# Return the solution of the sudoku.
global getans, visitx, visity
def check(x, y, grid):
x = x/3*3
y = y/3*3
use = set()
for i in range(3):
for j in range(3):
if grid[x+i][y+j] == 0:
return True
use.add(grid[x+i][y+j])
if len(use) == 9:
return True
return False
def dfs(grid):
global getans
for i in range(9):
for j in range(9):
if grid[i][j] == 0:
for k in range(1,10):
if k not in visitx[i] and k not in visity[j]:
grid[i][j] = k
if check(i, j, grid):
visitx[i].add(k)
visity[j].add(k)
dfs(grid)
visitx[i].remove(k)
visity[j].remove(k)
if getans == 1:
return
grid[i][j] = 0
return
getans = 1
def checkio(grid):
global getans, visity, visitx
visitx = [set() for i in range(9)]
visity = [set() for i in range(9)]
for i, row in enumerate(grid):
for j, cell in enumerate(row):
if cell != 0:
visitx[i].add(cell)
visity[j].add(cell)
getans = 0
dfs(grid)
return grid
#These "asserts" using only for self-checking and not necessary for auto-testing
if __name__ == '__main__':
assert checkio([[0, 7, 1, 6, 8, 4, 0, 0, 0],
[0, 4, 9, 7, 0, 0, 0, 0, 0],
[5, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 8, 0, 0, 0, 0, 5, 0, 4],
[0, 0, 0, 3, 0, 7, 0, 0, 0],
[2, 0, 3, 0, 0, 0, 0, 9, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 9],
[0, 0, 0, 0, 0, 3, 7, 2, 0],
[0, 0, 0, 4, 9, 8, 6, 1, 0]]) == [[3, 7, 1, 6, 8, 4, 9, 5, 2],
[8, 4, 9, 7, 2, 5, 3, 6, 1],
[5, 6, 2, 9, 3, 1, 4, 7, 8],
[6, 8, 7, 2, 1, 9, 5, 3, 4],
[9, 1, 4, 3, 5, 7, 2, 8, 6],
[2, 5, 3, 8, 4, 6, 1, 9, 7],
[1, 3, 6, 5, 7, 2, 8, 4, 9],
[4, 9, 8, 1, 6, 3, 7, 2, 5],
[7, 2, 5, 4, 9, 8, 6, 1, 3]], "first"
assert checkio([[5, 0, 0, 7, 1, 9, 0, 0, 4],
[0, 0, 1, 0, 3, 0, 5, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 8, 5, 9, 7, 2, 6, 4, 0],
[0, 0, 0, 6, 0, 1, 0, 0, 0],
[0, 2, 6, 3, 8, 5, 9, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 3, 0, 5, 0, 2, 0, 0],
[8, 0, 0, 4, 9, 7, 0, 0, 6]]) == [[5, 6, 8, 7, 1, 9, 3, 2, 4],
[9, 7, 1, 2, 3, 4, 5, 6, 8],
[2, 3, 4, 5, 6, 8, 7, 9, 1],
[1, 8, 5, 9, 7, 2, 6, 4, 3],
[3, 9, 7, 6, 4, 1, 8, 5, 2],
[4, 2, 6, 3, 8, 5, 9, 1, 7],
[6, 1, 9, 8, 2, 3, 4, 7, 5],
[7, 4, 3, 1, 5, 6, 2, 8, 9],
[8, 5, 2, 4, 9, 7, 1, 3, 6]], "second"
print('Done')
