Abstract
The most common application of graph theory is search problems. Using graph theory, this project aims to solve one such NP-hard problem, i.e., finding a path for a Rubik’s cube to reach the solved state from a scrambled one. Rubik’s cube is among one of the fascinating puzzles and solving them has been a challenge given its vast search space of 43 quintillion. This paper aims at demonstrating the application and performance of traditional search algorithms like breadth-first search, depth-limited search, and bidirectional search, and proposes a new approach to find the solution by integrating them. The proposed algorithm makes use of the fact that the God’s number for a 3\(\times \)3\(\times \)3 Rubik’s cube is 20, i.e., the fact that any cube scramble within the 43 quintillion states can be solved within a max of 20 moves.
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Khemani, C., Doshi, J., Duseja, J., Shah, K., Udmale, S., Sambhe, V. (2019). Solving Rubik’s Cube Using Graph Theory. In: Verma, N., Ghosh, A. (eds) Computational Intelligence: Theories, Applications and Future Directions - Volume I. Advances in Intelligent Systems and Computing, vol 798. Springer, Singapore. https://doi.org/10.1007/978-981-13-1132-1_24
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DOI: https://doi.org/10.1007/978-981-13-1132-1_24
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