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Anirban Mukhopadhyay 5d14dbab8a Implementation of n-queen solution generator		2016-07-06 01:06:49 -04:00
.gitignore	Skeleton for solver	2016-07-05 23:08:14 -04:00
gen_solutions.cpp	Implementation of n-queen solution generator	2016-07-06 01:06:49 -04:00
grid.h	Implementation of n-queen solution generator	2016-07-06 01:06:49 -04:00
Makefile	Implementation of n-queen solution generator	2016-07-06 01:06:49 -04:00
n_queens.cpp	Implementation of n-queen solution generator	2016-07-06 01:06:49 -04:00
n_queens.h	Implementation of n-queen solution generator	2016-07-06 01:06:49 -04:00
README.md	Implementation of n-queen solution generator	2016-07-06 01:06:49 -04:00

README.md

n-queens

Generates all solutions to the n-queen problem given a specific n.

Sample output generated for n = 8:

[ 0, 4, 7, 5, 2, 6, 1, 3 ]

Q x x x x x x x
x x x x Q x x x
x x x x x x x Q
x x x x x Q x x
x x Q x x x x x
x x x x x x Q x
x Q x x x x x x
x x x Q x x x x

[ 0, 5, 7, 2, 6, 3, 1, 4 ]

Q x x x x x x x
x x x x x Q x x
x x x x x x x Q
x x Q x x x x x
x x x x x x Q x
x x x Q x x x x
x Q x x x x x x
x x x x Q x x x

[ 0, 6, 3, 5, 7, 1, 4, 2 ]

Q x x x x x x x
x x x x x x Q x
x x x Q x x x x
x x x x x Q x x
x x x x x x x Q
x Q x x x x x x
x x x x Q x x x
x x Q x x x x x

[ 0, 6, 4, 7, 1, 3, 5, 2 ]

Q x x x x x x x
x x x x x x Q x
x x x x Q x x x
x x x x x x x Q
x Q x x x x x x
x x x Q x x x x
x x x x x Q x x
x x Q x x x x x

[ 1, 3, 5, 7, 2, 0, 6, 4 ]

x Q x x x x x x
x x x Q x x x x
x x x x x Q x x
x x x x x x x Q
x x Q x x x x x
Q x x x x x x x
x x x x x x Q x
x x x x Q x x x

[ 1, 4, 6, 0, 2, 7, 5, 3 ]

x Q x x x x x x
x x x x Q x x x
x x x x x x Q x
Q x x x x x x x
x x Q x x x x x
x x x x x x x Q
x x x x x Q x x
x x x Q x x x x

[ 1, 4, 6, 3, 0, 7, 5, 2 ]

x Q x x x x x x
x x x x Q x x x
x x x x x x Q x
x x x Q x x x x
Q x x x x x x x
x x x x x x x Q
x x x x x Q x x
x x Q x x x x x

[ 1, 5, 0, 6, 3, 7, 2, 4 ]

x Q x x x x x x
x x x x x Q x x
Q x x x x x x x
x x x x x x Q x
x x x Q x x x x
x x x x x x x Q
x x Q x x x x x
x x x x Q x x x

[ 1, 5, 7, 2, 0, 3, 6, 4 ]

x Q x x x x x x
x x x x x Q x x
x x x x x x x Q
x x Q x x x x x
Q x x x x x x x
x x x Q x x x x
x x x x x x Q x
x x x x Q x x x

[ 1, 6, 2, 5, 7, 4, 0, 3 ]

x Q x x x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x Q x x
x x x x x x x Q
x x x x Q x x x
Q x x x x x x x
x x x Q x x x x

[ 1, 6, 4, 7, 0, 3, 5, 2 ]

x Q x x x x x x
x x x x x x Q x
x x x x Q x x x
x x x x x x x Q
Q x x x x x x x
x x x Q x x x x
x x x x x Q x x
x x Q x x x x x

[ 1, 7, 5, 0, 2, 4, 6, 3 ]

x Q x x x x x x
x x x x x x x Q
x x x x x Q x x
Q x x x x x x x
x x Q x x x x x
x x x x Q x x x
x x x x x x Q x
x x x Q x x x x

