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Algorithms 2015, 8(3), 459-465; doi:10.3390/a8030459

Solving the (n2 − 1)-Puzzle with 8/3 n3 Expected Moves

Department of Computer Science & Engineering, University of North Texas, Denton, TX 76203–5017, USA
Academic Editor: Dimitris Fotakis
Received: 13 January 2015 / Revised: 28 May 2015 / Accepted: 30 June 2015 / Published: 10 July 2015
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Abstract

It is shown that the greedy algorithm for the \((n^2-1)\)-puzzle makes \(\tfrac{8}{3}n^3 +O(n^2)\) expected moves. This analysis is verified experimentally on 10,000 random instances each of the \((n^2-1)\)-puzzle for \(4 \leq n \leq 200\). View Full-Text
Keywords: 15-puzzle, 8-puzzle, analysis of algorithms, average case analysis, greedy algorithm, (n2 — 1)-puzzle 15-puzzle, 8-puzzle, analysis of algorithms, average case analysis, greedy algorithm, (n2 — 1)-puzzle
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Parberry, I. Solving the (n2 − 1)-Puzzle with 8/3 n3 Expected Moves. Algorithms 2015, 8, 459-465.

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