diff --git a/Demo/scripts/queens.py b/Demo/scripts/queens.py new file mode 100755 index 00000000000..74756be7d81 --- /dev/null +++ b/Demo/scripts/queens.py @@ -0,0 +1,85 @@ +#! /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()