[ 2, 0, 6, 4, 7, 1, 3, 5 ]

x x Q x x x x x
Q x x x x x x x
x x x x x x Q x
x x x x Q x x x
x x x x x x x Q
x Q x x x x x x
x x x Q x x x x
x x x x x Q x x

[ 2, 4, 1, 7, 0, 6, 3, 5 ]

x x Q x x x x x
x x x x Q x x x
x Q x x x x x x
x x x x x x x Q
Q x x x x x x x
x x x x x x Q x
x x x Q x x x x
x x x x x Q x x

[ 2, 4, 1, 7, 5, 3, 6, 0 ]

x x Q x x x x x
x x x x Q x x x
x Q x x x x x x
x x x x x x x Q
x x x x x Q x x
x x x Q x x x x
x x x x x x Q x
Q x x x x x x x

[ 2, 4, 6, 0, 3, 1, 7, 5 ]

x x Q x x x x x
x x x x Q x x x
x x x x x x Q x
Q x x x x x x x
x x x Q x x x x
x Q x x x x x x
x x x x x x x Q
x x x x x Q x x

[ 2, 4, 7, 3, 0, 6, 1, 5 ]

x x Q x x x x x
x x x x Q x x x
x x x x x x x Q
x x x Q x x x x
Q x x x x x x x
x x x x x x Q x
x Q x x x x x x
x x x x x Q x x

[ 2, 5, 1, 4, 7, 0, 6, 3 ]

x x Q x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x Q x x x
x x x x x x x Q
Q x x x x x x x
x x x x x x Q x
x x x Q x x x x

[ 2, 5, 1, 6, 0, 3, 7, 4 ]

x x Q x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x x x Q x
Q x x x x x x x
x x x Q x x x x
x x x x x x x Q
x x x x Q x x x

[ 2, 5, 1, 6, 4, 0, 7, 3 ]

x x Q x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x x x Q x
x x x x Q x x x
Q x x x x x x x
x x x x x x x Q
x x x Q x x x x

[ 2, 5, 3, 0, 7, 4, 6, 1 ]

x x Q x x x x x
x x x x x Q x x
x x x Q x x x x
Q x x x x x x x
x x x x x x x Q
x x x x Q x x x
x x x x x x Q x
x Q x x x x x x

[ 2, 5, 3, 1, 7, 4, 6, 0 ]

x x Q x x x x x
x x x x x Q x x
x x x Q x x x x
x Q x x x x x x
x x x x x x x Q
x x x x Q x x x
x x x x x x Q x
Q x x x x x x x

[ 2, 5, 7, 0, 3, 6, 4, 1 ]

x x Q x x x x x
x x x x x Q x x
x x x x x x x Q
Q x x x x x x x
x x x Q x x x x
x x x x x x Q x
x x x x Q x x x
x Q x x x x x x

[ 2, 5, 7, 0, 4, 6, 1, 3 ]

x x Q x x x x x
x x x x x Q x x
x x x x x x x Q
Q x x x x x x x
x x x x Q x x x
x x x x x x Q x
x Q x x x x x x
x x x Q x x x x

[ 2, 5, 7, 1, 3, 0, 6, 4 ]

x x Q x x x x x
x x x x x Q x x
x x x x x x x Q
x Q x x x x x x
x x x Q x x x x
Q x x x x x x x
x x x x x x Q x
x x x x Q x x x

[ 2, 6, 1, 7, 4, 0, 3, 5 ]

x x Q x x x x x
x x x x x x Q x
x Q x x x x x x
x x x x x x x Q
x x x x Q x x x
Q x x x x x x x
x x x Q x x x x
x x x x x Q x x

[ 2, 6, 1, 7, 5, 3, 0, 4 ]

x x Q x x x x x
x x x x x x Q x
x Q x x x x x x
x x x x x x x Q
x x x x x Q x x
x x x Q x x x x
Q x x x x x x x
x x x x Q x x x

[ 2, 7, 3, 6, 0, 5, 1, 4 ]

x x Q x x x x x
x x x x x x x Q
x x x Q x x x x
x x x x x x Q x
Q x x x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x Q x x x

[ 3, 0, 4, 7, 1, 6, 2, 5 ]

x x x Q x x x x
Q x x x x x x x
x x x x Q x x x
x x x x x x x Q
x Q x x x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x Q x x

