215 lines
6.6 KiB
Python
215 lines
6.6 KiB
Python
"""
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Module that generates a valid Sudoku Puzzle
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Credits for Solver : http://norvig.com/sudoku.html
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Credits for Generator: http://zhangroup.aporc.org/images/files/Paper_3485.pdf
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"""
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import random
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import re
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filledcell = re.compile('(?!0)')
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def cross(array1, array2):
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"""Cross product of elements in A and elements in B."""
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return [a+b for a in array1 for b in array2]
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digits = '123456789'
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rows = 'ABCDEFGHI'
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cols = digits
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squares = cross(rows, cols)
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unitlist = ([cross(rows, c) for c in cols] +
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[cross(r, cols) for r in rows] +
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[cross(rs, cs) for rs in ('ABC', 'DEF', 'GHI') for cs in ('123','456','789')])
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units = dict((s, [u for u in unitlist if s in u])
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for s in squares)
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peers = dict((s, set(sum(units[s], []))-set([s]))
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for s in squares)
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def parse_grid(grid):
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"""Convert grid to a dict of possible values, {square: digits}, or
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return False if a contradiction is detected."""
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# To start, every square can be any digit; then assign values from the grid.
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values = dict((s, digits) for s in squares)
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for s, d in grid_values(grid).items():
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if d in digits and not assign(values, s, d):
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return False # (Fail if we can't assign d to square s.)
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return values
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def grid_values(grid):
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"""Convert grid into a dict of {square: char} with '0' or '.' for empties."""
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chars = [c for c in grid if c in digits or c in '0.']
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assert len(chars) == 81
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return dict(zip(squares, chars))
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def display(values):
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"""Display these values as a 2-D grid."""
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width = 1+max(len(values[s]) for s in squares)
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line = '+'.join(['-'*(width*3)]*3)
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for r in rows:
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print(''.join(values[r+c].center(width)+('|' if c in '36' else '')
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for c in cols))
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if r in 'CF':
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print(line)
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print('')
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def assign(values, s, d):
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"""Eliminate all the other values (except d) from values[s] and propagate.
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Return values, except return False if a contradiction is detected."""
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other_values = values[s].replace(str(d), '')
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if all(eliminate(values, s, d2) for d2 in other_values):
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return values
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else:
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return False
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def eliminate(values, s, d):
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"""Eliminate d from values[s]; propagate when values or places <= 2.
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Return values, except return False if a contradiction is detected."""
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if d not in values[s]:
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return values # Already eliminated
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values[s] = values[s].replace(d, '')
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# (1) If a square s is reduced to one value d2, then eliminate d2 from the peers.
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if len(values[s]) == 0:
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return False # Contradiction: removed last value
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elif len(values[s]) == 1:
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d2 = values[s]
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if not all(eliminate(values, s2, d2) for s2 in peers[s]):
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return False
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# (2) If a unit u is reduced to only one place for a value d, then put it there.
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for u in units[s]:
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dplaces = [s for s in u if d in values[s]]
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if len(dplaces) == 0:
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return False # Contradiction: no place for this value
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elif len(dplaces) == 1:
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# d can only be in one place in unit; assign it there
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if not assign(values, dplaces[0], d):
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return False
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return values
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#def solve(grid): return search(parse_grid(grid))
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def solve(values): return search(values)
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def search(values):
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"""Using depth-first search and propagation, try all possible values."""
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if values is False:
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return False # Failed earlier
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if all(len(values[s]) == 1 for s in squares):
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return values # Solved!
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# Chose the unfilled square s with the fewest possibilities
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n, s = min((len(values[s]), s) for s in squares if len(values[s]) > 1)
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return some(search(assign(values.copy(), s, d))
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for d in values[s])
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def some(seq):
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"""Return some element of seq that is true."""
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for e in seq:
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if e:
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return e
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return False
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def las_vegas(n):
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# Generate a board by randomly picking n cells and
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# fill them a random digit from 1-9
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values = parse_grid('0' * 81)
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valid_assignments = 0
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while valid_assignments < n:
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#display(values)
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cell_to_assign = squares[random.randint(0, 80)]
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valid_values = values[cell_to_assign]
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if len(valid_values):
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value_to_assign = valid_values[random.randint(0, len(valid_values)-1)]
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assign(values, cell_to_assign, value_to_assign)
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valid_assignments += 1
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return values
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def generate_completed_grid():
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complete_values = solve(las_vegas(11))
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grid = ''
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for s in squares:
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grid += complete_values[s]
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return grid
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def generate_dig_sequence(difficulty):
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# TODO: Determine the number of givens and lower bound of given
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if difficulty <= 1:
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random_number = list(range(81))
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while len(random_number) > 0:
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print(len(random_number))
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yield random_number.pop(random.randint(0, len(random_number)-1))
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elif difficulty == 2:
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current = 0
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while current < 81:
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row = int(current / 9)
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if not row % 2:
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yield current
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else:
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yield (row+1) * 9 - 1 - (current % 9)
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current += 2
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elif difficulty == 3:
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current = 0
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while current < 81:
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row = int(current / 9)
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if not row % 2:
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yield current
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else:
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yield (row+1) * 9 - 1 - (current % 9)
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current += 1
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elif difficulty == 4:
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current = 0
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while current < 81:
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yield current
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current += 1
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def generate_sudoku_puzzle(difficulty):
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grid = generate_completed_grid()
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if difficulty == 0:
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n_givens = random.randint(50, 60)
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lower_bound = 5
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elif difficulty == 1:
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n_givens = random.randint(36, 49)
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lower_bound = 4
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elif difficulty == 2:
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n_givens = random.randint(32, 35)
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lower_bound = 3
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elif difficulty == 3:
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n_givens = random.randint(28, 31)
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lower_bound = 2
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elif difficulty == 4:
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n_givens = random.randint(22, 27)
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lower_bound = 0
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dig_sequence = generate_dig_sequence(difficulty)
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holes = 0
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while holes<81-n_givens:
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try:
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i = next(dig_sequence)
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except StopIteration:
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print("Reach end of Sequence")
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break
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# TODO: Check if givens at current row and column is at lower bound
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# TODO: Dig the current hole and check for uniqueness
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# TODO: Propagate and Output
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return grid
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if __name__ == "__main__":
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#print(generate_completed_grid())
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func = generate_dig_sequence(3)
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#print(next(func))
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[print(a) for a in next(func)] |