### CSC 550: Introduction to Artificial Intelligence Spring 2004 HW2: State Space Search

This assignment involves solving state space problems and comparing the performance of the different search strategies discussed in class. MzScheme provides a utility function, time, that can be useful in profiling code. The time function, when given an expression as input, evaluates that expression and reports the number of milliseconds of CPU time taken for the evaluation. It even identifies the amount of CPU time taken by garbage collection, so that number can be subtracted out to determine the amount of time spent doing actual computation.

1. Consider the Missionaries and Cannibals puzzle discussed in class. The file www.creighton.edu/~davereed/csc550/Code/mission.scm contains a state space definition for this puzzle. It utilizes states of the form ((MissionariesOnLeft CannibalsOnLeft) BoatPosition (MissionariesOnRight CannibalsOnRight)) where the numbers of missionaries and cannibals on each side of the river will be integers ranging from 0 to 3, and the boat position will be either left or right. For example, the initial state for the puzzle is ((3 3) left (0 0)), and the goal state is ((0 0) right (3 3)).

Using the time function and the implementations in www.creighton.edu/~davereed/csc550/Code/search.scm, compare the performances of DFS, DFS-nocycles, BFS, BFS-nocycles, and DFS-deepening on this puzzle. That is, when the strategy produces an answer, report the execution time (not counting garbage collection). Comment on the apparent tradeoffs between the strategies.

Note: the shortest time reportable by the time function is 10 ms. If a search succeeds in finding a solution in less than 10 ms, then it will register as no time at all. If this occurs, time multiple calls to the function and divide by the number of repetitions to get a more accurate timing. For example, the following call would time how long it takes for DFS to solve the problem five times.

(time (begin (dfs '((3 3) left (0 0)) '((0 0) right (3 3))) (dfs '((3 3) left (0 0)) '((0 0) right (3 3))) (dfs '((3 3) left (0 0)) '((0 0) right (3 3))) (dfs '((3 3) left (0 0)) '((0 0) right (3 3))) (dfs '((3 3) left (0 0)) '((0 0) right (3 3)))))
2. Consider the problem of traversing a maze, from one opening (identified as the Start) to another opening (identified as the Exit). For example, the diagram on the left shows an 8x9 maze, where the Start is at the upper-left corner, the Exit is at the lower-right corner, and walls are shown as black rectangles. To the right is a Scheme list structure that represents this maze.
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(define MAZE '("*********" "S *" "* ** * *" "* ** *" "* * *****" "* * *" "* * ** E" "*********"))

For maze traversals, a state space can be defined in which a state is defined by the coordinates of the person in the maze. For the above maze, we might identify the Start state as (1 0), designating the row at index 1 and the column at index 0. Likewise, the goal (Exit) state would be identified as (6 8).

Add the above definition of MAZE to a file named maze.scm, and define the GET-MOVES function for the maze state space using this state representation. For example, the call (GET-MOVES '(1 1)) should return '((1 0) (1 2) (2 1)), or some permutation of these three adjacent spaces in the maze. Note that your GET-MOVES function should work correctly even if a different maze is substituted for the above one. In particular, the maze dimensions might change and the Start and Exit positions might vary from maze to maze.

Once you have completed this function, compare the performances of the uninformed search strategies on this problem and comment on the apparent tradeoffs.

3. The Missionaries and Cannibals state space from mission.scm contains a HEURISTIC function, which assigns a value to a state based on how many people are in their goal positions. This heuristic can be used by the hill-climbing and best first search strategies defined in www.creighton.edu/~davereed/csc550/Code/heuristics.scm. Compare the performance of these informed search strategies on the Missionaries and Cannibals problem. Does hill-climbing find a solution? Does best first search outperform the uninformed strategies from problem 1? Explain your answers.

4. Similarly, define a HEURISTIC function for your maze state space that can be used by the informed search strategies. Your function should assign a value to a state based on its distance from the goal (Exit) state. In particular, the function should determine the differences in row and column numbers between the current and goal states, and return the negated sum of those differences. Thus, (HEURISTIC '(5 4) '(6 8)) should evaluate to -5. Compare the performance of the informed search strategies using this heuristic and comment on its behavior.