Check if given Sudoku solution is valid or not

Given a 2D array, board[][] of size 9 × 9, which represents a solution to the Sudoku puzzle, the task is to check if the given representation of a solved Sudoku puzzle is valid or not.

Examples:

Input:

board[][] = {{7, 9, 2, 1, 5, 4, 3, 8, 6}, 
             {6, 4, 3, 8, 2, 7, 1, 5, 9},
             {8, 5, 1, 3, 9, 6, 7, 2, 4},
             {2, 6, 5, 9, 7, 3, 8, 4, 1},
             {4, 8, 9, 5, 6, 1, 2, 7, 3},
             {3, 1, 7, 4, 8, 2, 9, 6, 5},
             {1, 3, 6, 7, 4, 8, 5, 9, 2},
             {9, 7, 4, 2, 1, 5, 6, 3, 8},
             {5, 2, 8, 6, 3, 9, 4, 1, 7}}

Output: Valid

Input:

board[][] = {{5, 5, 5, 5, 5, 5, 5, 5, 5}, 
             {5, 5, 5, 5, 5, 5, 5, 5, 5},
             {5, 5, 5, 5, 5, 5, 5, 5, 5},
             {5, 5, 5, 5, 5, 5, 5, 5, 5},
             {5, 5, 5, 5, 5, 5, 5, 5, 5},
             {5, 5, 5, 5, 5, 5, 5, 5, 5},
             {5, 5, 5, 5, 5, 5, 5, 5, 5},
             {5, 5, 5, 5, 5, 5, 5, 5, 5},
             {5, 5, 5, 5, 5, 5, 5, 5, 5}}

Output: Not Valid 

Approach: The problem can be solved by checking the following conditions:

• Check if each row of the board[][] array stores only unique values from the range [1, 9] or not.
• Check if each column of the board[][] array stores unique values from the range [1, 9] or not.
• Check if all possible 3 × 3 submatrices of the board[][] array stores unique values from the range [1, 9] or not.

Follow the steps below to solve the problem: 

• Traverse the given matrix board[][].
• Check if the above conditions are satisfied or not.
• If any of the above conditions is not satisfied, then print “Not valid“.
• Otherwise, print “Valid“.

Below is the implementation of the above approach: 

C++

// C++ program to implement
// the above approach

#include <bits/stdc++.h>
using namespace std;
#define N 9

// Function to check if all elements
// of the board[][] array store
// value in the range[1, 9]
bool isinRange(int board[][N])
{

    // Traverse board[][] array
    for (int i = 0; i < N;
         i++) {
        for (int j = 0; j < N;
             j++) {

            // Check if board[i][j]
            // lies in the range
            if (board[i][j] <= 0 || board[i][j] > 9) {
                return false;
            }
        }
    }
    return true;
}

// Function to check if the solution
// of sudoku puzzle is valid or not
bool isValidSudoku(int board[][N])
{
    // Check if all elements of board[][]
    // stores value in the range[1, 9]
    if (isinRange(board)
        == false) {
        return false;
    }

    // Stores unique value
    // from 1 to N
    bool unique[N + 1];

    // Traverse each row of
    // the given array
    for (int i = 0; i < N; i++) {

        // Initialize unique[]
        // array to false
        memset(unique, false,
               sizeof(unique));

        // Traverse each column
        // of current row
        for (int j = 0; j < N;
             j++) {

            // Stores the value
            // of board[i][j]
            int Z = board[i][j];

            // Check if current row
            // stores duplicate value
            if (unique[Z]) {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each column of
    // the given array
    for (int i = 0; i < N; i++) {

        // Initialize unique[]
        // array to false
        memset(unique, false,
               sizeof(unique));

        // Traverse each row
        // of current column
        for (int j = 0; j < N;
             j++) {

            // Stores the value
            // of board[j][i]
            int Z = board[j][i];

            // Check if current column
            // stores duplicate value
            if (unique[Z]) {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each block of
    // size 3 * 3 in board[][] array
    for (int i = 0; i < N - 2;
         i += 3) {

        // j stores first column of
        // each 3 * 3 block
        for (int j = 0; j < N - 2;
             j += 3) {

            // Initialize unique[]
            // array to false
            memset(unique, false,
                   sizeof(unique));

