the correct choices as a list, comma separated, without parentheses, for example, "1, 2, 4".
📗 Choices:
(1)
(2)
(3)
(4)
(5)
(6)
(7) None of the above
📗 Answer (comma separated vector): .
📗 [3 points] If \(h_{1}\) and \(h_{2}\) are both admissible heuristic functions, which ones of following are also admissible heuristic functions?
📗 Choices:
None of the above
📗 [4 points] Run search algorithm on the following graph, starting from state 0 with the goal state being . Write down the expansion path (in the order of the states expanded). The heuristic function \(h\) is shown as subscripts. Break tie by expanding the state with a smaller index.
📗 In case the diagram is not clear: the weights are (with heuristic values on the diagonal entries): .
📗 Answer (comma separated vector): .
📗 [4 points] Consider search algorithm on the following grid, starting from state 0 with the goal state being , and one can move left, right, up, or down one step at a time (no wrapping around). The cost is the number of moves taken, and the heuristic is the Manhattan distance to the goal. Write down the expansion path (in the order of the states expanded). Break tie by expanding the state with a smaller index.
0
1
2
3
4
5
6
7
8
📗 Answer (comma separated vector): .
📗 [3 points] Given the following two admissible heuristic for A* search, write down another admissible heuristic that (weakly) dominates the two. Write \(\left(h\left(s_{1}\right), h\left(s_{2}\right), h\left(s_{3}\right), h\left(s_{4}\right), h\left(s_{5}\right)\right)\) as a comma separate list. If there are multiple possible values, write one of them, if there are none, write \(-1, -1, -1, -1, -1\).
State
\(s_{1}\)
\(s_{2}\)
\(s_{3}\)
\(s_{4}\)
\(s_{5}\)
\(h_{1}\)
\(h_{2}\)
\(h\)
\(h\left(s_{1}\right)\)
\(h\left(s_{2}\right)\)
\(h\left(s_{3}\right)\)
\(h\left(s_{4}\right)\)
\(h\left(s_{5}\right)\)
📗 Answer (comma separated vector): .
📗 [3 points] Suppose there are \(n\) = states, \(1\) (initial state), \(2\), ..., \(n\) (goal state) and two heuristics \(h_{1}\) and \(h_{2}\), described in the table below, are both admissible. State \(i\) has successors \(i + 1, i + 2, ..., n\), for each \(i = 1, 2, ..., n - 1\). What is the minimum possible total cost from state \(1\) to state \(n\).
📗 Note: do not assume the cost between a state and its successor is 1.
📗 You could save the text in the above text box to a file using the button or copy and paste it into a file yourself .
📗 You could load your answers from the text (or txt file) in the text box below using the button . The first two lines should be "##m: 24" and "##id: your id", and the format of the remaining lines should be "##1: your answer to question 1" newline "##2: your answer to question 2", etc. Please make sure that your answers are loaded correctly before submitting them.
📗 You can find videos going through the questions on Link.