Implement generation of completed grids

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)