From 1b4348656052164ea5c0c73434cbd81ecc8d5f79 Mon Sep 17 00:00:00 2001 From: En Yi Date: Wed, 11 Jul 2018 16:52:13 +0800 Subject: [PATCH] Implement generation of completed grids --- gameplay/Sudoku_Generator.py | 172 +++++++++++++++++++++++++++++++++++ 1 file changed, 172 insertions(+) create mode 100644 gameplay/Sudoku_Generator.py diff --git a/gameplay/Sudoku_Generator.py b/gameplay/Sudoku_Generator.py new file mode 100644 index 0000000..6225db3 --- /dev/null +++ b/gameplay/Sudoku_Generator.py @@ -0,0 +1,172 @@ +""" +Module that generates a valid Sudoku Puzzle +Credits for Solver : http://norvig.com/sudoku.html +Credits for Generator: http://zhangroup.aporc.org/images/files/Paper_3485.pdf + +""" +import random + +def cross(array1, array2): + """Cross product of elements in A and elements in B.""" + return [a+b for a in array1 for b in array2] + + +digits = '123456789' +rows = 'ABCDEFGHI' +cols = digits +squares = cross(rows, cols) +unitlist = ([cross(rows, c) for c in cols] + + [cross(r, cols) for r in rows] + + [cross(rs, cs) for rs in ('ABC', 'DEF', 'GHI') for cs in ('123','456','789')]) +units = dict((s, [u for u in unitlist if s in u]) + for s in squares) +peers = dict((s, set(sum(units[s], []))-set([s])) + for s in squares) + + +def parse_grid(grid): + """Convert grid to a dict of possible values, {square: digits}, or + return False if a contradiction is detected.""" + # To start, every square can be any digit; then assign values from the grid. + values = dict((s, digits) for s in squares) + for s, d in grid_values(grid).items(): + if d in digits and not assign(values, s, d): + return False # (Fail if we can't assign d to square s.) + return values + + +def grid_values(grid): + """Convert grid into a dict of {square: char} with '0' or '.' for empties.""" + chars = [c for c in grid if c in digits or c in '0.'] + assert len(chars) == 81 + return dict(zip(squares, chars)) + + +def display(values): + """Display these values as a 2-D grid.""" + width = 1+max(len(values[s]) for s in squares) + line = '+'.join(['-'*(width*3)]*3) + for r in rows: + print(''.join(values[r+c].center(width)+('|' if c in '36' else '') + for c in cols)) + if r in 'CF': + print(line) + print('') + + +def assign(values, s, d): + """Eliminate all the other values (except d) from values[s] and propagate. + Return values, except return False if a contradiction is detected.""" + other_values = values[s].replace(str(d), '') + if all(eliminate(values, s, d2) for d2 in other_values): + return values + else: + return False + + +def eliminate(values, s, d): + """Eliminate d from values[s]; propagate when values or places <= 2. + Return values, except return False if a contradiction is detected.""" + if d not in values[s]: + return values # Already eliminated + values[s] = values[s].replace(d, '') + # (1) If a square s is reduced to one value d2, then eliminate d2 from the peers. + if len(values[s]) == 0: + return False # Contradiction: removed last value + elif len(values[s]) == 1: + d2 = values[s] + if not all(eliminate(values, s2, d2) for s2 in peers[s]): + return False + # (2) If a unit u is reduced to only one place for a value d, then put it there. + for u in units[s]: + dplaces = [s for s in u if d in values[s]] + if len(dplaces) == 0: + return False # Contradiction: no place for this value + elif len(dplaces) == 1: + # d can only be in one place in unit; assign it there + if not assign(values, dplaces[0], d): + return False + return values + + +#def solve(grid): return search(parse_grid(grid)) +def solve(values): return search(values) + + +def search(values): + """Using depth-first search and propagation, try all possible values.""" + if values is False: + return False # Failed earlier + if all(len(values[s]) == 1 for s in squares): + return values # Solved! + # Chose the unfilled square s with the fewest possibilities + n, s = min((len(values[s]), s) for s in squares if len(values[s]) > 1) + return some(search(assign(values.copy(), s, d)) + for d in values[s]) + + +def some(seq): + """Return some element of seq that is true.""" + for e in seq: + if e: + return e + return False + + +def las_vegas(n): + # Generate a board by randomly picking n cells and + # fill them a random digit from 1-9 + values = parse_grid('0' * 81) + valid_assignments = 0 + while valid_assignments < n: + #display(values) + cell_to_assign = squares[random.randint(0, 80)] + valid_values = values[cell_to_assign] + if len(valid_values): + value_to_assign = valid_values[random.randint(0, len(valid_values)-1)] + assign(values, cell_to_assign, value_to_assign) + valid_assignments += 1 + return values + + +def generate_completed_grid(): + complete_values = solve(las_vegas(11)) + grid = '' + for s in squares: + grid += complete_values[s] + + return grid + + +def dig_holes(board, difficulty): + # Empty out some cells in a completed board + pass + # TODO: Determine the number of givens and lower bound of given + + # TODO: Determine the sequence of digging + + # TODO: Set all cells as "Can be Dug" + + # TODO: Is there a cell that can be dug? + + # TODO: Select the next cell that "can be dug"and Yield unique solution? + + # TODO: Propagate and Output + + +def generate_sudoku_puzzle(difficulty): + grid = generate_completed_grid() + + puzzle = dig_holes(board, difficulty) + + return puzzle + + +if __name__ == "__main__": + #print(generate_completed_grid()) + success = True + for i in range(500): + if not parse_grid(generate_completed_grid()): + print("failed at test" + str(i)) + success = False + print(success) \ No newline at end of file