Abstract
The 8-puzzle is a classical sliding puzzle that consists of 8 numbered tiles placed in random order on a board with 9 cells. The goal is to rearrange the tiles by sliding them horizontally or vertically into the vacant cell such that the number in each tile is ordered in ascending order. 8-puzzles can be solved by using the path searching algorithms such as Best-first search, Depth-fist search, Dijkstra’s algorithm, or the A* algorithm. In this paper, the A* algorithm will be the one chosen. The A* algorithm is known to be an improvement to the Dijkstra’s algorithm since not all potential paths need to be searched before the optimal one is found. The key of the A* algorithm is choosing the right heuristic formula as an estimation to the cost of each path. Two heuristics, the Hamming distance and the Manhattan distance are chosen to be implemented in the A* algorithm. The computing time for our several test puzzles suggests that the Manhattan distance is found to be the more efficient heuristic.
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Lee, S.C., See, T.H. (2022). Comparing the Hamming and Manhattan Heuristics in Solving the 8—Puzzle by A* Algorithm. In: Mustapha, A.B., Shamsuddin, S., Zuhaib Haider Rizvi, S., Asman, S.B., Jamaian, S.S. (eds) Proceedings of the 7th International Conference on the Applications of Science and Mathematics 2021. Springer Proceedings in Physics, vol 273. Springer, Singapore. https://doi.org/10.1007/978-981-16-8903-1_19
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DOI: https://doi.org/10.1007/978-981-16-8903-1_19
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