The 8-tiles puzzle solver takes in the state of an 8-tiles puzzle, and gives an output of moves that solves the puzzle.
This project was done as a case study on the effects that differing heuristics may have on the run time of solving the 8-tile puzzle despite using the same search algorithm (A* search), and was undertaken as Assignment 1 of Introduction to Artificial Intelligence (CS3243). Additional helper functions in helper_scripts were written for testing and validation of inputs and outputs.
Written in Python 2.6. However, you may run the scripts with Python 3.7, just change the import from Queue to queue.
Takes in puzzle in input_file, and writes move sequences as output into specified output_file.
python 8tile_heuristic1.py input_file output_file #to use heuristic 1
python 8tile_heuristic2.py input_file output_file #to use heuristic 2To avoid an unnecessarily long and meaningless attempt to solve a potentially unsolvable puzzle, it is best to check whether puzzle is solvable before running 8tile_*.py by counting the number of inversions, using helper_scripts/check_solvable.py
Prints True if puzzle in input_file is solvable. Prints False otherwise.
python check_solvable.py input_filePrints True if sequence of moves in moves_output solves the puzzle. Prints False otherwise.
python move_executor.py input_file moves_outputTakes in 3 lines of numbers, each number signifies a puzzle tile (0 signifies empty space in puzzle), and is separated by spacebar. E.g
1 2 3
0 4 6
7 5 8
An example of move output to solving the above puzzle:
LEFT
UP
LEFT
Check out the sample_inputs and sample_outputs for more clarity.
Sum of manhattan distance
For input_1.txt:
Number of nodes generated: 10
Maximum size of the frontier: 6
For input_2.txt:
Number of nodes generated: 9
Maximum size of the frontier: 6
For input_3.txt:
Number of nodes generated: 10501
Maximum size of the frontier: 3721
For input_4.txt:
Not solvable
Max of 2 heuristics. h1 is the sum of Euclidean distances of the tiles from their goal positions. h2 is the number of tiles out of row + number of tiles out of column.
For input_1.txt:
Number of nodes generated: 36
Maximum size of the frontier: 14
For input_2.txt:
Number of nodes generated: 12
Maximum size of the frontier: 7
For input_3.txt:
Number of nodes generated: 194071
Maximum size of the frontier: 41796
For input_4.txt:
Not solvable
Based on the statistics, heuristic 1 yields significantly better time complexity and consumes significantly less memory than heuristic 2. Overall, the performance of heuristic 1 is better than heuristic 2.
The reason being that both h1 and h2 in heuristic 2 are dominated by the Manhattan distance heuristic. This can be proven by taking a closer look on how both h1 and h2 of heuristic 2 are dominated by heuristic 1.