Check if given Sudoku board configuration is valid or not

Given a Sudoku Board configuration, check whether it is valid or not.

Examples:

Input:    [5 3 – – 7 – – – -]
              [6 – – 1 9 5 – – -]
              [- 9 8 – – – – 6 -]
              [8 – – – 6 – – – 3]
              [4 – – 8 – 3 – – 1]
              [7 – – – 2 – – – 6]
              [- 6 – – – – 2 8 -]
              [- – – 4 1 9 – – 5]
              [- – – – 8 – – 7 9]

Output: True

Input:    [3 9 – 7 5 2 – – -]
              [5 – 4 – – – – 7 -]
              [- – 2 – 8 – – 9 -]
              [1 8 9 6 – – 4 5 7]
              [2 – – – 1 – 3 8 6]
              [6 – 7 8 – – – 1 9]
              [8 – 1 2 – 6 9 4 5]
              [9 5 – 1 – 4 6 – -]
              [- – – 5 9 8 7 3 1]

Output: True 

Brute force approach to check if the given sudoku board configuration is valid or not:

Every number between 1 to 9 appears only once in every row, column and 3X3 box of the sudoku. So check for every cell of the configuration that it’s value is appearing only once in it’s row, column and 3X3 box.

Follow the given steps to solve the problem:

• Loop over every cell of the sudoku
• For every cell check, if that value appears only once in its row, column, and 3X3 box. If it is so then move on, else return false
• Repeat this process until all cells have been checked
• After this process return true, as no cell was violating the conditions

Below is the implementation of the above approach:

C++

// C++ Program to check whether given sudoku
// board is valid or not

#include <bits/stdc++.h>
using namespace std;

// Checks whether there is any duplicate
// in current row or not
bool notInRow(char arr[][9], int row)
{
    // Set to store characters seen so far.
    set<char> st;

    for (int i = 0; i < 9; i++) {

        // If already encountered before, return false
        if (st.find(arr[row][i]) != st.end())
            return false;

        // If it is not an empty cell, insert value
        // at the current cell in the set
        if (arr[row][i] != '.')
            st.insert(arr[row][i]);
    }
    return true;
}

// Checks whether there is any duplicate
// in current column or not.
bool notInCol(char arr[][9], int col)
{
    set<char> st;

    for (int i = 0; i < 9; i++) {

        // If already encountered before, return false
        if (st.find(arr[i][col]) != st.end())
            return false;

        // If it is not an empty cell,
        // insert value at the current cell in the set
        if (arr[i][col] != '.')
            st.insert(arr[i][col]);
    }
    return true;
}

// Checks whether there is any duplicate
// in current 3x3 box or not.
bool notInBox(char arr[][9], int startRow, int startCol)
{
    set<char> st;

    for (int row = 0; row < 3; row++) {
        for (int col = 0; col < 3; col++) {
            char curr = arr[row + startRow][col + startCol];

            // If already encountered before, return false
            if (st.find(curr) != st.end())
                return false;

            // If it is not an empty cell,
            // insert value at current cell in set
            if (curr != '.')
                st.insert(curr);
        }
    }
    return true;
}

// Checks whether current row and current column and
// current 3x3 box is valid or not
bool isValid(char arr[][9], int row, int col)
{
    return notInRow(arr, row) && notInCol(arr, col)
           && notInBox(arr, row - row % 3, col - col % 3);
}

bool isValidConfig(char arr[][9], int n)
{
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {

            // If current row or current column or
            // current 3x3 box is not valid, return false
            if (!isValid(arr, i, j))
                return false;
        }
    }
    return true;
}

// Driver's code
int main()
{
    char board[9][9]
        = { { '5', '3', '.', '.', '7', '.', '.', '.', '.' },
            { '6', '.', '.', '1', '9', '5', '.', '.', '.' },
            { '.', '9', '8', '.', '.', '.', '.', '6', '.' },
            { '8', '.', '.', '.', '6', '.', '.', '.', '3' },
            { '4', '.', '.', '8', '.', '3', '.', '.', '1' },
            { '7', '.', '.', '.', '2', '.', '.', '.', '6' },
            { '.', '6', '.', '.', '.', '.', '2', '8', '.' },
            { '.', '.', '.', '4', '1', '9', '.', '.', '5' },
            { '.', '.', '.', '.', '8', '.', '.', '7',
              '9' } };