            // Traverse current block
            for (int k = 0; k < 3;
                 k++) {

                for (int l = 0; l < 3;
                     l++) {

                    // Stores row number
                    // of current block
                    int X = i + k;

                    // Stores column number
                    // of current block
                    int Y = j + l;

                    // Stores the value
                    // of board[X][Y]
                    int Z = board[X][Y];

                    // Check if current block
                    // stores duplicate value
                    if (unique[Z]) {
                        return false;
                    }
                    unique[Z] = true;
                }
            }
        }
    }

    // If all conditions satisfied
    return true;
}

// Driver Code
int main()
{
    int board[N][N]
        = { { 7, 9, 2, 1, 5, 4, 3, 8, 6 },
            { 6, 4, 3, 8, 2, 7, 1, 5, 9 },
            { 8, 5, 1, 3, 9, 6, 7, 2, 4 },
            { 2, 6, 5, 9, 7, 3, 8, 4, 1 },
            { 4, 8, 9, 5, 6, 1, 2, 7, 3 },
            { 3, 1, 7, 4, 8, 2, 9, 6, 5 },
            { 1, 3, 6, 7, 4, 8, 5, 9, 2 },
            { 9, 7, 4, 2, 1, 5, 6, 3, 8 },
            { 5, 2, 8, 6, 3, 9, 4, 1, 7 } };

    if (isValidSudoku(board)) {
        cout << "Valid";
    }
    else {
        cout << "Not Valid";
    }
}

Java

// Java program to implement
// the above approach
import java.io.*;
import java.util.*;

class GFG{

static int N = 9;

// Function to check if all elements
// of the board[][] array store
// value in the range[1, 9]
static boolean isinRange(int[][] board)
{

    // Traverse board[][] array
    for(int i = 0; i < N; i++)
    {
        for(int j = 0; j < N; j++)
        {

            // Check if board[i][j]
            // lies in the range
            if (board[i][j] <= 0 ||
                board[i][j] > 9)
            {
                return false;
            }
        }
    }
    return true;
}

// Function to check if the solution
// of sudoku puzzle is valid or not
static boolean isValidSudoku(int board[][])
{

    // Check if all elements of board[][]
    // stores value in the range[1, 9]
    if (isinRange(board) == false)
    {
        return false;
    }

    // Stores unique value
    // from 1 to N
    boolean[] unique = new boolean[N + 1];

    // Traverse each row of
    // the given array
    for(int i = 0; i < N; i++)
    {

        // Initialize unique[]
        // array to false
        Arrays.fill(unique, false);

        // Traverse each column
        // of current row
        for(int j = 0; j < N; j++)
        {

            // Stores the value
            // of board[i][j]
            int Z = board[i][j];

            // Check if current row
            // stores duplicate value
            if (unique[Z])
            {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each column of
    // the given array
    for(int i = 0; i < N; i++)
    {

        // Initialize unique[]
        // array to false
        Arrays.fill(unique, false);

        // Traverse each row
        // of current column
        for(int j = 0; j < N; j++)
        {

            // Stores the value
            // of board[j][i]
            int Z = board[j][i];

            // Check if current column
            // stores duplicate value
            if (unique[Z])
            {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each block of
    // size 3 * 3 in board[][] array
    for(int i = 0; i < N - 2; i += 3)
    {

        // j stores first column of
        // each 3 * 3 block
        for(int j = 0; j < N - 2; j += 3)
        {

            // Initialize unique[]
            // array to false
            Arrays.fill(unique, false);

            // Traverse current block
            for(int k = 0; k < 3; k++)
            {
                for(int l = 0; l < 3; l++)
                {

                    // Stores row number
                    // of current block
                    int X = i + k;

                    // Stores column number
                    // of current block
                    int Y = j + l;

                    // Stores the value
                    // of board[X][Y]
                    int Z = board[X][Y];

                    // Check if current block
                    // stores duplicate value
                    if (unique[Z])
                    {
                        return false;
                    }
                    unique[Z] = true;
                }
            }
        }
    }

