Kindly refer to the below python algorithm that uses a simple backtracking algorithm to solve the puzzle.
The algorithm is going to take the 9X9 grid, which is partially filled with numbers. A record with the value 0 indicates that it is not filled.
def findNextCellToFill(grid, i, j):
for x in range(i,9):
for y in range(j,9):
if grid[x][y] == 0:
return x,y
for x in range(0,9):
for y in range(0,9):
if grid[x][y] == 0:
return x,y
return -1,-1
def isValid(grid, i, j, e):
rowOk = all([e != grid[i][x] for x in range(9)])
if rowOk:
columnOk = all([e != grid[x][j] for x in range(9)])
if columnOk:
# finding the top left x,y co-ordinates of the section containing the i,j cell
secTopX, secTopY = 3 *(i//3), 3 *(j//3) #floored quotient should be used here.
for x in range(secTopX, secTopX+3):
for y in range(secTopY, secTopY+3):
if grid[x][y] == e:
return False
return True
return False
def solveSudoku(grid, i=0, j=0):
i,j = findNextCellToFill(grid, i, j)
if i == -1:
return True
for e in range(1,10):
if isValid(grid,i,j,e):
grid[i][j] = e
if solveSudoku(grid, i, j):
return True
# Undo the current cell for backtracking
grid[i][j] = 0
return False
Testing the code
>>> input = [[5,1,7,6,0,0,0,3,4],[2,8,9,0,0,4,0,0,0],[3,4,6,2,0,5,0,9,0],[6,0,2,0,0,0,0,1,0],[0,3,8,0,0,6,0,4,7],[0,0,0,0,0,0,0,0,0],[0,9,0,0,0,0,0,7,8],[7,0,3,4,0,0,5,6,0],[0,0,0,0,0,0,0,0,0]]
>>> solveSudoku(input)
True
>>> input
[[5, 1, 7, 6, 9, 8, 2, 3, 4], [2, 8, 9, 1, 3, 4, 7, 5, 6], [3, 4, 6, 2, 7, 5, 8, 9, 1], [6, 7, 2, 8, 4, 9, 3, 1, 5], [1, 3, 8, 5, 2, 6, 9, 4, 7], [9, 5, 4, 7, 1, 3, 6, 8, 2], [4, 9, 5, 3, 6, 2, 1, 7, 8], [7, 2, 3, 4, 8, 1, 5, 6, 9], [8, 6, 1, 9, 5, 7, 4, 2, 3]]