added comments
This commit is contained in:
Daniel Tsvetkov
parent
2264ff4663
commit
9997434ac2
189
main.py
189
main.py
@ -28,72 +28,6 @@ BOX_H_LABELS = 'ABCDEF'
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BOX_V_LABELS = '654321'
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class Block(object):
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def __init__(self, boxes, operation, result):
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self.boxes = boxes
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self.operation = operation
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self.result = result
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self.solutions = set()
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self.verify()
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def verify(self):
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assert self.operation in OP_LAMBDAS
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if self.operation in [OP_NONE]:
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assert len(self.boxes) == 1
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elif self.operation in [OP_MINUS, OP_DIVIDE]:
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assert len(self.boxes) == 2
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else:
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assert len(self.boxes) > 1
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for box in self.boxes:
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assert len(box) == 2
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assert box[0] in BOX_H_LABELS
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assert box[1] in BOX_V_LABELS
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def all_boxes_in_one_row_or_column(self):
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is_same_column, is_same_row = True, True
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for box in self.boxes[1:]:
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if self.boxes[0][0] != box[0]:
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is_same_column = False
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if self.boxes[0][1] != box[1]:
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is_same_row = False
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return is_same_row or is_same_column
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def generate_combinations(self, k, n):
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assert 1 <= k < n
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# Exploit the structure of the problem
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# For block of size 2, we don't need comb with replacement as they will
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# neccesarily be in different columns/rows
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if k == 2:
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return list(combinations(range(1, n + 1), k))
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# for 3 and more we don't need if all of the boxes are on the
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# same row or same column
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elif k > 2:
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if self.all_boxes_in_one_row_or_column():
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return list(combinations(range(1, n + 1), k))
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return list(combinations_with_replacement(range(1, n + 1), k))
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def generate_hypotheses(self, grid_size):
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rv = []
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op = OP_LAMBDAS[self.operation]
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hypotheses = self.generate_combinations(k=len(self.boxes), n=grid_size)
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for hypothesis in hypotheses:
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if op(hypothesis) == self.result:
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rv.append(hypothesis)
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return rv
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def generate_solutions(self, grid_size):
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self.generate_hypotheses(grid_size)
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for hyp in self.generate_hypotheses(grid_size):
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for perm in itertools.permutations(hyp):
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sol = tuple(zip(self.boxes, perm))
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self.solutions.add(sol)
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def __repr__(self):
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return 'Block {}'.format(self.boxes)
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def translate_box_to_rc(box):
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return BOX_V_LABELS.index(box[1]), BOX_H_LABELS.index(box[0])
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@ -118,6 +52,98 @@ def fill_grid(grid, solution):
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return grid
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def check_grid(grid):
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for row in grid:
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if not has_line_integrity(row):
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return False
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for col_id in range(len(grid)):
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col = [grid[r][col_id] for r in range(len(grid))]
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if not has_line_integrity(col):
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return False
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return True
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def init_grid(grid_size):
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return [[0] * grid_size for _ in range(grid_size)]
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class Block(object):
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def __init__(self, boxes, operation, result):
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self.boxes = boxes
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self.operation = operation
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self.result = result
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self.solutions = set()
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self.verify()
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def verify(self):
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"""
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Verifies that the box location are valid in the range A-F and 1-6
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Operations are in +-*/ or None.
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Where -/ have exactly 2, None has exactly 1.
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"""
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assert self.operation in OP_LAMBDAS
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if self.operation in [OP_NONE]:
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assert len(self.boxes) == 1
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elif self.operation in [OP_MINUS, OP_DIVIDE]:
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assert len(self.boxes) == 2
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else:
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assert len(self.boxes) > 1
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for box in self.boxes:
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assert len(box) == 2
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assert box[0] in BOX_H_LABELS
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assert box[1] in BOX_V_LABELS
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def all_boxes_in_one_row_or_column(self):
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"""Returns true if all of the boxes are in the same row OR the same column"""
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is_same_column, is_same_row = True, True
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for box in self.boxes[1:]:
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if self.boxes[0][0] != box[0]:
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is_same_column = False
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if self.boxes[0][1] != box[1]:
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is_same_row = False
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return is_same_row or is_same_column
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def generate_combinations(self, k, n):
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"""Generates k|n combinations for 2 boxes or if they are in the same row OR column.
