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A319284
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The profiles of the backtrack tree for the n queens problem, triangle read by rows.
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6
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1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 1, 4, 6, 4, 2, 1, 5, 12, 14, 12, 10, 1, 6, 20, 36, 46, 40, 4, 1, 7, 30, 76, 140, 164, 94, 40, 1, 8, 42, 140, 344, 568, 550, 312, 92, 1, 9, 56, 234, 732, 1614, 2292, 2038, 1066, 352, 1, 10, 72, 364, 1400, 3916, 7552, 9632, 7828, 4040, 724, 1, 11, 90, 536, 2468, 8492, 21362, 37248, 44148, 34774, 15116, 2680
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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The profile (p_0, p_1, ..., p_n) is the number of nodes at each level of the tree.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Volume 4, Pre-fascicle 5B, Introduction to Backtracking, 7.2.2. Backtrack programming. 2018.
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LINKS
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EXAMPLE
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[1]
[1, 1]
[1, 2, 0]
[1, 3, 2, 0]
[1, 4, 6, 4, 2]
[1, 5, 12, 14, 12, 10]
[1, 6, 20, 36, 46, 40, 4]
[1, 7, 30, 76, 140, 164, 94, 40]
[1, 8, 42, 140, 344, 568, 550, 312, 92]
[1, 9, 56, 234, 732, 1614, 2292, 2038, 1066, 352]
[1, 10, 72, 364, 1400, 3916, 7552, 9632, 7828, 4040, 724]
[1, 11, 90, 536, 2468, 8492, 21362, 37248, 44148, 34774, 15116, 2680]
[1, 12, 110, 756, 4080, 16852, 52856, 120104, 195270, 222720, 160964, 68264, 14200]
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PROG
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(Julia) # See the link section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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