Recursion issue in sudoku solver

Question

I’m getting an error that I’ve exceeded the maximum number of errors in the method recuSolve. I’m using recursion to find the correct value for each sudoku box 1 by 1.
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import numpy as np

grid = [[2, 5, 0, 0, 3, 0, 9, 0, 1],
        [0, 1, 0, 0, 0, 4, 0, 0, 0],
        [4, 0, 7, 0, 0, 0, 2, 0, 8],
        [0, 0, 5, 2, 0, 0, 0, 0, 0],
        [0, 0, 0, 0, 9, 8, 1, 0, 0],
        [0, 4, 0, 0, 0, 3, 0, 0, 0],
        [0, 0, 0, 3, 6, 0, 0, 7, 2],
        [0, 7, 0, 0, 0, 0, 0, 0, 3],
        [9, 0, 3, 0, 0, 0, 6, 0, 4]]

def printBoard(board): #prints the board
    horLine = '-'*22
    board_str = board.astype(str)
    for num in range(9):
        if num%3==0 and num!=0:
            print(horLine)
        row=board_str[num]
        print(' '.join(row[0:3])+' | '+' '.join(row[3:6])+' | '+' '.join(row[6:]))

def nextSpace(board): # returns the next open space
    for r in range(9):
        for c in range(9):
            if board[r][c] == 0:
                return (r,c)
    return -1

def check(board,row,col,num): #checks if a value(num) works as a solution to an open spot
    for x in range(9):
        if board[row][x]==num and x!=row:
            return False
        if board[x][col]==num and x!=col:
            return False
    ro=row//3*3
    co=col//3*3
    for r in range(ro,ro+3):
        for c in range(co,co+3):
            if board[r][c]==num and (row,col)!=(r,c):
                return False
    return True

def recuSolve(board): # this is where I think I'm messing up
    space = nextSpace(board)
    if space == -1:
        printBoard(board)
        return True
    row, col = space
    for x in range(9):
        if check(board, row, col, x+1):
            board[row][col]=x+1
    return recuSolve(board)


recuSolve(grid)

Asked By: Mohit Singh

||

Source

Answer 1

For completeness, I removed the import of numpy, which you weren’t using, and made these few changes:

def printBoard(board): #prints the board
    horLine = '-'*22
    for num in range(9):
        if num%3==0 and num!=0:
            print(horLine)
        row = list(map(str, board[num]))
        print(' '.join(row[0:3])+' | '+' '.join(row[3:6])+' | '+' '.join(row[6:]))

and

def recuSolve(board):
    space = nextSpace(board)
    if space == -1:
        printBoard(board)
        return True
    row, col = space
    for x in range(9):
        if check(board, row, col, x+1):
            board[row][col]=x+1
            if recuSolve(board):
                return True
    board[row][col] = 0
    return False

recuSolve(grid)

Answered By: Tim Roberts

Answer 2

Apart from the changes that Tim mentioned above, there was a bug (unnecessary row, column confusion) in check() method, that caused wrong answers.
Fixing that as well, below is the complete program.

grid = [[2, 5, 0, 0, 3, 0, 9, 0, 1],
        [0, 1, 0, 0, 0, 4, 0, 0, 0],
        [4, 0, 7, 0, 0, 0, 2, 0, 8],
        [0, 0, 5, 2, 0, 0, 0, 0, 0],
        [0, 0, 0, 0, 9, 8, 1, 0, 0],
        [0, 4, 0, 0, 0, 3, 0, 0, 0],
        [0, 0, 0, 3, 6, 0, 0, 7, 2],
        [0, 7, 0, 0, 0, 0, 0, 0, 3],
        [9, 0, 3, 0, 0, 0, 6, 0, 4]]

def printBoard(board): #prints the board
    horLine = '-'*22
    for num in range(9):
        if num%3==0 and num!=0:
            print(horLine)
        row = list(map(str, board[num]))
        print(' '.join(row[0:3])+' | '+' '.join(row[3:6])+' | '+' '.join(row[6:]))


def nextSpace(board): # returns the next open space
    for r in range(9):
        for c in range(9):
            if board[r][c] == 0:
                return (r,c)
    return -1

def check(board,row,col,num): #checks if a value(num) works as a solution to an open spot
    for x in range(9):
        if board[row][x]==num:
            return False
        if board[x][col]==num:
            return False
    ro=row//3*3
    co=col//3*3
    for r in range(ro,ro+3):
        for c in range(co,co+3):
            if board[r][c]==num and (row,col)!=(r,c):
                return False
    return True

def recuSolve(board): # this is where I think I'm messing up
    space = nextSpace(board)
    if space == -1:
        printBoard(board)
        return True
    row, col = space
    for x in range(9):
        if check(board, row, col, x+1):
            board[row][col]=x+1
            if recuSolve(board):
                return True
    board[row][col]=0
    return False


recuSolve(grid)

Output:

2 5 8 | 7 3 6 | 9 4 1
6 1 9 | 8 2 4 | 3 5 7
4 3 7 | 9 1 5 | 2 6 8
----------------------
3 9 5 | 2 7 1 | 4 8 6
7 6 2 | 4 9 8 | 1 3 5
8 4 1 | 6 5 3 | 7 2 9
----------------------
1 8 4 | 3 6 9 | 5 7 2
5 7 6 | 1 4 2 | 8 9 3
9 2 3 | 5 8 7 | 6 1 4

Answered By: Liju

Recursion issue in sudoku solver

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