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++
// 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
# 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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