    // If all conditions satisfied
    return true;
}

// Driver Code
public static void main(String[] args)
{
    int[][] board = { { 7, 9, 2, 1, 5, 4, 3, 8, 6 },
                      { 6, 4, 3, 8, 2, 7, 1, 5, 9 },
                      { 8, 5, 1, 3, 9, 6, 7, 2, 4 },
                      { 2, 6, 5, 9, 7, 3, 8, 4, 1 },
                      { 4, 8, 9, 5, 6, 1, 2, 7, 3 },
                      { 3, 1, 7, 4, 8, 2, 9, 6, 5 },
                      { 1, 3, 6, 7, 4, 8, 5, 9, 2 },
                      { 9, 7, 4, 2, 1, 5, 6, 3, 8 },
                      { 5, 2, 8, 6, 3, 9, 4, 1, 7 } };

    if (isValidSudoku(board))
    {
        System.out.println("Valid");
    }
    else
    {
        System.out.println("Not Valid");
    }
}
}

// This code is contributed by akhilsaini

Python3

# Python3 program to implement
# the above approach

# Function to check if all elements
# of the board[][] array store
# value in the range[1, 9]
def isinRange(board):

  N = 9

  # Traverse board[][] array
  for i in range(0, N):
    for j in range(0, N):

      # Check if board[i][j]
      # lies in the range
      if ((board[i][j] <= 0) or
          (board[i][j] > 9)):
        return False

  return True

# Function to check if the solution
# of sudoku puzzle is valid or not
def isValidSudoku(board):

  N = 9

  # Check if all elements of board[][]
  # stores value in the range[1, 9]
  if (isinRange(board) == False):
    return False

  # Stores unique value
  # from 1 to N
  unique = [False] * (N + 1)

  # Traverse each row of
  # the given array
  for i in range(0, N):

    # Initialize unique[]
    # array to false
    for m in range(0, N + 1):
      unique[m] = False

    # Traverse each column
    # of current row
    for j in range(0, N):

      # Stores the value
      # of board[i][j]
      Z = board[i][j]

      # Check if current row
      # stores duplicate value
      if (unique[Z] == True):
        return False

      unique[Z] = True

  # Traverse each column of
  # the given array
  for i in range(0, N):

    # Initialize unique[]
    # array to false
    for m in range(0, N + 1):
      unique[m] = False

    # Traverse each row
    # of current column
    for j in range(0, N):

      # Stores the value
      # of board[j][i]
      Z = board[j][i]

      # Check if current column
      # stores duplicate value
      if (unique[Z] == True):
        return False

      unique[Z] = True

  # Traverse each block of
  # size 3 * 3 in board[][] array
  for i in range(0, N - 2, 3):

    # j stores first column of
    # each 3 * 3 block
    for j in range(0, N - 2, 3):

      # Initialize unique[]
      # array to false
      for m in range(0, N + 1):
        unique[m] = False

      # Traverse current block
      for k in range(0, 3):
        for l in range(0, 3):

          # Stores row number
          # of current block
          X = i + k

          # Stores column number
          # of current block
          Y = j + l

          # Stores the value
          # of board[X][Y]
          Z = board[X][Y]

          # Check if current block
          # stores duplicate value
          if (unique[Z] == True):
            return False

          unique[Z] = True

  # If all conditions satisfied
  return True

# Driver Code
if __name__ == '__main__':

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

  if (isValidSudoku(board)):
    print("Valid")
  else:
    print("Not Valid")

# This code is contributed by akhilsaini

C#

// C# program to implement
// the above approach
using System;
using System.Collections.Generic;

class GFG{

static int N = 9;

// Function to check if all elements
// of the board[][] array store
// value in the range[1, 9]
static bool isinRange(int[, ] board)
{

    // Traverse board[][] array
    for(int i = 0; i < N; i++)
    {
        for(int j = 0; j < N; j++)
        {

            // Check if board[i][j]
            // lies in the range
            if (board[i, j] <= 0 ||
                board[i, j] > 9)
            {
                return false;
            }
        }
    }
    return true;
}

// Function to check if the solution
// of sudoku puzzle is valid or not
static bool isValidSudoku(int[, ] board)
{

    // Check if all elements of board[][]
    // stores value in the range[1, 9]
    if (isinRange(board) == false)
    {
        return false;
    }

    // Stores unique value
    // from 1 to N
    bool[] unique = new bool[N + 1];

    // Traverse each row of
    // the given array
    for(int i = 0; i < N; i++)
    {

        // Initialize unique[]
        // array to false
        Array.Fill(unique, false);

