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Description
tab: English
<p>Write a program to solve a Sudoku puzzle by filling the empty cells.</p>
<p>A sudoku solution must satisfy <strong>all of the following rules</strong>:</p>
<ol>
<li>Each of the digits <code>1-9</code> must occur exactly once in each row.</li>
<li>Each of the digits <code>1-9</code> must occur exactly once in each column.</li>
<li>Each of the digits <code>1-9</code> must occur exactly once in each of the 9 <code>3x3</code> sub-boxes of the grid.</li>
</ol>
<p>The <code>'.'</code> character indicates empty cells.</p>
<p> </p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png" style="height:250px; width:250px" />
<pre>
<strong>Input:</strong> 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"]]
<strong>Output:</strong> [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
<strong>Explanation:</strong> The input board is shown above and the only valid solution is shown below:
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png" style="height:250px; width:250px" />
</pre>
<p> </p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>board.length == 9</code></li>
<li><code>board[i].length == 9</code></li>
<li><code>board[i][j]</code> is a digit or <code>'.'</code>.</li>
<li>It is <strong>guaranteed</strong> that the input board has only one solution.</li>
</ul>
> [!tip]- Hint 1
>
> For each cell, place a valid number and try solving for the remaining empty cells.
> [!tip]- Hint 2
>
> If stuck, undo (backtrack) and try another valid number.
---
[submissions](https://leetcode.com/problems/sudoku-solver/submissions/) | [solutions](https://leetcode.com/problems/sudoku-solver/solutions/)
tab: 中文
<p>编写一个程序，通过填充空格来解决数独问题。</p>
<p>数独的解法需<strong> 遵循如下规则</strong>：</p>
<ol>
<li>数字 <code>1-9</code> 在每一行只能出现一次。</li>
<li>数字 <code>1-9</code> 在每一列只能出现一次。</li>
<li>数字 <code>1-9</code> 在每一个以粗实线分隔的 <code>3x3</code> 宫内只能出现一次。（请参考示例图）</li>
</ol>
<p>数独部分空格内已填入了数字，空白格用 <code>'.'</code> 表示。</p>
<p> </p>
<div class="top-view__1vxA">
<div class="original__bRMd">
<div>
<p><strong>示例 1：</strong></p>
<img src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/04/12/250px-sudoku-by-l2g-20050714svg.png" style="height:250px; width:250px" />
<pre>
<strong>输入：</strong>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"]]
<strong>输出：</strong>[["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
<strong>解释：</strong>输入的数独如上图所示，唯一有效的解决方案如下所示：
<img src=" https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/04/12/250px-sudoku-by-l2g-20050714_solutionsvg.png" style="height:250px; width:250px" />
</pre>
<p> </p>
<p><strong>提示：</strong></p>
<ul>
<li><code>board.length == 9</code></li>
<li><code>board[i].length == 9</code></li>
<li><code>board[i][j]</code> 是一位数字或者 <code>'.'</code></li>
<li>题目数据 <strong>保证</strong> 输入数独仅有一个解</li>
</ul>
</div>
</div>
</div>
> [!tip]- 提示 1
>
> For each cell, place a valid number and try solving for the remaining empty cells.
> [!tip]- 提示 2
>
> If stuck, undo (backtrack) and try another valid number.
---
[提交记录](https://leetcode.cn/problems/sudoku-solver/submissions/) | [题解](https://leetcode.cn/problems/sudoku-solver/solution/)
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