    // Function call
    cout << (isValidConfig(board, 9) ? "YES\n" : "NO\n");
    return 0;
}

Java

// Java Program to check whether given sudoku
// board is valid or not

import java.io.*;
import java.util.*;

class GFG {

    // Checks whether there is any duplicate
    // in current row or not
    public static boolean notInRow(char arr[][], int row)
    {

        // Set to store characters seen so far.
        HashSet<Character> st = new HashSet<>();

        for (int i = 0; i < 9; i++) {

            // If already encountered before,
            // return false
            if (st.contains(arr[row][i]))
                return false;

            // If it is not an empty cell, insert value
            // at the current cell in the set
            if (arr[row][i] != '.')
                st.add(arr[row][i]);
        }
        return true;
    }

    // Checks whether there is any duplicate
    // in current column or not.
    public static boolean notInCol(char arr[][], int col)
    {
        HashSet<Character> st = new HashSet<>();

        for (int i = 0; i < 9; i++) {

            // If already encountered before,
            // return false
            if (st.contains(arr[i][col]))
                return false;

            // If it is not an empty cell,
            // insert value at the current
            // cell in the set
            if (arr[i][col] != '.')
                st.add(arr[i][col]);
        }
        return true;
    }

    // Checks whether there is any duplicate
    // in current 3x3 box or not.
    public static boolean
    notInBox(char arr[][], int startRow, int startCol)
    {
        HashSet<Character> st = new HashSet<>();

        for (int row = 0; row < 3; row++) {
            for (int col = 0; col < 3; col++) {
                char curr
                    = arr[row + startRow][col + startCol];

                // If already encountered before, return
                // false
                if (st.contains(curr))
                    return false;

                // If it is not an empty cell,
                // insert value at current cell in set
                if (curr != '.')
                    st.add(curr);
            }
        }
        return true;
    }

    // Checks whether current row and current column and
    // current 3x3 box is valid or not
    public static boolean isValid(char arr[][], int row,
                                  int col)
    {
        return notInRow(arr, row) && notInCol(arr, col)
            && notInBox(arr, row - row % 3, col - col % 3);
    }

    public static boolean isValidConfig(char arr[][], int n)
    {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {

                // If current row or current column or
                // current 3x3 box is not valid, return
                // false
                if (!isValid(arr, i, j))
                    return false;
            }
        }
        return true;
    }

    // Driver's code
    public static void main(String[] args)
    {
        char[][] board = new char[][] {
            { '5', '3', '.', '.', '7', '.', '.', '.', '.' },
            { '6', '.', '.', '1', '9', '5', '.', '.', '.' },
            { '.', '9', '8', '.', '.', '.', '.', '6', '.' },
            { '8', '.', '.', '.', '6', '.', '.', '.', '3' },
            { '4', '.', '.', '8', '.', '3', '.', '.', '1' },
            { '7', '.', '.', '.', '2', '.', '.', '.', '6' },
            { '.', '6', '.', '.', '.', '.', '2', '8', '.' },
            { '.', '.', '.', '4', '1', '9', '.', '.', '5' },
            { '.', '.', '.', '.', '8', '.', '.', '7', '9' }
        };

        // Function call
        System.out.println(
            (isValidConfig(board, 9) ? "YES" : "NO"));
    }
}

// This code is contributed by Rohit OBeroi

Python3

# Python3 program to check whether
# given sudoku board is valid or not

# Checks whether there is any
# duplicate in current row or not


def notInRow(arr, row):

    # Set to store characters seen so far.
    st = set()

    for i in range(0, 9):

        # If already encountered before,
        # return false
        if arr[row][i] in st:
            return False

        # If it is not an empty cell, insert value
        # at the current cell in the set
        if arr[row][i] != '.':
            st.add(arr[row][i])

    return True

# Checks whether there is any
# duplicate in current column or not.


def notInCol(arr, col):

    st = set()

    for i in range(0, 9):

