323 lines
10 KiB
Python
Executable File
323 lines
10 KiB
Python
Executable File
#!/usr/bin/env python3
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"This module does something"
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from itertools import combinations_with_replacement
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import sys
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def solve1(width, pattern):
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"""
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This yields a tuple for each possible layout of
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pattern inside the row. The tuple elements are the
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gaps before each block in pattern.
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The tuple doesn't include the last gap, since that's
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just: width - sum(sol) - sum(pattern)
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"""
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spaces = width - (sum(pattern) + len(pattern) - 1)
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for sol in combinations_with_replacement(range(spaces + 1), len(pattern)):
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sol = sol[0:1] + tuple((sol[i] - sol[i-1] + 1) for i in range(1, len(sol)))
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yield sol
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def expand_solution(solution, width, pattern):
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"""
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expands a solution to a tuple of 1 (ON) and 0 (OFF)
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"""
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r = []
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for s, p in zip(solution, pattern):
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r.extend([0] * s)
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r.extend([1] * p)
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r.extend([0] * (width - sum(solution) - sum(pattern)))
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return tuple(r)
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def matches(expanded_solution, constraints):
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"""
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solution is a tuple of spaces, the output of solve1
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constraints is a tuple of values from 1, 0 and -1, that
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mean:
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0 -> OFF
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1 -> ON
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-1 -> not constrained
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"""
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for s, c in zip(expanded_solution, constraints):
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if c == -1:
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continue
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if c != s:
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return False
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return True
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def solve2(width, pattern, constraints=None):
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"""
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@width: int
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@pattern: sequence of ints
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@constraints: optional list of length width containing 1,0,-1 as elements
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Does the same as solve1, but takes constraints
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in consideration to be faster than solve1 + matches
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"""
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if len(pattern) == 0:
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return tuple()
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if constraints is None:
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constraints = [-1] * width
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p = pattern[0]
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# the first gap can go from 0 to the following, inclusive
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maxgap = width - sum(pattern[1:]) - (len(pattern) - 1) - p
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for gap in range(maxgap + 1):
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# constraint width
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cw = (gap + p + 1) if len(pattern) > 1 else width
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e = expand_solution((gap,), cw, (p,))
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if not matches(e, constraints[:cw]):
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continue
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if len(pattern) == 1:
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yield (gap,)
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continue
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subwidth = width - gap - p - 1
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subpattern = pattern[1:]
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subconstraints = constraints[-subwidth:]
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for s in solve2(subwidth, subpattern, subconstraints):
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yield (gap, s[0]+1) + s[1:]
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def invariants(width, pattern, constraints=None):
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"compute invariants"
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invs = []
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for sol in solve2(width, pattern, constraints):
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exp = list(expand_solution(sol, width, pattern))
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if len(invs) == 0:
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invs = exp
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else:
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for i, e in enumerate(exp):
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if invs[i] != e:
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invs[i] = -1
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return invs
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def visual(constraints):
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"returns a visual representation of constraints"
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return "".join({
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1:'\N{FULL BLOCK}\N{LEFT SEVEN EIGHTHS BLOCK}',
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0:'__',
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-1:'??'
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}[x] for x in constraints)
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class Board:
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"""Board
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A board is actually a list of constraints.
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A cell with 1 or 0 is fixed. A cell with -1
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doesn't have a known value yet.
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"""
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def __init__(self, patterns):
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self.col_patterns = patterns[0]
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self.row_patterns = patterns[1]
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self.width = len(patterns[0])
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self.height = len(patterns[1])
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self.rows = [None] * self.height
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for i in range(self.height):
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self.rows[i] = [-1] * self.width
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# print("rows:")
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# for y in range(self.height):
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# n, c = invariants(self.width, self.row_patterns[y])
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# print(n, self.row_patterns[y], visual(c))
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# print("cols:")
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# for x in range(self.height):
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# n, c = invariants(self.width, self.col_patterns[x])
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# print(n, self.col_patterns[x], visual(c))
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# print(self.row(0))
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def col(self, i):
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"""a column"""
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return [self.rows[x][i] for x in range(self.height)]
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def row(self, i):
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"""a row"""
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return self.rows[i]
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def replace_row(self, i, row):
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self.rows[i] = row
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def replace_col(self, i , col):
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for y in range(self.height):
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self.rows[y][i] = col[y]
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def compute_invariants(self):
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while True:
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changed = False
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row_sols = [0] * self.height
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col_sols = [0] * self.width
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# rows
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for y in range(self.height):
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invs = None; count = 0
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for sol in solve2(self.width, self.row_patterns[y], self.row(y)):
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count += 1
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exp = list(expand_solution(sol, self.width, self.row_patterns[y]))
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if invs == None:
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invs = exp
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for i, e in enumerate(exp):
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if invs[i] != e:
