Talk:Peaceful chess queen armies

Original Python exhaustive search

I was experimenting with various things when doing the Python. This is the original:

Exhaustive search. <lang python>from itertools import combinations, count from functools import lru_cache, reduce

1. n-by-n board

n = 5

def _2d(n=n):

 for i in range(n):
     print('  '.join(f'{i},{j}' for j in range(n)))

def _1d(n=n):

 for i in range(0, n*n, n):
     print(',  '.join(f'{i+j:2}' for j in range(n)))

_bbullet, _wbullet = '\u2022\u25E6'

1. _bqueen, _wqueen = 'BW'

_bqueen, _wqueen = '\u265B\u2655' _bqueenh, _wqueenh = '♛', '♕' _or = set.__or__

def place(m, n):

   "Place m black and white queens, peacefully, on an n-by-n board"
   
   # 2-D Board as 1-D array:  2D(x, y) == 1D(t%n, t//n)
   board = set(range(n*n))

   #placements = list(combinations(board, m))
   placements = {frozenset(c) for c in combinations(board, m)}
   for blacks in placements:
       black_attacks = reduce(_or, 
                              (queen_attacks_from(pos, n) for pos in blacks), 
                              set())
       #for whites in placements:
       for whites in {frozenset(c) for c in combinations(board - black_attacks, m)}:
           if not black_attacks & whites:
               return blacks, whites
   return set(), set()

@lru_cache(maxsize=None) def queen_attacks_from(pos, n=n):

   a = set([pos])    # Its position
   a.update(range(pos//n*n, pos//n*n+n))    # Its row
   a.update(range(pos%n, n*n, n))           # Its column
   # Diagonals
   x0, y0 = pos%n, pos//n
   for x1 in range(n):
       # l-to-r diag
       y1 = y0 -x0 +x1
       if 0 <= y1 < n: 
           a.add(x1 + y1 * n)
       # r-to-l diag
       y1 = y0 +x0 -x1
       if 0 <= y1 < n: 
           a.add(x1 + y1 * n)
   return a

def pboard(black_white=None, n=n):

   if black_white is None: 
       blk, wht = set(), set()
   else:
       blk, wht = black_white
   print(f"## {len(blk)} black and {len(wht)} white queens "
         f"on a {n}-by-{n} board:", end=)
   for xy in range(n*n):
       if xy %n == 0:
           print()
       ch = ('?' if xy in blk and xy in wht 
             else _bqueen if xy in blk
             else _wqueen if xy in wht
             else _bbullet if (xy%n + xy//n)%2 else _wbullet)
       print('%s' % ch, end=)
   print()

def hboard(black_white=None, n=n):

   if black_white is None: 
       blk, wht = set(), set()
   else:
       blk, wht = black_white
   out = (f"
## {len(blk)} black and {len(wht)} white queens "
          f"on a {n}-by-{n} board:
\n")

out += "

\n " tbl = for xy in range(n*n): if xy %n == 0: tbl += '\n \n' ch = ('?' if xy in blk and xy in wht else _bqueenh if xy in blk else _wqueenh if xy in wht else "") bg = "" if (xy%n + xy//n)%2 else ' bgcolor="silver"' tbl += f' \n'

   out += tbl[7:]

out += '\n

{ch}

\n
\n'

   return out

if __name__ == '__main__':

   n=2
   html = 
   for n in range(2, 7):
       print()
       queen_attacks_from.cache_clear()    # memoization cache
       #
       for m in count(1):
           ans = place(m, n)
           if ans[0]:
               pboard(ans, n)
               html += hboard(ans, n)
           else:
               comment = f"# Can't place {m}+ queens on a {n}-by-{n} board"
               print (comment)
               html += f"{comment}

\n\n"
               break
   print('\n')
   html += '
\n'
   #
   m, n = 5, 7
   queen_attacks_from.cache_clear()
   ans = place(m, n)
   pboard(ans, n)    
   html += hboard(ans, n)
   with open('peaceful_queen_armies.htm', 'w') as f:
       f.write(html)</lang>

Output:

The console output Unicode queen characters display wider than other characters in monospace font so the alternative HTML output is shown below.

# Can't place 1+ queens on a 2-by-2 board

## 1 black and 1 white queens on a 3-by-3 board:

		♛
♕

# Can't place 2+ queens on a 3-by-3 board

## 1 black and 1 white queens on a 4-by-4 board:

		♛
			♕

## 2 black and 2 white queens on a 4-by-4 board:

		♛	♛
♕
	♕

# Can't place 3+ queens on a 4-by-4 board

## 1 black and 1 white queens on a 5-by-5 board:

♛
			♕

## 2 black and 2 white queens on a 5-by-5 board:

		♛
			♛
	♕
				♕

## 3 black and 3 white queens on a 5-by-5 board:

			♕	♕
♛
				♕
	♛	♛

## 4 black and 4 white queens on a 5-by-5 board:

	♕		♕
				♕
♛		♛
				♕
♛		♛

# Can't place 5+ queens on a 5-by-5 board

## 1 black and 1 white queens on a 6-by-6 board:

				♕
		♛

## 2 black and 2 white queens on a 6-by-6 board:

				♛
♕					♕
	♛

## 3 black and 3 white queens on a 6-by-6 board:

		♛
	♕
			♛		♛
♕	♕

## 4 black and 4 white queens on a 6-by-6 board:

♕				♕
		♛
♕				♕
		♛
			♛
		♛

## 5 black and 5 white queens on a 6-by-6 board:

♛			♛	♛
♛			♛
	♕	♕			♕
	♕	♕

# Can't place 6+ queens on a 6-by-6 board

## 5 black and 5 white queens on a 7-by-7 board:

♕				♕
						♛
			♛
						♛
	♛
		♛
♕				♕	♕

--Paddy3118 (talk) 10:08, 27 March 2019 (UTC)

Error in solution?

No solutions for {8,9},{10,14} and some other boards. For {9, 12} correctly:

12 black and 12 white queens on a 9 x 9 board:
B * x * B * x * B
* x W x * x W x *
B * x * B * x * B
* x W x * x W x *
B * x * B * x * B
* x W x * x W x *
B * x * B * x * B
* x W x * x W x *
x W x W x W x W x

I checked C and C++ codes and compare results from https://oeis.org/A250000

Hi, Please sign your contribution bove, thanks. --Paddy3118 (talk) 10:58, 19 January 2020 (UTC)

If you carefully check the wording of the task, it doesn't ask for maximum numbers of armies.

Language implementations might well have implied this though which may need individual mods.

Thanks for spotting it. --Paddy3118 (talk) 10:58, 19 January 2020 (UTC)