        # If already encountered before,
        # return false
        if arr[i][col] in st:
            return False

        # If it is not an empty cell, insert
        # value at the current cell in the set
        if arr[i][col] != '.':
            st.add(arr[i][col])

    return True

# Checks whether there is any duplicate
# in current 3x3 box or not.


def notInBox(arr, startRow, startCol):

    st = set()

    for row in range(0, 3):
        for col in range(0, 3):
            curr = arr[row + startRow][col + startCol]

            # If already encountered before,
            # return false
            if curr in st:
                return False

            # If it is not an empty cell,
            # insert value at current cell in set
            if curr != '.':
                st.add(curr)

    return True

# Checks whether current row and current
# column and current 3x3 box is valid or not


def isValid(arr, row, col):

    return (notInRow(arr, row) and notInCol(arr, col) and
            notInBox(arr, row - row % 3, col - col % 3))


def isValidConfig(arr, n):

    for i in range(0, n):
        for j in range(0, n):

            # If current row or current column or
            # current 3x3 box is not valid, return false
            if not isValid(arr, i, j):
                return False

    return True


# Driver's code
if __name__ == "__main__":

    board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'],
             ['6', '.', '.', '1', '9', '5', '.', '.', '.'],
             ['.', '9', '8', '.', '.', '.', '.', '6', '.'],
             ['8', '.', '.', '.', '6', '.', '.', '.', '3'],
             ['4', '.', '.', '8', '.', '3', '.', '.', '1'],
             ['7', '.', '.', '.', '2', '.', '.', '.', '6'],
             ['.', '6', '.', '.', '.', '.', '2', '8', '.'],
             ['.', '.', '.', '4', '1', '9', '.', '.', '5'],
             ['.', '.', '.', '.', '8', '.', '.', '7', '9']]

    # Function call
    if isValidConfig(board, 9):
        print("YES")
    else:
        print("NO")

# This code is contributed by Rituraj Jain

C#

// C# Program to check whether given sudoku
// board is valid or not

using System;
using System.Collections.Generic;
class GFG {

    // Checks whether there is any duplicate
    // in current row or not
    public static bool notInRow(char[, ] arr, int row)
    {

        // Set to store characters seen so far.
        HashSet<char> st = new HashSet<char>();

        for (int i = 0; i < 9; i++) {

            // If already encountered before,
            // return false
            if (st.Contains(arr[row, i]))
                return false;

            // If it is not an empty cell, insert value
            // at the current cell in the set
            if (arr[row, i] != '.')
                st.Add(arr[row, i]);
        }
        return true;
    }

    // Checks whether there is any duplicate
    // in current column or not.
    public static bool notInCol(char[, ] arr, int col)
    {
        HashSet<char> st = new HashSet<char>();

        for (int i = 0; i < 9; i++) {

            // If already encountered before,
            // return false
            if (st.Contains(arr[i, col]))
                return false;

            // If it is not an empty cell,
            // insert value at the current
            // cell in the set
            if (arr[i, col] != '.')
                st.Add(arr[i, col]);
        }
        return true;
    }

    // Checks whether there is any duplicate
    // in current 3x3 box or not.
    public static bool notInBox(char[, ] arr, int startRow,
                                int startCol)
    {
        HashSet<char> st = new HashSet<char>();

        for (int row = 0; row < 3; row++) {
            for (int col = 0; col < 3; col++) {
                char curr
                    = arr[row + startRow, col + startCol];

                // If already encountered before, return
                // false
                if (st.Contains(curr))
                    return false;

                // If it is not an empty cell,
                // insert value at current cell in set
                if (curr != '.')
                    st.Add(curr);
            }
        }
        return true;
    }

    // Checks whether current row and current column and
    // current 3x3 box is valid or not
    public static bool isValid(char[, ] arr, int row,
                               int col)
    {
        return notInRow(arr, row) && notInCol(arr, col)
            && notInBox(arr, row - row % 3, col - col % 3);
    }

    public static bool isValidConfig(char[, ] arr, int n)
    {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {

