Project Notes

Unique Paths II

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Description

tab: English
 
<p>You are given an <code>m x n</code> integer array <code>grid</code>. There is a robot initially located at the <b>top-left corner</b> (i.e., <code>grid[0][0]</code>). The robot tries to move to the <strong>bottom-right corner</strong> (i.e., <code>grid[m - 1][n - 1]</code>). The robot can only move either down or right at any point in time.</p>
 
<p>An obstacle and space are marked as <code>1</code> or <code>0</code> respectively in <code>grid</code>. A path that the robot takes cannot include <strong>any</strong> square that is an obstacle.</p>
 
<p>Return <em>the number of possible unique paths that the robot can take to reach the bottom-right corner</em>.</p>
 
<p>The testcases are generated so that the answer will be less than or equal to <code>2 * 10<sup>9</sup></code>.</p>
 
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/04/robot1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> obstacleGrid = [[0,0,0],[0,1,0],[0,0,0]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> There is one obstacle in the middle of the 3x3 grid above.
There are two ways to reach the bottom-right corner:
1. Right -&gt; Right -&gt; Down -&gt; Down
2. Down -&gt; Down -&gt; Right -&gt; Right
</pre>
 
<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/04/robot2.jpg" style="width: 162px; height: 162px;" />
<pre>
<strong>Input:</strong> obstacleGrid = [[0,1],[0,0]]
<strong>Output:</strong> 1
</pre>
 
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
 
<ul>
	<li><code>m == obstacleGrid.length</code></li>
	<li><code>n == obstacleGrid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>obstacleGrid[i][j]</code> is <code>0</code> or <code>1</code>.</li>
</ul>
 
 
 
> [!tip]- Hint 1
> 
> Use dynamic programming since, from each cell, you can move to the right or down.
 
> [!tip]- Hint 2
> 
> assume dp[i][j] is the number of unique paths to reach (i, j). dp[i][j] = dp[i][j -1] + dp[i - 1][j]. Be careful when you encounter an obstacle. set its value in dp to 0.
 
 
---
 
[submissions](https://leetcode.com/problems/unique-paths-ii/submissions/) | [solutions](https://leetcode.com/problems/unique-paths-ii/solutions/)
 
 
tab: 中文
 
<p>给定一个&nbsp;<code>m x n</code>&nbsp;的整数数组&nbsp;<code>grid</code>。一个机器人初始位于 <strong>左上角</strong>（即 <code>grid[0][0]</code>）。机器人尝试移动到 <strong>右下角</strong>（即 <code>grid[m - 1][n - 1]</code>）。机器人每次只能向下或者向右移动一步。</p>
 
<p>网格中的障碍物和空位置分别用 <code>1</code> 和 <code>0</code> 来表示。机器人的移动路径中不能包含 <strong>任何</strong>&nbsp;有障碍物的方格。</p>
 
<p>返回机器人能够到达右下角的不同路径数量。</p>
 
<p>测试用例保证答案小于等于 <code>2 * 10<sup>9</sup></code>。</p>
 
<p>&nbsp;</p>
 
<p><strong>示例 1：</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/04/robot1.jpg" />
<pre>
<strong>输入：</strong>obstacleGrid = [[0,0,0],[0,1,0],[0,0,0]]
<strong>输出：</strong>2
<strong>解释：</strong>3x3 网格的正中间有一个障碍物。
从左上角到右下角一共有 <code>2</code> 条不同的路径：
1. 向右 -&gt; 向右 -&gt; 向下 -&gt; 向下
2. 向下 -&gt; 向下 -&gt; 向右 -&gt; 向右
</pre>
 
<p><strong>示例 2：</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/04/robot2.jpg" />
<pre>
<strong>输入：</strong>obstacleGrid = [[0,1],[0,0]]
<strong>输出：</strong>1
</pre>
 
<p>&nbsp;</p>
 
<p><strong>提示：</strong></p>
 
<ul>
	<li><code>m ==&nbsp;obstacleGrid.length</code></li>
	<li><code>n ==&nbsp;obstacleGrid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>obstacleGrid[i][j]</code> 为 <code>0</code> 或 <code>1</code></li>
</ul>
 
 
 
> [!tip]- 提示 1
> 
> Use dynamic programming since, from each cell, you can move to the right or down.
 
> [!tip]- 提示 2
> 
> assume dp[i][j] is the number of unique paths to reach (i, j). dp[i][j] = dp[i][j -1] + dp[i - 1][j]. Be careful when you encounter an obstacle. set its value in dp to 0.
 
 
---
 
[提交记录](https://leetcode.cn/problems/unique-paths-ii/submissions/) | [题解](https://leetcode.cn/problems/unique-paths-ii/solution/)

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