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invs[i] = -1
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if invs != None and self.row(y) != invs:
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self.replace_row(y, invs)
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changed = True
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row_sols[y] = count
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# columns
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for x in range(self.width):
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invs = None; count = 0
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for sol in solve2(self.height, self.col_patterns[x], self.col(x)):
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count += 1
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exp = list(expand_solution(sol, self.height, self.col_patterns[x]))
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if invs == None:
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invs = exp
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for i, e in enumerate(exp):
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if invs[i] != e:
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invs[i] = -1
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if invs != None and self.col(x) != invs:
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self.replace_col(x, invs)
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changed = True
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col_sols[x] = count
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if not changed:
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break
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return row_sols, col_sols
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def solve(self, solved=lambda x: None, depth=0):
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row_sols, col_sols = self.compute_invariants()
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# if depth < 2:
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# print("depth:", depth)
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# print(self)
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# print("row_sols:", row_sols)
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# print("col_sols:", col_sols)
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if min(row_sols) == 0 or min(col_sols) == 0:
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return False
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if max(row_sols) == 1:
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print("solved")
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solved(self)
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return True
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min_row, y = min((a,b) for b,a in enumerate(row_sols) if a > 1)
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min_col, x = min((a,b) for b,a in enumerate(col_sols) if a > 1)
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if min_row < min_col:
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for sol in solve2(self.width, self.row_patterns[y], self.row(y)):
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b = self.copy()
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b.replace_row(y, expand_solution(sol, self.width, self.row_patterns[y]))
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if b.solve(solved, depth + 1):
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return True
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else:
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for sol in solve2(self.height, self.col_patterns[x], self.col(x)):
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b = self.copy()
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b.replace_col(x, expand_solution(sol, self.height, self.col_patterns[x]))
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if b.solve(solved, depth + 1):
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return True
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def copy(self):
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newboard = Board((self.col_patterns, self.row_patterns))
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for i in range(self.height):
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newboard.rows[i] = self.rows[i][:]
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return newboard
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def __str__(self):
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s = ""
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for y in range(self.height):
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s += visual(self.rows[y])
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s += "\n"
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return s
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if __name__ == "__main__":
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def draw(solution, width, pattern):
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"draws a solution"
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for s, p in zip(solution, pattern):
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print('__' * s, end="")
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print('\N{FULL BLOCK}\N{LEFT SEVEN EIGHTHS BLOCK}' * p, end="")
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print('__' * (width - sum(solution) - sum(pattern)))
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# width = int(sys.argv[1])
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# pattern = tuple(int(x) for x in sys.argv[2].split())
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# constraints = [-1] * width
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# try:
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# for i, c in enumerate(sys.argv[3]):
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# constraints[i] = {'1':1, '0':0, '?':-1}[c]
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# except:
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# constraints = [-1] * width
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# for solution in solve1(width, pattern):
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# e = expand_solution(solution, width, pattern)
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# if matches(e, constraints):
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# draw(solution, width, pattern)
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def parse(rows):
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"parses '1 1, 1 2 3' into [[1, 1], [1, 2, 3]]"
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rows = rows.split(",")
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rows = [[int(y) for y in x.strip().split()] for x in rows]
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return rows
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def parse_constraints(s, width):
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constraints = [-1] * width
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for i, c in enumerate(s):
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constraints[i] = {'1':1, '0':0, '?':-1, '.':0, '\N{LEFT SEVEN EIGHTHS BLOCK}': 1}[c]
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return constraints
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# width = 15
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# pattern = (1, 1, 1, 2)
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# constraints = parse_constraints('????????010?', width)
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# for sol in solve2(width, pattern, constraints):
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# draw(sol, width, pattern)
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# b = Board((
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# parse("1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1"),
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# parse("1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1, 1 1 1")
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# ))
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# b.solve(print)
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# b = Board((
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# 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,
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# 3 1, 1 1, 1 2 6 1, 2 1, 2 3 1, 1 1, 1 1 3 1, 2 1 1"""),
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# 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,
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# 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""")
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# ))
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# b.solve(print)
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# b = Board((
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# parse("""2 4, 1 1 3 1, 6, 3 3, 3 4, 1 3 2, 3 4 1, 3 5 1 1, 12,
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# 5 3 3, 6 4, 2 3, 1 2 2, 3 4, 3 5"""),
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# parse("""1 6, 2 2 4 2, 3 5 2, 11, 1 6 1, 4 1 5, 5 3 3, 10 2, 1 7 1 1, 5 1 1 1,
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# 1 3 1, 3, 3, 1 1, 3"""),
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# ))
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# b.solve()
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c = Board((
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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,
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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"""),
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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,
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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""")
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))
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c.solve(print)
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# c = Board(([[2, 1], [2, 1, 1], [1, 1, 1, 1], [2, 1], [1, 1, 1], [1, 1, 1, 1], [3], [3, 2, 1], [1, 1, 3, 1],
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# [1, 1, 1, 1], [1, 2, 1, 1, 1], [1, 1, 1, 1], [1, 2, 1], [1], [1, 4, 1]],
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# [[1, 2, 1], [1, 3, 1], [1, 1, 3], [1, 1, 1], [1, 1], [1, 1], [1, 2, 1, 1, 1], [2, 3, 3, 1, 1],
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# [1, 1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1], [1, 2], [1, 1], [1, 1, 1]]))
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# c.solve(print)
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if len(sys.argv) > 2:
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b = Board((parse(sys.argv[1]), parse(sys.argv[2])))
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b.solve(print)
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