        // Traverse each column
        // of current row
        for(int j = 0; j < N; j++)
        {

            // Stores the value
            // of board[i][j]
            int Z = board[i, j];

            // Check if current row
            // stores duplicate value
            if (unique[Z])
            {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each column of
    // the given array
    for(int i = 0; i < N; i++)
    {

        // Initialize unique[]
        // array to false
        Array.Fill(unique, false);

        // Traverse each row
        // of current column
        for(int j = 0; j < N; j++)
        {

            // Stores the value
            // of board[j][i]
            int Z = board[j, i];

            // Check if current column
            // stores duplicate value
            if (unique[Z])
            {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each block of
    // size 3 * 3 in board[][] array
    for(int i = 0; i < N - 2; i += 3)
    {

        // j stores first column of
        // each 3 * 3 block
        for(int j = 0; j < N - 2; j += 3)
        {

            // Initialize unique[]
            // array to false
            Array.Fill(unique, false);

            // Traverse current block
            for(int k = 0; k < 3; k++)
            {
                for(int l = 0; l < 3; l++)
                {

                    // Stores row number
                    // of current block
                    int X = i + k;

                    // Stores column number
                    // of current block
                    int Y = j + l;

                    // Stores the value
                    // of board[X][Y]
                    int Z = board[X, Y];

                    // Check if current block
                    // stores duplicate value
                    if (unique[Z])
                    {
                        return false;
                    }
                    unique[Z] = true;
                }
            }
        }
    }

    // If all conditions satisfied
    return true;
}

// Driver Code
public static void Main()
{
    int[,] board = { { 7, 9, 2, 1, 5, 4, 3, 8, 6 },
                      { 6, 4, 3, 8, 2, 7, 1, 5, 9 },
                      { 8, 5, 1, 3, 9, 6, 7, 2, 4 },
                      { 2, 6, 5, 9, 7, 3, 8, 4, 1 },
                      { 4, 8, 9, 5, 6, 1, 2, 7, 3 },
                      { 3, 1, 7, 4, 8, 2, 9, 6, 5 },
                      { 1, 3, 6, 7, 4, 8, 5, 9, 2 },
                      { 9, 7, 4, 2, 1, 5, 6, 3, 8 },
                      { 5, 2, 8, 6, 3, 9, 4, 1, 7 } };

    if (isValidSudoku(board))
    {
        Console.WriteLine("Valid");
    }
    else
    {
        Console.WriteLine("Not Valid");
    }
}
}

// This code is contributed by akhilsaini

Javascript

<script>

// JavaScript program to implement
// the above approach

var N = 9;

// Function to check if all elements
// of the board[][] array store
// value in the range[1, 9]
function isinRange(board)
{

    // Traverse board[][] array
    for(var i = 0; i < N; i++)
    {
        for(var j = 0; j < N; j++)
        {

            // Check if board[i][j]
            // lies in the range
            if (board[i][j] <= 0 ||
                board[i][j] > 9)
            {
                return false;
            }
        }
    }
    return true;
}

// Function to check if the solution
// of sudoku puzzle is valid or not
function isValidSudoku(board)
{

    // Check if all elements of board[][]
    // stores value in the range[1, 9]
    if (isinRange(board) == false)
    {
        return false;
    }

    // Stores unique value
    // from 1 to N
    var unique = Array(N+1).fill(false);

    // Traverse each row of
    // the given array
    for(var i = 0; i < N; i++)
    {
        unique = Array(N+1).fill(false);

        // Traverse each column
        // of current row
        for(var j = 0; j < N; j++)
        {

            // Stores the value
            // of board[i][j]
            var Z = board[i][j];

            // Check if current row
            // stores duplicate value
            if (unique[Z])
            {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each column of
    // the given array
    for(var i = 0; i < N; i++)
    {

        // Initialize unique[]
        // array to false
        unique = Array(N+1).fill(false);

        // Traverse each row
        // of current column
        for(var j = 0; j < N; j++)
        {

            // Stores the value
            // of board[j][i]
            var Z = board[j][i];

            // Check if current column
            // stores duplicate value
            if (unique[Z])
            {
                return false;
            }
            unique[Z] = true;
        }
    }

    // Traverse each block of
    // size 3 * 3 in board[][] array
    for(var i = 0; i < N - 2; i += 3)
    {

