"John Machin" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
| It's *91* distinct solutions to what appears to be *exactly* your
| problem:
|
| """
| Dudeney (1970, pp. 95-96) also gave the following results for the
| number of distinct arrangements N_u(k,n) of k queens attacking or
| occupying every square of an nxn board for which no two queens attack
| one another (they are "not protected").
| k queens nxn N_u(k,n)
| 1 2 1
| 1 3 1
| 3 4 2
| 3 5 2
| 4 6 17
| 4 7 1
| 5 8 91
| """
If you don't want to work out everything for yourself, I would go to the
Wolffram site and find the Dudeney reference and see if it has an algorithm
or merely a list of solutions (even that would help).
A brute force search off the top of my head goes as follows:
The 'topmost' queen can potentially be in any column of rows 0 to 3;
The second queen in the next row to 4, any column;
Etc.
r8 = range(8)
for i0 in range(0, 4):
for j0 in r8:
for i1 in range(i0+1,5):
for j1 in r8:
for i2 in range(i1+1, 6):
for j2 in r8:
for i3 in range(i2+1,7):
for ji in r8:
for i4 in range(i3+1):
for j4 in r8:
test_position:
Optimizations: test non-attacking property as add each queen.
Change range of j0 to range(4) to delete reflections about vertical axis.
To detect all duplicates by reflection and rotation, one needs a
'canonical' form for each position. With that, I think one could do much
better in not generating duplicates.
Terry Jan Reedy
--
http://mail.python.org/mailman/listinfo/python-list
