#!/usr/bin/env python3 from itertools import combinations_with_replacement def solve1(width, pattern): """ This yields a tuple for each possible layout of pattern inside the row. The tuple elements are the gaps before each block in pattern. The tuple doesn't include the last gap, since that's just: width - sum(sol) - sum(pattern) """ spaces = width - (sum(pattern) + len(pattern) - 1) for sol in combinations_with_replacement(range(spaces + 1), len(pattern)): sol = sol[0:1] + tuple((sol[i] - sol[i-1] + 1) for i in range(1,len(sol))) yield sol def expand_solution(solution, width, pattern): """ expands a solution to a tuple of 1 (ON) and 0 (OFF) """ r = [] for s,p in zip(solution, pattern): r.extend([0] * s) r.extend([1] * p) r.extend([0] * (width - sum(solution) - sum(pattern))) return tuple(r) def matches(expanded_solution, constraints): """ solution is a tuple of spaces, the output of solve1 constraints is a tuple of values from 1, 0 and -1, that mean: 0 -> OFF 1 -> ON -1 -> not constrained """ for s,c in zip(expanded_solution, constraints): if c == -1: continue if c != s: return False return True def solve2(width, pattern, constraints=None): """ @width: int @pattern: sequence of ints @constraints: optional list of length width containing 1,0,-1 as elements Does the same as solve1, but takes constraints in consideration to be faster than solve1 + matches """ if len(pattern) == 0: return tuple() if constraints is None: constraints = [-1] * width p = pattern[0] # the first gap can go from 0 to the following, inclusive maxgap = width - sum(pattern[1:]) - (len(pattern) - 1) - p for gap in range(maxgap + 1): e = expand_solution((gap,), gap + p + 1, (p,)) if not matches(e, constraints[:gap + p + 1]): continue if len(pattern) == 1: yield (gap,) continue subwidth = width - gap - p - 1 subpattern = pattern[1:] subconstraints = constraints[-subwidth:] for s in solve2(subwidth, subpattern, subconstraints): yield (gap,s[0]+1) + s[1:] if __name__ == "__main__": import sys def draw(solution, width, pattern): for s,p in zip(solution, pattern): print('.' * s, end="") print('\N{LEFT SEVEN EIGHTHS BLOCK}' * p, end="") print('.' * (width - sum(solution) - sum(pattern))) width = int(sys.argv[1]) pattern = tuple(int(x) for x in sys.argv[2].split()) constraints = [-1] * width try: for i,c in enumerate(sys.argv[3]): constraints[i]= {'1':1, '0':0, '?':-1}[c] except: constraints = [-1] * width # for solution in solve1(width, pattern): # e = expand_solution(solution, width, pattern) # if matches(e, constraints): # draw(solution, width, pattern) for sol in solve2(width, pattern, constraints): draw(sol, width, pattern)