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

The basic idea is to check whether each row, column, and the 3×3 box is valid or not on the basis of following points:



  • The Sudoku board could be partially filled, where empty cells are filled with the character ‘.’.
  • An empty Sudoku board is also valid.
  • A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.

Below is the implementation of above approach:

C++

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

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Python3

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# 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
  
# Drivers 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' ]]
          
    if isValidConfig(board, 9): 
        print("YES")
    else:
        print("NO")
  
# This code is contributed by Rituraj Jain

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Output:

YES


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