create-grid-with-exactly-one-path

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Algorithms

You are given two integers <code>m</code> and <code>n</code>, representing the number of rows and columns of a grid.

Construct any <code>m x n</code> grid consisting only of the characters <code>&#39;.&#39;</code> and <code>&#39;#&#39;</code>, where:

<ul>
	<li><code>&#39;.&#39;</code> represents a free cell.</li>
	<li><code>&#39;#&#39;</code> represents an obstacle cell.</li>
</ul>

A valid path is a sequence of free cells that:

<ul>
	<li>Starts at the top-left cell <code>(0, 0)</code>.</li>
	<li>Ends at the bottom-right cell <code>(m - 1, n - 1)</code>.</li>
	<li>Moves only:
	<ul>
		<li>Right, from <code>(i, j)</code> to <code>(i, j + 1)</code>, or</li>
		<li>Down, from <code>(i, j)</code> to <code>(i + 1, j)</code>.</li>
	</ul>
	</li>
</ul>

Return any grid such that there is exactly one valid path from the top-left cell to the bottom-right cell.

&nbsp;
Example 1:

<div class="example-block">
Input: m = 2, n = 3

Output: [&quot;..#&quot;,&quot;#..&quot;]

Explanation:

<img src="https://assets.leetcode.com/uploads/2026/05/26/screenshot-2026-05-26-at-61005pm.png" style="width: 200px; height: 95px;" />

The only valid path is: <code>(0,0) &rarr; (0,1) &rarr; (1,1) &rarr; (1,2)</code>
</div>

Example 2:

<div class="example-block">
Input: m = 3, n = 3

Output: [&quot;..#&quot;,&quot;#..&quot;,&quot;##.&quot;]

Explanation:

<img src="https://assets.leetcode.com/uploads/2026/05/26/screenshot-2026-05-26-at-61129pm.png" style="width: 220px; height: 150px;" />

The only valid path is: <code>(0,0) &rarr; (0,1) &rarr; (1,1) &rarr; (1,2) &rarr; (2,2)</code>
</div>

Example 3:

<div class="example-block">
Input: m = 1, n = 4

Output: [&quot;....&quot;]

Explanation:

The only valid path is: <code>(0,0) &rarr; (0,1) &rarr; (0,2) &rarr; (0,3)</code>
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= m, n &lt;= 25</code></li>
</ul>

第 185 场双周赛

biweekly-contest-185

createGrid

中级工程师

Create Grid With Exactly One Path

Create Grid With Exactly K Paths I

create-grid-with-exactly-k-paths-i

创建一个恰好有 K 条路径的网格图 I

给你两个整数 <code>m</code> 和 <code>n</code>，分别表示网格的行数和列数。

请你构造 任意 一个只包含字符 <code>'.'</code> 和 <code>'#'</code> 的 <code>m x n</code> 网格，其中：

<ul>
	<li><code>'.'</code> 表示空单元格。</li>
	<li><code>'#'</code> 表示障碍物单元格。</li>
</ul>

有效路径 是满足以下条件的空单元格序列：

<ul>
	<li>从左上角单元格 <code>(0, 0)</code> 开始。</li>
	<li>在右下角单元格 <code>(m - 1, n - 1)</code> 结束。</li>
	<li>只能向：
	<ul>
		<li>右移动，从 <code>(i, j)</code> 到 <code>(i, j + 1)</code>，或者</li>
		<li>下移动，从 <code>(i, j)</code> 到 <code>(i + 1, j)</code>。</li>
	</ul>
	</li>
</ul>

返回任意一个从左上角到右下角 恰好只有一条有效路径 的网格。

&nbsp;

示例 1：

<div class="example-block">
输入： m = 2, n = 3

输出： ["..#","#.."]

解释：

<img src="https://assets.leetcode.com/uploads/2026/05/26/screenshot-2026-05-26-at-61005pm.png" style="width: 200px; height: 95px;" />

唯一的有效路径是：<code>(0,0) → (0,1) → (1,1) → (1,2)</code>
</div>

示例 2：

<div class="example-block">
输入： m = 3, n = 3

输出： ["..#","#..","##."]

解释：

<img src="https://assets.leetcode.com/uploads/2026/05/26/screenshot-2026-05-26-at-61129pm.png" style="width: 220px; height: 150px;" />

唯一的有效路径是：<code>(0,0) → (0,1) → (1,1) → (1,2) → (2,2)</code>
</div>

示例 3：

<div class="example-block">
输入： m = 1, n = 4

输出： ["...."]

解释：

唯一的有效路径是：<code>(0,0) → (0,1) → (0,2) → (0,3)</code>
</div>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= m, n &lt;= 25</code></li>
</ul>