[ 3, 0, 4, 7, 5, 2, 6, 1 ]

x x x Q x x x x
Q x x x x x x x
x x x x Q x x x
x x x x x x x Q
x x x x x Q x x
x x Q x x x x x
x x x x x x Q x
x Q x x x x x x

[ 3, 1, 4, 7, 5, 0, 2, 6 ]

x x x Q x x x x
x Q x x x x x x
x x x x Q x x x
x x x x x x x Q
x x x x x Q x x
Q x x x x x x x
x x Q x x x x x
x x x x x x Q x

[ 3, 1, 6, 2, 5, 7, 0, 4 ]

x x x Q x x x x
x Q x x x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x Q x x
x x x x x x x Q
Q x x x x x x x
x x x x Q x x x

[ 3, 1, 6, 2, 5, 7, 4, 0 ]

x x x Q x x x x
x Q x x x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x Q x x
x x x x x x x Q
x x x x Q x x x
Q x x x x x x x

[ 3, 1, 6, 4, 0, 7, 5, 2 ]

x x x Q x x x x
x Q x x x x x x
x x x x x x Q x
x x x x Q x x x
Q x x x x x x x
x x x x x x x Q
x x x x x Q x x
x x Q x x x x x

[ 3, 1, 7, 4, 6, 0, 2, 5 ]

x x x Q x x x x
x Q x x x x x x
x x x x x x x Q
x x x x Q x x x
x x x x x x Q x
Q x x x x x x x
x x Q x x x x x
x x x x x Q x x

[ 3, 1, 7, 5, 0, 2, 4, 6 ]

x x x Q x x x x
x Q x x x x x x
x x x x x x x Q
x x x x x Q x x
Q x x x x x x x
x x Q x x x x x
x x x x Q x x x
x x x x x x Q x

[ 3, 5, 0, 4, 1, 7, 2, 6 ]

x x x Q x x x x
x x x x x Q x x
Q x x x x x x x
x x x x Q x x x
x Q x x x x x x
x x x x x x x Q
x x Q x x x x x
x x x x x x Q x

[ 3, 5, 7, 1, 6, 0, 2, 4 ]

x x x Q x x x x
x x x x x Q x x
x x x x x x x Q
x Q x x x x x x
x x x x x x Q x
Q x x x x x x x
x x Q x x x x x
x x x x Q x x x

[ 3, 5, 7, 2, 0, 6, 4, 1 ]

x x x Q x x x x
x x x x x Q x x
x x x x x x x Q
x x Q x x x x x
Q x x x x x x x
x x x x x x Q x
x x x x Q x x x
x Q x x x x x x

[ 3, 6, 0, 7, 4, 1, 5, 2 ]

x x x Q x x x x
x x x x x x Q x
Q x x x x x x x
x x x x x x x Q
x x x x Q x x x
x Q x x x x x x
x x x x x Q x x
x x Q x x x x x

[ 3, 6, 2, 7, 1, 4, 0, 5 ]

x x x Q x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x x x Q
x Q x x x x x x
x x x x Q x x x
Q x x x x x x x
x x x x x Q x x

[ 3, 6, 4, 1, 5, 0, 2, 7 ]

x x x Q x x x x
x x x x x x Q x
x x x x Q x x x
x Q x x x x x x
x x x x x Q x x
Q x x x x x x x
x x Q x x x x x
x x x x x x x Q

[ 3, 6, 4, 2, 0, 5, 7, 1 ]

x x x Q x x x x
x x x x x x Q x
x x x x Q x x x
x x Q x x x x x
Q x x x x x x x
x x x x x Q x x
x x x x x x x Q
x Q x x x x x x

[ 3, 7, 0, 2, 5, 1, 6, 4 ]

x x x Q x x x x
x x x x x x x Q
Q x x x x x x x
x x Q x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x x x Q x
x x x x Q x x x

[ 3, 7, 0, 4, 6, 1, 5, 2 ]

x x x Q x x x x
x x x x x x x Q
Q x x x x x x x
x x x x Q x x x
x x x x x x Q x
x Q x x x x x x
x x x x x Q x x
x x Q x x x x x

