## Description

Introduction

On page 103 of your textbook, you will find a diagram of the 8-puzzle. Your

work for this assignment is to implement several search techniques to find the shortest

path between the start state and the goal state.

Programming Assignment

Here is the goal state and four start states for the 8-puzzle.

Goal: Easy: Medium: Hard: Worst:

1 2 3 1 3 4 2 8 1 2 8 1 5 6 7

8 4 8 6 2 4 3 4 6 3 4 8

7 6 5 7 5 7 6 5 7 5 3 2 1

Implement the following search algorithms and test them on the start states and goal

state shown above. Only A* needs to detect duplicate states and eliminate them from the

remainder of the search.

1. A* search using the heuristic function f*(n) = g(n) + h*(n), where h*(n) is the

number of tiles out of place (not counting the blank).

2. A* search using the Manhattan heuristic function.

3. Iterative deepening A* with the Manhattan heuristic function.

4. Depth-first Branch and Bound with the Manhattan heuristic function.

When defining the successor function, it is helpful to define the actions in terms of

the empty tile, that is, the four actions are moving the empty tile right, down, left, and

up. Consider the actions in this order in your implementation.

If your algorithms take too long or too much memory to find any solution, your

implementation may be inefficient. Consider optimizing it. If you still can’t find solutions

within a reasonable amount of time, enforce a time limit, say 30 minutes, on your

algorithm and specify it in your report.

Problem Analysis:

For all the algorithms, include in your report a table the number of nodes expanded,

the total time required to solve the puzzle, and the sequence of moves in the optimal

solution. For Depth-first Branch and Bound, also record the time the optimal solution is

found (typically not the same as the finish time).

Besides, answer the following questions:

1. What is the number of possible states of the board?

2. What is the average number of possible moves from a given position of the board?

3. Estimate how many moves might be required for an optimal (minimum number of

moves) solution to a “worst-case” problem (maximum distance between starting and

goal states). Explain how you made your estimate (Note this is an open-ended

question; any logical answer may suffice).

4. Assuming the answer to question #2 is the “average branching factor” and a depth as

in the answer to question #3, estimate the number of nodes that would have to be

examined to find an answer by the brute force breadth-first search.

5. Assuming that your computer can examine one move per millisecond, would such a

blind-search solution to the problem terminate before the end of the semester?

6. The “worst” example problem given above is actually one of the easiest for humans to

solve. Why do you think that is the case? What lessons for AI programs are suggested

by this difference between human performance and performance of your search

program?

7. Compare A*, DFBnB, and IDA* and discuss their advantages and disadvantages.

Deliverables:

Send a single .zip file named LastName.FirstInitial.HW# containing the following

to the instructor:

1) Well commented code;

2) A readme file explaining how to compile and run your code;

3) A written report explaining your experimental results and analysis.

Also submit the report in hardcopy before the class.

Academic honesty: Please do your own work; do not give or receive any assistance in

implementing the algorithms.