Algorithm for solving Sudoku

Question

I want to write a code in python to solve a sudoku puzzle. Do you guys have any idea about a good algorithm for this purpose. I read somewhere in net about a algorithm which

Answer 1

There are four steps to solve a sudoku puzzle:

1. Identify all possibilities for each cell (getting from the row, column and box) and try to develop a possible matrix. 2.Check for double pair, if it exists then remove these two values from all the cells in that row/column/box, wherever the pair exists If any cell is having single possiblity then assign that run step 1 again
2. Check for each cell with each row, column and box. If the cell has one value which does not belong in the other possible values then assign that value to that cell. run step 1 again
3. If the sudoku is still not solved, then we need to start the following assumption, Assume the first possible value and assign. Then run step 1–3 If still not solved then do it for next possible value and run it in recursion.
4. If the sudoku is still not solved, then we need to start the following assumption, Assume the first possible value and assign. Then run step 1–3

If still not solved then do it for next possible value and run it in recursion.

import math
import sys


def is_solved(l):
    for x, i in enumerate(l):
        for y, j in enumerate(i):
            if j == 0:
                # Incomplete
                return None
            for p in range(9):
                if p != x and j == l[p][y]:
                    # Error
                    print('horizontal issue detected!', (x, y))
                    return False
                if p != y and j == l[x][p]:
                    # Error
                    print('vertical issue detected!', (x, y))
                    return False
            i_n, j_n = get_box_start_coordinate(x, y)
            for (i, j) in [(i, j) for p in range(i_n, i_n + 3) for q in range(j_n, j_n + 3)
                           if (p, q) != (x, y) and j == l[p][q]]:
                    # Error
                print('box issue detected!', (x, y))
                return False
    # Solved
    return True


def is_valid(l):
    for x, i in enumerate(l):
        for y, j in enumerate(i):
            if j != 0:
                for p in range(9):
                    if p != x and j == l[p][y]:
                        # Error
                        print('horizontal issue detected!', (x, y))
                        return False
                    if p != y and j == l[x][p]:
                        # Error
                        print('vertical issue detected!', (x, y))
                        return False
                i_n, j_n = get_box_start_coordinate(x, y)
                for (i, j) in [(i, j) for p in range(i_n, i_n + 3) for q in range(j_n, j_n + 3)
                               if (p, q) != (x, y) and j == l[p][q]]:
                        # Error
                    print('box issue detected!', (x, y))
                    return False
    # Solved
    return True


def get_box_start_coordinate(x, y):
    return 3 * int(math.floor(x/3)), 3 * int(math.floor(y/3))


def get_horizontal(x, y, l):
    return [l[x][i] for i in range(9) if l[x][i] > 0]


def get_vertical(x, y, l):
    return [l[i][y] for i in range(9) if l[i][y] > 0]


def get_box(x, y, l):
    existing = []
    i_n, j_n = get_box_start_coordinate(x, y)
    for (i, j) in [(i, j) for i in range(i_n, i_n + 3) for j in range(j_n, j_n + 3)]:
        existing.append(l[i][j]) if l[i][j] > 0 else None
    return existing


def detect_and_simplify_double_pairs(l, pl):
    for (i, j) in [(i, j) for i in range(9) for j in range(9) if len(pl[i][j]) == 2]:
        temp_pair = pl[i][j]
        for p in (p for p in range(j+1, 9) if len(pl[i][p]) == 2 and len(set(pl[i][p]) & set(temp_pair)) == 2):
            for q in (q for q in range(9) if q != j and q != p):
                pl[i][q] = list(set(pl[i][q]) - set(temp_pair))
                if len(pl[i][q]) == 1:
                    l[i][q] = pl[i][q].pop()
                    return True
        for p in (p for p in range(i+1, 9) if len(pl[p][j]) == 2 and len(set(pl[p][j]) & set(temp_pair)) == 2):
            for q in (q for q in range(9) if q != i and p != q):
                pl[q][j] = list(set(pl[q][j]) - set(temp_pair))
                if len(pl[q][j]) == 1:
                    l[q][j] = pl[q][j].pop()
                    return True
        i_n, j_n = get_box_start_coordinate(i, j)
        for (a, b) in [(a, b) for a in range(i_n, i_n+3) for b in range(j_n, j_n+3)
                       if (a, b) != (i, j) and len(pl[a][b]) == 2 and len(set(pl[a][b]) & set(temp_pair)) == 2]:
            for (c, d) in [(c, d) for c in range(i_n, i_n+3) for d in range(j_n, j_n+3)
                           if (c, d) != (a, b) and (c, d) != (i, j)]:
                pl[c][d] = list(set(pl[c][d]) - set(temp_pair))
                if len(pl[c][d]) == 1:
                    l[c][d] = pl[c][d].pop()
                    return True
    return False