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Generates k|n combinations with replacements for other cases."""
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assert 1 <= k < n
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# Exploit the structure of the problem
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# For block of size 2, we don't need comb with replacement as they will
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# neccesarily be in different columns/rows
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if k == 2:
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return list(combinations(range(1, n + 1), k))
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# for 3 and more we don't need if all of the boxes are on the
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# same row or same column
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elif k > 2:
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if self.all_boxes_in_one_row_or_column():
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return list(combinations(range(1, n + 1), k))
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return list(combinations_with_replacement(range(1, n + 1), k))
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def generate_hypotheses(self, grid_size):
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"""Generates hypothesis for this block based on the operation and result."""
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rv = []
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op = OP_LAMBDAS[self.operation]
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hypotheses = self.generate_combinations(k=len(self.boxes), n=grid_size)
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for hypothesis in hypotheses:
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if op(hypothesis) == self.result:
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rv.append(hypothesis)
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return rv
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def generate_solutions(self, grid_size):
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"""Generates possible solutions for the block, including the limiting row/column requirement."""
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self.generate_hypotheses(grid_size)
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for hyp in self.generate_hypotheses(grid_size):
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for perm in itertools.permutations(hyp):
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sol = tuple(zip(self.boxes, perm))
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if check_grid(fill_grid(init_grid(grid_size), sol)):
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self.solutions.add(sol)
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def __repr__(self):
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return 'Block {}'.format(self.boxes)
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class Game(object):
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def __init__(self, grid_size, blocks):
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self.blocks = blocks
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@ -127,10 +153,8 @@ class Game(object):
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for block in self.blocks:
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block.generate_solutions(self.grid_size)
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def init_grid(self):
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return [[0] * self.grid_size for _ in range(self.grid_size)]
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def verify(self):
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"""Check that each block is found exactly once in the grid."""
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found = set()
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for block in self.blocks:
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for box in block.boxes:
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@ -138,30 +162,17 @@ class Game(object):
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found.add(box)
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assert len(found) == self.grid_size ** 2
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def find_blocks_in_row(self, row_num):
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rv = set()
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for block in self.blocks:
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for box in block.boxes:
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if int(box[1]) == row_num:
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rv.add(block)
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return rv
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def check_grid(self, grid):
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for row in grid:
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if not has_line_integrity(row):
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return False
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for col_id in range(self.grid_size):
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col = [grid[r][col_id] for r in range(self.grid_size)]
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if not has_line_integrity(col):
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return False
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return True
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def solve(self, grid, current_block_id=0):
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"""
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Recursive solution - Start by filling up the first block.
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For each solution that passes the row/column requirement, check the recursive solution
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with the next block. Break when it's the last block and the row/col requirement is filled.
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"""
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block = self.blocks[current_block_id]
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for solution in block.solutions:
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prev_grid = deepcopy(grid)
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grid = fill_grid(grid, solution)
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if not self.check_grid(grid):
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if not check_grid(grid):
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grid = prev_grid
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else:
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if current_block_id == len(self.blocks) - 1:
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@ -189,7 +200,7 @@ def main():
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Block(boxes=['D1', 'E1'], operation=OP_MINUS, result=1),
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Block(boxes=['F1', 'F2', 'F3', 'E3'], operation=OP_PLUS, result=16),
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])
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grid = game.solve(grid=game.init_grid())
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grid = game.solve(grid=init_grid(game.grid_size))
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for line in grid:
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print(line)
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