#!/usr/bin/env python3

"This module does something"

from itertools import combinations_with_replacement
import sys


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:]

def invariants(width, pattern, constraints=None):
    "compute invariants"
    invs = []
    for sol in solve2(width, pattern, constraints):
        exp = list(expand_solution(sol, width, pattern))
        count += 1
        if len(invs) == 0:
            invs = exp
        else:
            for i, e in enumerate(exp):
                if invs[i] != e:
                    invs[i] = -1
    return count, invs

def visual(constraints):
    "returns a visual representation of constraints"
    return "".join({1:'\N{LEFT SEVEN EIGHTHS BLOCK}', 0:'.', -1:'?'}[x] for x in constraints)

class Board:
    """Board

    A board is actually a list of constraints.
    A cell with 1 or 0 is fixed. A cell with -1
    doesn't have a known value yet.
    """

    def __init__(self, patterns):
        self.col_patterns = patterns[0]
        self.row_patterns = patterns[1]
        self.width = len(patterns[0])
        self.height = len(patterns[1])
        self.rows = [None] * self.height
        for i in range(self.height):
            self.rows[i] = [-1] * self.width

        print("rows:")
        for y in range(self.height):
            n, c = invariants(self.width, self.row_patterns[y])
            print(n, self.row_patterns[y], visual(c))

        print("cols:")
        for x in range(self.height):
            n, c = invariants(self.width, self.col_patterns[x])
            print(n, self.col_patterns[x], visual(c))

        print(self.row(0))

    def col(self, i):
        """a column"""
        return [self.rows[x][i] for x in range(self.height)]

    def row(self, i):
        """a row"""
        return self.rows[i]

    def solve(self):
        min_row_index = 0
        min_row_count = 0
        for y in range(self.height):
            count = 0
            for sol in solve2(self.width, self.row_patterns[y], self.row(y)):
                count += 1
            if count < min_row_count:
                min_row_count = count
                min_row_index = y


        pass

if __name__ == "__main__":

    def draw(solution, width, pattern):
        "draws a solution"
        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)

    def parse(rows):
        "parses '1 1, 1 2 3' into [[1, 1], [1, 2, 3]]"
        rows = rows.split(",")
        rows = [[int(y) for y in x.strip().split()] for x in rows]
        return rows


    b = Board((
        parse("""1 1 1 1 1, 1 1 1, 1 1 1 1, 1 2, 1 1 1 1, 1 1 1, 1 1 1,
                 3 1, 1 1, 1 2 6 1, 2 1, 2 3 1, 1 1, 1 1 3 1, 2 1 1"""),
        parse("""1 2, 1 1 2, 2 1 1 1 1, 3 1, 1 1 1 1, 1 2 1, 1, 1 1 1 2,
                 2 2 1 1, 1 1 1 1 1, 1 2 2, 2 2, 1 1 1 1 1, 1 1 1 1, 1 1""")
    ))

    # c = Board((
    #     parse("""1 5 2, 1 1 2, 1 1 2 1 2, 2 2, 2 1 1 1, 1 1 1, 1 1, 1 1 1, 2 3 1 1,
    #              1 2 3 1 1, 1 3 1 1, 2 1 1 1, 1 1 1 2 1, 1 1 1 2 1, 2 1"""),
    #     parse("""1 2 1 1, 1 1 4, 2 1, 1 1 1 1 2, 1 3 1 1, 1 2, 1 1 1 1 1 1,
    #              1 1 1 1 1 2, 1 1 2, 1 2 1 1, 3 1 4, 1 4 1, 3, 3 1 1, 1 2 1""")
    # ))