def update_unique_horizontal(x, y, l, pl):
    tl = pl[x][y]
    for i in (i for i in range(9) if i != y):
        tl = list(set(tl) - set(pl[x][i]))
    if len(tl) == 1:
        l[x][y] = tl.pop()
        return True
    return False


def update_unique_vertical(x, y, l, pl):
    tl = pl[x][y]
    for i in (i for i in range(9) if i != x):
        tl = list(set(tl) - set(pl[i][y]))
    if len(tl) == 1:
        l[x][y] = tl.pop()
        return True
    return False


def update_unique_box(x, y, l, pl):
    tl = pl[x][y]
    i_n, j_n = get_box_start_coordinate(x, y)
    for (i, j) in [(i, j) for i in range(i_n, i_n+3) for j in range(j_n, j_n+3) if (i, j) != (x, y)]:
        tl = list(set(tl) - set(pl[i][j]))
    if len(tl) == 1:
        l[x][y] = tl.pop()
        return True
    return False


def find_and_place_possibles(l):
    while True:
        pl = populate_possibles(l)
        if pl != False:
            return pl


def populate_possibles(l):
    pl = [[[]for j in i] for i in l]
    for (i, j) in [(i, j) for i in range(9) for j in range(9) if l[i][j] == 0]:
        p = list(set(range(1, 10)) - set(get_horizontal(i, j, l) +
                                         get_vertical(i, j, l) + get_box(i, j, l)))
        if len(p) == 1:
            l[i][j] = p.pop()
            return False
        else:
            pl[i][j] = p
    return pl


def find_and_remove_uniques(l, pl):
    for (i, j) in [(i, j) for i in range(9) for j in range(9) if l[i][j] == 0]:
        if update_unique_horizontal(i, j, l, pl) == True:
            return True
        if update_unique_vertical(i, j, l, pl) == True:
            return True
        if update_unique_box(i, j, l, pl) == True:
            return True
    return False


def try_with_possibilities(l):
    while True:
        improv = False
        pl = find_and_place_possibles(l)
        if detect_and_simplify_double_pairs(
                l, pl) == True:
            continue
        if find_and_remove_uniques(
                l, pl) == True:
            continue
        if improv == False:
            break
    return pl


def get_first_conflict(pl):
    for (x, y) in [(x, y) for x, i in enumerate(pl) for y, j in enumerate(i) if len(j) > 0]:
        return (x, y)


def get_deep_copy(l):
    new_list = [i[:] for i in l]
    return new_list


def run_assumption(l, pl):
    try:
        c = get_first_conflict(pl)
        fl = pl[c[0]
                ][c[1]]
        # print('Assumption Index : ', c)
        # print('Assumption List: ',  fl)
    except:
        return False
    for i in fl:
        new_list = get_deep_copy(l)
        new_list[c[0]][c[1]] = i
        new_pl = try_with_possibilities(new_list)
        is_done = is_solved(new_list)
        if is_done == True:
            l = new_list
            return new_list
        else:
            new_list = run_assumption(new_list, new_pl)
            if new_list != False and is_solved(new_list) == True:
                return new_list
    return False


if __name__ == "__main__":
    l = [
        [0, 0, 0, 0, 0, 0, 0, 0, 0],
        [0, 0, 8, 0, 0, 0, 0, 4, 0],
        [0, 0, 0, 0, 0, 0, 0, 0, 0],
        [0, 0, 0, 0, 0, 6, 0, 0, 0],
        [0, 0, 0, 0, 0, 0, 0, 0, 0],
        [0, 0, 0, 0, 0, 0, 0, 0, 0],
        [2, 0, 0, 0, 0, 0, 0, 0, 0],
        [0, 0, 0, 0, 0, 0, 2, 0, 0],
        [0, 0, 0, 0, 0, 0, 0, 0, 0]
    ]
    # This puzzle copied from Hacked rank test case
    if is_valid(l) == False:
        print("Sorry! Invalid.")
        sys.exit()
    pl = try_with_possibilities(l)
    is_done = is_solved(l)
    if is_done == True:
        for i in l:
            print(i)
        print("Solved!!!")
        sys.exit()

    print("Unable to solve by traditional ways")
    print("Starting assumption based solving")
    new_list = run_assumption(l, pl)
    if new_list != False:
        is_done = is_solved(new_list)
        print('is solved ? - ', is_done)
        for i in new_list:
            print(i)
        if is_done == True:
            print("Solved!!! with assumptions.")
        sys.exit()
    print(l)
    print("Sorry! No Solution. Need to fix the valid function :(")
    sys.exit()