[ 3, 7, 4, 2, 0, 6, 1, 5 ]

x x x Q x x x x
x x x x x x x Q
x x x x Q x x x
x x Q x x x x x
Q x x x x x x x
x x x x x x Q x
x Q x x x x x x
x x x x x Q x x

[ 4, 0, 3, 5, 7, 1, 6, 2 ]

x x x x Q x x x
Q x x x x x x x
x x x Q x x x x
x x x x x Q x x
x x x x x x x Q
x Q x x x x x x
x x x x x x Q x
x x Q x x x x x

[ 4, 0, 7, 3, 1, 6, 2, 5 ]

x x x x Q x x x
Q x x x x x x x
x x x x x x x Q
x x x Q x x x x
x Q x x x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x Q x x

[ 4, 0, 7, 5, 2, 6, 1, 3 ]

x x x x Q x x x
Q x x x x x x x
x x x x x x x Q
x x x x x Q x x
x x Q x x x x x
x x x x x x Q x
x Q x x x x x x
x x x Q x x x x

[ 4, 1, 3, 5, 7, 2, 0, 6 ]

x x x x Q x x x
x Q x x x x x x
x x x Q x x x x
x x x x x Q x x
x x x x x x x Q
x x Q x x x x x
Q x x x x x x x
x x x x x x Q x

[ 4, 1, 3, 6, 2, 7, 5, 0 ]

x x x x Q x x x
x Q x x x x x x
x x x Q x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x x x Q
x x x x x Q x x
Q x x x x x x x

[ 4, 1, 5, 0, 6, 3, 7, 2 ]

x x x x Q x x x
x Q x x x x x x
x x x x x Q x x
Q x x x x x x x
x x x x x x Q x
x x x Q x x x x
x x x x x x x Q
x x Q x x x x x

[ 4, 1, 7, 0, 3, 6, 2, 5 ]

x x x x Q x x x
x Q x x x x x x
x x x x x x x Q
Q x x x x x x x
x x x Q x x x x
x x x x x x Q x
x x Q x x x x x
x x x x x Q x x

[ 4, 2, 0, 5, 7, 1, 3, 6 ]

x x x x Q x x x
x x Q x x x x x
Q x x x x x x x
x x x x x Q x x
x x x x x x x Q
x Q x x x x x x
x x x Q x x x x
x x x x x x Q x

[ 4, 2, 0, 6, 1, 7, 5, 3 ]

x x x x Q x x x
x x Q x x x x x
Q x x x x x x x
x x x x x x Q x
x Q x x x x x x
x x x x x x x Q
x x x x x Q x x
x x x Q x x x x

[ 4, 2, 7, 3, 6, 0, 5, 1 ]

x x x x Q x x x
x x Q x x x x x
x x x x x x x Q
x x x Q x x x x
x x x x x x Q x
Q x x x x x x x
x x x x x Q x x
x Q x x x x x x

[ 4, 6, 0, 2, 7, 5, 3, 1 ]

x x x x Q x x x
x x x x x x Q x
Q x x x x x x x
x x Q x x x x x
x x x x x x x Q
x x x x x Q x x
x x x Q x x x x
x Q x x x x x x

[ 4, 6, 0, 3, 1, 7, 5, 2 ]

x x x x Q x x x
x x x x x x Q x
Q x x x x x x x
x x x Q x x x x
x Q x x x x x x
x x x x x x x Q
x x x x x Q x x
x x Q x x x x x

[ 4, 6, 1, 3, 7, 0, 2, 5 ]

x x x x Q x x x
x x x x x x Q x
x Q x x x x x x
x x x Q x x x x
x x x x x x x Q
Q x x x x x x x
x x Q x x x x x
x x x x x Q x x

[ 4, 6, 1, 5, 2, 0, 3, 7 ]

x x x x Q x x x
x x x x x x Q x
x Q x x x x x x
x x x x x Q x x
x x Q x x x x x
Q x x x x x x x
x x x Q x x x x
x x x x x x x Q

[ 4, 6, 1, 5, 2, 0, 7, 3 ]

x x x x Q x x x
x x x x x x Q x
x Q x x x x x x
x x x x x Q x x
x x Q x x x x x
Q x x x x x x x
x x x x x x x Q
x x x Q x x x x

