infinitequeens.py

#!/usr/bin/env python

# Infinite queens
# Prints the lex-minimal infinite nonattacking queen placement
# in the first quadrant - amazingly, they form two lines with slopes
# phi and 1/phi

import sys
N = int(sys.argv[1])

queens = []

def attacking(q,r):
  if q[0] == r[0]:
    return True
  if q[1] == r[1]:
    return True
  if (q[0] - r[0]) == (q[1] - r[1]):
    return True
  if (q[0] - r[0]) == (r[1] - q[1]):
    return True
  return False

for i in xrange(N):
  j = 0
  while any(attacking(q, (i,j)) for q in queens):
    j += 1
  queens.append((i,j))

for q in reversed(queens):
  print ("-" * q[1]) + "Q" + "-" * (int(1.7*N) - q[1]) + "%.2f" % ((1.0 + q[1]) / (1.0 + q[0]))