How to extend the n-Queens problem to three dimensions?
I am facing a problem that "How to extend the n-Queens problem to three dimensions?" I cannot figure it out.
java n-queens
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
add a comment |
I am facing a problem that "How to extend the n-Queens problem to three dimensions?" I cannot figure it out.
java n-queens
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
add a comment |
I am facing a problem that "How to extend the n-Queens problem to three dimensions?" I cannot figure it out.
java n-queens
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
I am facing a problem that "How to extend the n-Queens problem to three dimensions?" I cannot figure it out.
java n-queens
java n-queens
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
asked Nov 14 '18 at 5:18
Judith8899Judith8899
11
11
add a comment |
add a comment |
1 Answer
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Answer could be very long but esentially you add one more rule to the most known problem:
height
The solution is represented by a set D, if for the Cartesian product, D×D, each element ((ik, jk), (il, jl)) either satisfies all of the following rules or fails all of them.
(1) ik ≠ il (not on same column)
(2) jk ≠ jl (not on same row)
(3) ik + jk ≠ il + jl (not on same diagonal)
(4) ik − jk ≠ il − jl (not on same diagonal)
To make it 3d you add:
(5) ih ≠ jh (not on the same vertical plane with height h)
https://medium.com/@abhijith0505/the-n-queens-in-3-d-640e20130912
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
Don't forget about diagonals with height.
– Mad Physicist
Nov 14 '18 at 5:26
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Answer could be very long but esentially you add one more rule to the most known problem:
height
The solution is represented by a set D, if for the Cartesian product, D×D, each element ((ik, jk), (il, jl)) either satisfies all of the following rules or fails all of them.
(1) ik ≠ il (not on same column)
(2) jk ≠ jl (not on same row)
(3) ik + jk ≠ il + jl (not on same diagonal)
(4) ik − jk ≠ il − jl (not on same diagonal)
To make it 3d you add:
(5) ih ≠ jh (not on the same vertical plane with height h)
https://medium.com/@abhijith0505/the-n-queens-in-3-d-640e20130912
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
Don't forget about diagonals with height.
– Mad Physicist
Nov 14 '18 at 5:26
add a comment |
Answer could be very long but esentially you add one more rule to the most known problem:
height
The solution is represented by a set D, if for the Cartesian product, D×D, each element ((ik, jk), (il, jl)) either satisfies all of the following rules or fails all of them.
(1) ik ≠ il (not on same column)
(2) jk ≠ jl (not on same row)
(3) ik + jk ≠ il + jl (not on same diagonal)
(4) ik − jk ≠ il − jl (not on same diagonal)
To make it 3d you add:
(5) ih ≠ jh (not on the same vertical plane with height h)
https://medium.com/@abhijith0505/the-n-queens-in-3-d-640e20130912
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
Don't forget about diagonals with height.
– Mad Physicist
Nov 14 '18 at 5:26
add a comment |
Answer could be very long but esentially you add one more rule to the most known problem:
height
The solution is represented by a set D, if for the Cartesian product, D×D, each element ((ik, jk), (il, jl)) either satisfies all of the following rules or fails all of them.
(1) ik ≠ il (not on same column)
(2) jk ≠ jl (not on same row)
(3) ik + jk ≠ il + jl (not on same diagonal)
(4) ik − jk ≠ il − jl (not on same diagonal)
To make it 3d you add:
(5) ih ≠ jh (not on the same vertical plane with height h)
https://medium.com/@abhijith0505/the-n-queens-in-3-d-640e20130912
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
Answer could be very long but esentially you add one more rule to the most known problem:
height
The solution is represented by a set D, if for the Cartesian product, D×D, each element ((ik, jk), (il, jl)) either satisfies all of the following rules or fails all of them.
(1) ik ≠ il (not on same column)
(2) jk ≠ jl (not on same row)
(3) ik + jk ≠ il + jl (not on same diagonal)
(4) ik − jk ≠ il − jl (not on same diagonal)
To make it 3d you add:
(5) ih ≠ jh (not on the same vertical plane with height h)
https://medium.com/@abhijith0505/the-n-queens-in-3-d-640e20130912
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
answered Nov 14 '18 at 5:22
cMinorcMinor
13k64198335
13k64198335
Don't forget about diagonals with height.
– Mad Physicist
Nov 14 '18 at 5:26
add a comment |
Don't forget about diagonals with height.
– Mad Physicist
Nov 14 '18 at 5:26
Don't forget about diagonals with height.
– Mad Physicist
Nov 14 '18 at 5:26
Don't forget about diagonals with height.
– Mad Physicist
Nov 14 '18 at 5:26
add a comment |
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