[ 4, 6, 3, 0, 2, 7, 5, 1 ]

x x x x Q x x x
x x x x x x Q x
x x x Q x x x x
Q x x x x x x x
x x Q x x x x x
x x x x x x x Q
x x x x x Q x x
x Q x x x x x x

[ 4, 7, 3, 0, 2, 5, 1, 6 ]

x x x x Q x x x
x x x x x x x Q
x x x Q x x x x
Q x x x x x x x
x x Q x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x x x Q x

[ 4, 7, 3, 0, 6, 1, 5, 2 ]

x x x x Q x x x
x x x x x x x Q
x x x Q x x x x
Q x x x x x x x
x x x x x x Q x
x Q x x x x x x
x x x x x Q x x
x x Q x x x x x

[ 5, 0, 4, 1, 7, 2, 6, 3 ]

x x x x x Q x x
Q x x x x x x x
x x x x Q x x x
x Q x x x x x x
x x x x x x x Q
x x Q x x x x x
x x x x x x Q x
x x x Q x x x x

[ 5, 1, 6, 0, 2, 4, 7, 3 ]

x x x x x Q x x
x Q x x x x x x
x x x x x x Q x
Q x x x x x x x
x x Q x x x x x
x x x x Q x x x
x x x x x x x Q
x x x Q x x x x

[ 5, 1, 6, 0, 3, 7, 4, 2 ]

x x x x x Q x x
x Q x x x x x x
x x x x x x Q x
Q x x x x x x x
x x x Q x x x x
x x x x x x x Q
x x x x Q x x x
x x Q x x x x x

[ 5, 2, 0, 6, 4, 7, 1, 3 ]

x x x x x Q x x
x x Q x x x x x
Q x x x x x x x
x x x x x x Q x
x x x x Q x x x
x x x x x x x Q
x Q x x x x x x
x x x Q x x x x

[ 5, 2, 0, 7, 3, 1, 6, 4 ]

x x x x x Q x x
x x Q x x x x x
Q x x x x x x x
x x x x x x x Q
x x x Q x x x x
x Q x x x x x x
x x x x x x Q x
x x x x Q x x x

[ 5, 2, 0, 7, 4, 1, 3, 6 ]

x x x x x Q x x
x x Q x x x x x
Q x x x x x x x
x x x x x x x Q
x x x x Q x x x
x Q x x x x x x
x x x Q x x x x
x x x x x x Q x

[ 5, 2, 4, 6, 0, 3, 1, 7 ]

x x x x x Q x x
x x Q x x x x x
x x x x Q x x x
x x x x x x Q x
Q x x x x x x x
x x x Q x x x x
x Q x x x x x x
x x x x x x x Q

[ 5, 2, 4, 7, 0, 3, 1, 6 ]

x x x x x Q x x
x x Q x x x x x
x x x x Q x x x
x x x x x x x Q
Q x x x x x x x
x x x Q x x x x
x Q x x x x x x
x x x x x x Q x

[ 5, 2, 6, 1, 3, 7, 0, 4 ]

x x x x x Q x x
x x Q x x x x x
x x x x x x Q x
x Q x x x x x x
x x x Q x x x x
x x x x x x x Q
Q x x x x x x x
x x x x Q x x x

[ 5, 2, 6, 1, 7, 4, 0, 3 ]

x x x x x Q x x
x x Q x x x x x
x x x x x x Q x
x Q x x x x x x
x x x x x x x Q
x x x x Q x x x
Q x x x x x x x
x x x Q x x x x

[ 5, 2, 6, 3, 0, 7, 1, 4 ]

x x x x x Q x x
x x Q x x x x x
x x x x x x Q x
x x x Q x x x x
Q x x x x x x x
x x x x x x x Q
x Q x x x x x x
x x x x Q x x x

[ 5, 3, 0, 4, 7, 1, 6, 2 ]

x x x x x Q x x
x x x Q x x x x
Q x x x x x x x
x x x x Q x x x
x x x x x x x Q
x Q x x x x x x
x x x x x x Q x
x x Q x x x x x

