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Problem Space of the Tower of London

Number of steps as a function of distance

Each cell is the number of steps of  a random broad-first exploration algorithm with bounded memory averaged over tasks of N moves and 2048 repetitions.

columns : distance between initial and final configuration


N 0 1 2 3 4 5 6 7 8
average 1.00 2.58 9.03 26.90 87.68 283.24 873.39 2862.22 6224.68
stdev 0.00 0.50 1.78 6.14 20.22 62.33 201.97 658.12 1062.70
min 1.00 2.00 6.00 15.00 49.00 183.00 586.00 1855.00 4254.00
max 1.00 3.00 11.00 37.00 119.00 379.00 1214.00 3896.00 7999.00




Figure 1. Average number of steps  as a function of distance between
initial and final configuration. Thick bars: average. Thin bars: standard deviation.



Copyright: (c) 2009 E.J. Fimbel, S. Lauzon, C. Rainville. This is open-access content distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.