/Demo/scripts/queens.py
http://unladen-swallow.googlecode.com/ · Python · 85 lines · 63 code · 13 blank · 9 comment · 14 complexity · 14ea69976d102fa11af3966ef4865305 MD5 · raw file
- #! /usr/bin/env python
- """N queens problem.
- The (well-known) problem is due to Niklaus Wirth.
- This solution is inspired by Dijkstra (Structured Programming). It is
- a classic recursive backtracking approach.
- """
- N = 8 # Default; command line overrides
- class Queens:
- def __init__(self, n=N):
- self.n = n
- self.reset()
- def reset(self):
- n = self.n
- self.y = [None]*n # Where is the queen in column x
- self.row = [0]*n # Is row[y] safe?
- self.up = [0] * (2*n-1) # Is upward diagonal[x-y] safe?
- self.down = [0] * (2*n-1) # Is downward diagonal[x+y] safe?
- self.nfound = 0 # Instrumentation
- def solve(self, x=0): # Recursive solver
- for y in range(self.n):
- if self.safe(x, y):
- self.place(x, y)
- if x+1 == self.n:
- self.display()
- else:
- self.solve(x+1)
- self.remove(x, y)
- def safe(self, x, y):
- return not self.row[y] and not self.up[x-y] and not self.down[x+y]
- def place(self, x, y):
- self.y[x] = y
- self.row[y] = 1
- self.up[x-y] = 1
- self.down[x+y] = 1
- def remove(self, x, y):
- self.y[x] = None
- self.row[y] = 0
- self.up[x-y] = 0
- self.down[x+y] = 0
- silent = 0 # If set, count solutions only
- def display(self):
- self.nfound = self.nfound + 1
- if self.silent:
- return
- print '+-' + '--'*self.n + '+'
- for y in range(self.n-1, -1, -1):
- print '|',
- for x in range(self.n):
- if self.y[x] == y:
- print "Q",
- else:
- print ".",
- print '|'
- print '+-' + '--'*self.n + '+'
- def main():
- import sys
- silent = 0
- n = N
- if sys.argv[1:2] == ['-n']:
- silent = 1
- del sys.argv[1]
- if sys.argv[1:]:
- n = int(sys.argv[1])
- q = Queens(n)
- q.silent = silent
- q.solve()
- print "Found", q.nfound, "solutions."
- if __name__ == "__main__":
- main()