[ 5, 3, 1, 7, 4, 6, 0, 2 ]

x x x x x Q x x
x x x Q x x x x
x Q x x x x x x
x x x x x x x Q
x x x x Q x x x
x x x x x x Q x
Q x x x x x x x
x x Q x x x x x

[ 5, 3, 6, 0, 2, 4, 1, 7 ]

x x x x x Q x x
x x x Q x x x x
x x x x x x Q x
Q x x x x x x x
x x Q x x x x x
x x x x Q x x x
x Q x x x x x x
x x x x x x x Q

[ 5, 3, 6, 0, 7, 1, 4, 2 ]

x x x x x Q x x
x x x Q x x x x
x x x x x x Q x
Q x x x x x x x
x x x x x x x Q
x Q x x x x x x
x x x x Q x x x
x x Q x x x x x

[ 5, 7, 1, 3, 0, 6, 4, 2 ]

x x x x x Q x x
x x x x x x x Q
x Q x x x x x x
x x x Q x x x x
Q x x x x x x x
x x x x x x Q x
x x x x Q x x x
x x Q x x x x x

[ 6, 0, 2, 7, 5, 3, 1, 4 ]

x x x x x x Q x
Q x x x x x x x
x x Q x x x x x
x x x x x x x Q
x x x x x Q x x
x x x Q x x x x
x Q x x x x x x
x x x x Q x x x

[ 6, 1, 3, 0, 7, 4, 2, 5 ]

x x x x x x Q x
x Q x x x x x x
x x x Q x x x x
Q x x x x x x x
x x x x x x x Q
x x x x Q x x x
x x Q x x x x x
x x x x x Q x x

[ 6, 1, 5, 2, 0, 3, 7, 4 ]

x x x x x x Q x
x Q x x x x x x
x x x x x Q x x
x x Q x x x x x
Q x x x x x x x
x x x Q x x x x
x x x x x x x Q
x x x x Q x x x

[ 6, 2, 0, 5, 7, 4, 1, 3 ]

x x x x x x Q x
x x Q x x x x x
Q x x x x x x x
x x x x x Q x x
x x x x x x x Q
x x x x Q x x x
x Q x x x x x x
x x x Q x x x x

[ 6, 2, 7, 1, 4, 0, 5, 3 ]

x x x x x x Q x
x x Q x x x x x
x x x x x x x Q
x Q x x x x x x
x x x x Q x x x
Q x x x x x x x
x x x x x Q x x
x x x Q x x x x

[ 6, 3, 1, 4, 7, 0, 2, 5 ]

x x x x x x Q x
x x x Q x x x x
x Q x x x x x x
x x x x Q x x x
x x x x x x x Q
Q x x x x x x x
x x Q x x x x x
x x x x x Q x x

[ 6, 3, 1, 7, 5, 0, 2, 4 ]

x x x x x x Q x
x x x Q x x x x
x Q x x x x x x
x x x x x x x Q
x x x x x Q x x
Q x x x x x x x
x x Q x x x x x
x x x x Q x x x

[ 6, 4, 2, 0, 5, 7, 1, 3 ]

x x x x x x Q x
x x x x Q x x x
x x Q x x x x x
Q x x x x x x x
x x x x x Q x x
x x x x x x x Q
x Q x x x x x x
x x x Q x x x x

[ 7, 1, 3, 0, 6, 4, 2, 5 ]

x x x x x x x Q
x Q x x x x x x
x x x Q x x x x
Q x x x x x x x
x x x x x x Q x
x x x x Q x x x
x x Q x x x x x
x x x x x Q x x

[ 7, 1, 4, 2, 0, 6, 3, 5 ]

x x x x x x x Q
x Q x x x x x x
x x x x Q x x x
x x Q x x x x x
Q x x x x x x x
x x x x x x Q x
x x x Q x x x x
x x x x x Q x x

[ 7, 2, 0, 5, 1, 4, 6, 3 ]

x x x x x x x Q
x x Q x x x x x
Q x x x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x Q x x x
x x x x x x Q x
x x x Q x x x x

[ 7, 3, 0, 2, 5, 1, 6, 4 ]

x x x x x x x Q
x x x Q x x x x
Q x x x x x x x
x x Q x x x x x
x x x x x Q x x
x Q x x x x x x
x x x x x x Q x
x x x x Q x x x