sudoku4.py

## Solve Every Sudoku Puzzle - Question 4

## See http://norvig.com/sudoku.html

## Throughout this program we have:
##   r is a row,    e.g. 'A'
##   c is a column, e.g. '3'
##   s is a square, e.g. 'A3'
##   d is a digit,  e.g. '9'
##   u is a unit,   e.g. ['A1','B1','C1','D1','E1','F1','G1','H1','I1']
##   grid is a grid,e.g. 81 non-blank chars, e.g. starting with '.18...7...
##   values is a dict of possible values, e.g. {'A1':'12349', 'A2':'8', ...}

import random
import time


def cross(A, B):
    "Cross product of elements in A and elements in B."
    return [a + b for a in A for b in B]


digits = '123456789'
rows = 'ABCDEFGHI'
cols = digits
squares = cross(rows, cols)
columns = [cross(rows, c) for c in cols]
lines = [cross(r, cols) for r in rows]
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)
boxes = dict((s, set(sum([units[s][2]], [])) - set([s]))
             for s in squares)
peers = dict((s, set(sum(units[s], [])) - set([s]))
             for s in squares)


################ Unit Tests ################

def test():
    "A set of tests that must pass."
    assert len(squares) == 81
    assert len(unitlist) == 27
    assert all(len(units[s]) == 3 for s in squares)
    assert all(len(peers[s]) == 20 for s in squares)
    assert units['C2'] == [['A2', 'B2', 'C2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2'],
                           ['C1', 'C2', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9'],
                           ['A1', 'A2', 'A3', 'B1', 'B2', 'B3', 'C1', 'C2', 'C3']]
    assert peers['C2'] == set(['A2', 'B2', 'D2', 'E2', 'F2', 'G2', 'H2', 'I2',
                               'C1', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9',
                               'A1', 'A3', 'B1', 'B3'])
    print('All tests pass.')


################ Parse a Grid ################

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))


################ Constraint Propagation ################

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(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 evaluation(values):
    """The evaluation is equal to: 0 - number of conflicts on rows and columns"""
    conflicts = 0  # Number of conflicts (-inf < conflicts =< 0)
    for line in lines:  # We run through each row
        filled_line = []
        for s in line:  # We run through the row_i
            filled_line.append(values[s])  # We append the value of box_ij
        conflicts += len(set(filled_line)) - len(rows)  # We decrement the number of unfilled box in row
    for column in columns:  # We run through each column
        filled_column = []
        for s in column:  # We run through the column_j
            filled_column.append(values[s])  # We append the value of box_ij
        conflicts += len(set(filled_column)) - len(cols)  # We decrement the number of unfilled box in column
    return conflicts


################ Display as 2-D grid ################

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)


######################## Hill Climbing ###############################

## http://aima.cs.berkeley.edu/python/search.html
## http://en.wikipedia.org/wiki/Hill_climbing_algorithm
## https://github.com/aimacode/aima-pseudocode/blob/master/md/Hill-Climbing.md

def solve_hill_climbing(grid):
    return hill_climbing(initialize_hill_climbing(parse_grid(grid)))


def initialize_hill_climbing(values):
    """Taking into account only the boxes, fill each square with one of the possible numbers at random"""
    updated_box = values.copy()
    # As long as there is an empty square
    while max(len(updated_box[s]) for s in squares) > 1:
        # Choose the unfilled square s with the fewest possibilities
        n, s = min((len(updated_box[s]), s) for s in squares if len(updated_box[s]) > 1)
        d = random.choice(updated_box[s])
        assign(updated_box, s, d)
    return updated_box


def hill_climbing(values):
    """From the initial node, keep choosing the neighbor with highest value,
    stopping when no neighbor is better."""
    current_grid = values
    while True:
        list_neighbors = neighbors(current_grid)
        next_eval = float("-inf")  # We choose the smallest value for the iteration
        next_square = None
        for x in list_neighbors:  # We run through the list of neighbors
            if evaluation(x) > next_eval:
                next_square = x
                next_eval = evaluation(x)
        if next_eval <= evaluation(current_grid):  # If the next value is worse than the current value
            return current_grid  # Return current grid since no better neighbors exist
        current_grid = next_square


