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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

// 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; 
} 

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 3×3 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 3×3 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 3×3 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

Output: