[LeetCode] 36. Valid Sudoku 驗證數獨

 

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

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

Example 2:

Input:
[
  ["8","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: false
Explanation: Same as Example 1, except with the 5 in the top left corner being 
    modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Note:

• A Sudoku board (partially filled) could be valid but is not necessarily solvable.
• Only the filled cells need to be validated according to the mentioned rules.
• The given board contain only digits 1-9and the character '.'.
• The given board size is always 9x9.

 

這道題讓驗證一個方陣是否為數獨矩陣，想必數獨游戲我們都玩過，就是給一個 9x9 大小的矩陣，可以分為9個 3x3 大小的矩陣，要求是每個小矩陣內必須都是1到9的數字不能有重復，同時大矩陣的橫縱列也不能有重復數字，是一種很經典的益智類游戲，經常在飛機上看見有人拿着紙筆在填數，感覺是消磨時光的利器。這道題給了一個殘缺的二維數組，讓我們判斷當前的這個數獨數組是否合法，即要滿足上述的條件。判斷標准是看各行各列是否有重復數字，以及每個小的 3x3 的小方陣里面是否有重復數字，如果都無重復，則當前矩陣是數獨矩陣，但不代表待數獨矩陣有解，只是單純的判斷當前未填完的矩陣是否是數獨矩陣。那么根據數獨矩陣的定義，在遍歷每個數字的時候，就看看包含當前位置的行和列以及 3x3 小方陣中是否已經出現該數字，這里需要三個 boolean 型矩陣，大小跟原數組相同，分別記錄各行，各列，各小方陣是否出現某個數字，其中行和列標志下標很好對應，就是小方陣的下標需要稍稍轉換一下，具體代碼如下：

 

解法一：

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        vector<vector<bool>> rowFlag(9, vector<bool>(9));
        vector<vector<bool>> colFlag(9, vector<bool>(9));
        vector<vector<bool>> cellFlag(9, vector<bool>(9));
        for (int i = 0; i < 9; ++i) {
            for (int j = 0; j < 9; ++j) {
                if (board[i][j] == '.') continue;
                int c = board[i][j] - '1';
                if (rowFlag[i][c] || colFlag[c][j] || cellFlag[3 * (i / 3) + j / 3][c]) return false;
                rowFlag[i][c] = true;
                colFlag[c][j] = true;
                cellFlag[3 * (i / 3) + j / 3][c] = true;
            }
        }
        return true;
    }
};

 

我們也可以對空間進行些優化，只使用一個 HashSet 來記錄已經存在過的狀態，將每個狀態編碼成為一個字符串，能將如此大量信息的狀態編碼成一個單一的字符串還是需要有些技巧的。對於每個1到9內的數字來說，其在每行每列和每個小區間內都是唯一的，將數字放在一個括號中，每行上的數字就將行號放在括號左邊，每列上的數字就將列數放在括號右邊，每個小區間內的數字就將在小區間內的行列數分別放在括號的左右兩邊，這樣每個數字的狀態都是獨一無二的存在，就可以在 HashSet 中愉快地查找是否有重復存在啦，參見代碼如下：

 

解法二：

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        unordered_set<string> st;
        for (int i = 0; i < 9; ++i) {
            for (int j = 0; j < 9; ++j) {
                if (board[i][j] == '.') continue;
                string t = "(" + to_string(board[i][j]) + ")";
                string row = to_string(i) + t, col = t + to_string(j), cell = to_string(i / 3) + t + to_string(j / 3);
                if (st.count(row) || st.count(col) || st.count(cell)) return false;
                st.insert(row);
                st.insert(col);
                st.insert(cell);
            }
        }
        return true;
    }
};

 

Github 同步地址：

https://github.com/grandyang/leetcode/issues/36

 

類似題目：

Sudoku Solver

 

參考資料：

https://leetcode.com/problems/valid-sudoku/

https://leetcode.com/problems/valid-sudoku/discuss/15450/Shared-my-concise-Java-code

https://leetcode.com/problems/valid-sudoku/discuss/15472/Short%2BSimple-Java-using-Strings

 

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