def neighbors(current_grid):
    """Return a list of the neighbors of the node which is obtained by exchanging the numbers of two
    squares belonging to the same box (36 possibilities per box)"""
    list_neighbors = []
    done = []
    for s in squares:  # We run through the sudoku
        copy_current_grid = current_grid.copy()
        # print(newNode)
        box = boxes[s] - set(done)  # We remove the visited square
        for s2 in box:
            copy_current_grid[s], copy_current_grid[s2] = copy_current_grid[s2], copy_current_grid[
                s]  # Swap cell_ij with cell_kl
            list_neighbors.append(copy_current_grid)  # We add the neighbor to the list
        done.append(s)  # We mark the visited box
    return list_neighbors


################ Utilities ################


def from_file(filename, sep='\n'):
    "Parse a file into a list of strings, separated by sep."
    return open(filename).read().strip().split(sep)


def shuffled(seq):
    "Return a randomly shuffled copy of the input sequence."
    seq = list(seq)
    random.shuffle(seq)
    return seq


################ System test ################


def solve_all(grids, name='', showif=0.0):
    """Attempt to solve a sequence of grids. Report results.
    When showif is a number of seconds, display puzzles that take longer.
    When showif is None, don't display any puzzles."""

    def time_solve(grid):
        start = time.perf_counter()
        values = solve_hill_climbing(grid)
        t = time.perf_counter() - start
        ## Display puzzles that take long enough
        if showif is not None and t > showif:
            display(grid_values(grid))
            if values: display(values)
            print('(%.2f seconds)\n' % t)
        return (t, solved(values))

    times, results = zip(*[time_solve(grid) for grid in grids])
    N = len(grids)
    if N > 1:
        print("Solved %d of %d %s puzzles (avg %.2f secs (%d Hz), max %.2f secs)." % (
            sum(results), N, name, sum(times) / N, N / sum(times), max(times)))


def solved(values):
    "A puzzle is solved if each unit is a permutation of the digits 1 to 9."

    def unitsolved(unit): return set(values[s] for s in unit) == set(digits)

    return values is not False and all(unitsolved(unit) for unit in unitlist)


def random_puzzle(N=17):
    """Make a random puzzle with N or more assignments. Restart on contradictions.
    Note the resulting puzzle is not guaranteed to be solvable, but empirically
    about 99.8% of them are solvable. Some have multiple solutions."""
    values = dict((s, digits) for s in squares)
    for s in shuffled(squares):
        if not assign(values, s, random.choice(values[s])):
            break
        ds = [values[s] for s in squares if len(values[s]) == 1]
        if len(ds) >= N and len(set(ds)) >= 8:
            return ''.join(values[s] if len(values[s]) == 1 else '.' for s in squares)
    return random_puzzle(N)  ## Give up and make a new puzzle


grid1 = '003020600900305001001806400008102900700000008006708200002609500800203009005010300'
grid2 = '4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......'
hard1 = '.....6....59.....82....8....45........3........6..3.54...325..6..................'

if __name__ == '__main__':
    test()
    solve_all(from_file("100sudoku.txt"), "100sudoku", None)
    solve_all(from_file("top95.txt"), "top95", None)
    # solve_all(from_file("easy50.txt", '========'), "easy", None)
    # solve_all(from_file("easy50.txt", '========'), "easy", None)
    # solve_all(from_file("top95.txt"), "hard", None)
    # solve_all(from_file("hardest.txt"), "hardest", None)
    # solve_all([random_puzzle() for _ in range(99)], "random", 100.0)

## References used:
## http://www.scanraid.com/BasicStrategies.htm
## http://www.sudokudragon.com/sudokustrategy.htm
## http://www.krazydad.com/blog/2005/09/29/an-index-of-sudoku-strategies/
## http://www2.warwick.ac.uk/fac/sci/moac/currentstudents/peter_cock/python/sudoku/