| #!/usr/bin/env python3 |
| |
| """ |
| 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 true, 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('|', end=' ') |
| for x in range(self.n): |
| if self.y[x] == y: |
| print("Q", end=' ') |
| else: |
| print(".", end=' ') |
| 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() |
