检查给定的数独板配置是否有效

给定一个数独板配置，检查它是否有效。

例子：

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

基本思想是根据以下几点来检查每一行、每一列、每一个3×3的框是否有效：

• 数独棋盘可以部分填充，其中空单元格填充字符“.”。
• 空的数独板也是有效的。
• 有效的数独板（部分填满）不一定是可解的。只需要验证填充的单元格。

下面是上述方法的实现：

C++

// C++ Program to check whether given sudoku
// board is valid or not
#include 
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 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 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 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;
}

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 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 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 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 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' }
    };
 
    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
 
# 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

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 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 bool notInCol(char[, ] arr, int col)
    {
        HashSet 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 bool notInBox(char[, ] arr, int startRow,
                                int startCol)
    {
        HashSet 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 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 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' }
        };
 
        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 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' ]];
     
    document.write((isValidConfig(board, 9) ?
                       "YES" : "NO"));
     
     
    // This code is contributed by rag2127

输出：

YES

如果您希望与专家一起参加现场课程，请参阅DSA 现场工作专业课程和学生竞争性编程现场课程。