                // If current row or current column or
                // current 3x3 box is not valid, return
                // false
                if (!isValid(arr, i, j))
                    return false;
            }
        }
        return true;
    }

    // Driver's code
    public static void Main(string[] args)
    {
        char[, ] board = new char[, ] {
            { '5', '3', '.', '.', '7', '.', '.', '.', '.' },
            { '6', '.', '.', '1', '9', '5', '.', '.', '.' },
            { '.', '9', '8', '.', '.', '.', '.', '6', '.' },
            { '8', '.', '.', '.', '6', '.', '.', '.', '3' },
            { '4', '.', '.', '8', '.', '3', '.', '.', '1' },
            { '7', '.', '.', '.', '2', '.', '.', '.', '6' },
            { '.', '6', '.', '.', '.', '.', '2', '8', '.' },
            { '.', '.', '.', '4', '1', '9', '.', '.', '5' },
            { '.', '.', '.', '.', '8', '.', '.', '7', '9' }
        };

          // Function call
        Console.WriteLine(
            (isValidConfig(board, 9) ? "YES" : "NO"));
    }
}

// This code is contributed by ukasp.

Javascript

// Javascript Program to check whether given sudoku
// board is valid or not

// Checks whether there is any duplicate
// in current row or not
    function notInRow(arr,row)
    {
        // Set to store characters seen so far.
        let st = new Set();

        for(let i = 0; i < 9; i++)
        {

            // If already encountered before,
            // return false
            if (st.has(arr[row][i]))
                return false;

            // If it is not an empty cell, insert value
            // at the current cell in the set
            if (arr[row][i] != '.')
                st.add(arr[row][i]);
        }
        return true;
    }

// Checks whether there is any duplicate
// in current column or not.
    function  notInCol(arr,col)
    {
        let st = new Set();

        for(let i = 0; i < 9; i++)
        {

            // If already encountered before,
            // return false
            if (st.has(arr[i][col]))
                return false;

            // If it is not an empty cell,
            // insert value at the current
            // cell in the set
            if (arr[i][col] != '.')
                st.add(arr[i][col]);
        }
        return true;
    }

// Checks whether there is any duplicate
// in current 3x3 box or not.
    function notInBox(arr,startRow,startCol)
    {
        let st = new Set();

        for(let row = 0; row < 3; row++)
        {
        for(let col = 0; col < 3; col++)
        {
            let curr = arr[row + startRow][col + startCol];

            // If already encountered before, return
            // false
            if (st.has(curr))
                return false;

            // If it is not an empty cell,
            // insert value at current cell in set
            if (curr != '.')
                st.add(curr);
        }
    }
    return true;
    }


    // Checks whether current row and current column and
// current 3x3 box is valid or not
    function  isValid(arr,row,col)
    {
        return notInRow(arr, row) && notInCol(arr, col) &&
           notInBox(arr, row - row % 3, col - col % 3);
    }


    function isValidConfig(arr,n)
    {
        for(let i = 0; i < n; i++)
    {
        for(let j = 0; j < n; j++)
        {

            // If current row or current column or
            // current 3x3 box is not valid, return
            // false
            if (!isValid(arr, i, j))
                return false;
        }
    }
    return true;
    }

    // Driver's code
    let board = [[ '5', '3', '.', '.', '7', '.', '.', '.', '.' ],
             [ '6', '.', '.', '1', '9', '5', '.', '.', '.' ],
             [ '.', '9', '8', '.', '.', '.', '.', '6', '.' ],
             [ '8', '.', '.', '.', '6', '.', '.', '.', '3' ],
             [ '4', '.', '.', '8', '.', '3', '.', '.', '1' ],
             [ '7', '.', '.', '.', '2', '.', '.', '.', '6' ],
             [ '.', '6', '.', '.', '.', '.', '2', '8', '.' ],
             [ '.', '.', '.', '4', '1', '9', '.', '.', '5' ],
             [ '.', '.', '.', '.', '8', '.', '.', '7', '9' ]];

    // Function call
    document.write((isValidConfig(board, 9) ?
                       "YES" : "NO"));


    // This code is contributed by rag2127

Output:

YES

Time Complexity: O(N * N)
Auxiliary Space: O(1)