        // j stores first column of
        // each 3 * 3 block
        for(var j = 0; j < N - 2; j += 3)
        {

            // Initialize unique[]
            // array to false
            unique = Array(N+1).fill(false);

            // Traverse current block
            for(var k = 0; k < 3; k++)
            {
                for(var l = 0; l < 3; l++)
                {

                    // Stores row number
                    // of current block
                    var X = i + k;

                    // Stores column number
                    // of current block
                    var Y = j + l;

                    // Stores the value
                    // of board[X][Y]
                    var Z = board[X][Y];

                    // Check if current block
                    // stores duplicate value
                    if (unique[Z])
                    {
                        return false;
                    }
                    unique[Z] = true;
                }
            }
        }
    }

    // If all conditions satisfied
    return true;
}

// Driver Code
var board = [ [ 7, 9, 2, 1, 5, 4, 3, 8, 6 ],
                  [ 6, 4, 3, 8, 2, 7, 1, 5, 9 ],
                  [ 8, 5, 1, 3, 9, 6, 7, 2, 4 ],
                  [ 2, 6, 5, 9, 7, 3, 8, 4, 1 ],
                  [ 4, 8, 9, 5, 6, 1, 2, 7, 3 ],
                  [ 3, 1, 7, 4, 8, 2, 9, 6, 5 ],
                  [ 1, 3, 6, 7, 4, 8, 5, 9, 2 ],
                  [ 9, 7, 4, 2, 1, 5, 6, 3, 8 ],
                  [ 5, 2, 8, 6, 3, 9, 4, 1, 7 ] ];
if (isValidSudoku(board))
{
    document.write("Valid");
}
else
{
    document.write("Not Valid");
}


</script>

Output:

Valid

Time Complexity: O(N²)
Auxiliary Space: O(N)

 Approach 2: Using Set:

• In the above approach, a set is used to check if a number is repeated in each row, column, and subgrid of the Sudoku board. A set is a container that stores unique elements in no particular order.
• In this approach, we initialize three sets, one for each row, one for each column, and one for each subgrid. We iterate through each cell in the board and check if its value is not equal to 0. If the value is not 0, we insert it into the corresponding set for its row, column, and subgrid. If the value is already in the set, it means that the value is repeated in that particular row, column, or subgrid, and the Sudoku board is invalid.
• If we iterate through all the cells in the board without finding any duplicates, the Sudoku board is valid. This approach is efficient because it avoids nested loops and only iterates through the board once. It also allows us to quickly check if a number is repeated in each row, column, and subgrid using sets, which have an average constant-time complexity for insertions and lookups.

Here is the Code of above Approach:

C++

#include <bits/stdc++.h>
using namespace std;
#define N 9

bool isValidSudoku(int board[][N]) {
    unordered_set<int> rows[N], cols[N], subgrids[N];

    // Traverse board[][] array
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            int num = board[i][j];
            if (num == 0) continue; // Skip empty cells

            int subgrid_index = (i / 3) * 3 + j / 3; // Get sub-grid index

            // Check if num is already present in current row, column or sub-grid
            if (rows[i].count(num) || cols[j].count(num) || subgrids[subgrid_index].count(num))
                return false;

            // Add num to the corresponding sets
            rows[i].insert(num);
            cols[j].insert(num);
            subgrids[subgrid_index].insert(num);
        }
    }
    return true;
}

// Driver code
int main() {
    int board[N][N] = {
        {5, 3, 0, 0, 7, 0, 0, 0, 0},
        {6, 0, 0, 1, 9, 5, 0, 0, 0},
        {0, 9, 8, 0, 0, 0, 0, 6, 0},
        {8, 0, 0, 0, 6, 0, 0, 0, 3},
        {4, 0, 0, 8, 0, 3, 0, 0, 1},
        {7, 0, 0, 0, 2, 0, 0, 0, 6},
        {0, 6, 0, 0, 0, 0, 2, 8, 0},
        {0, 0, 0, 4, 1, 9, 0, 0, 5},
        {0, 0, 0, 0, 8, 0, 0, 7, 9}
    };
    if (isValidSudoku(board))
        cout << "Valid" << endl;
    else
        cout << "Invalid" << endl;
    return 0;
}

Output

Valid

Time Complexity: O(N2)
Auxiliary Space: O(N)