# 63. Unique Paths II

## Problem Statement

<br>

You are given an `m x n` integer array `grid`. There is a robot initially located at the top-left corner (i.e., `grid[0][0]`). The robot tries to move to the **bottom-right corner** (i.e., `grid[m - 1][n - 1]`). The robot can only move either down or right at any point in time.

An obstacle and space are marked as `1` or `0` respectively in `grid`. A path that the robot takes cannot include **any** square that is an obstacle.

Return *the number of possible unique paths that the robot can take to reach the bottom-right corner*.

The testcases are generated so that the answer will be less than or equal to `2 * 109`.

&#x20;

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/11/04/robot1.jpg)

<pre><code><strong>Input: obstacleGrid = [[0,0,0],[0,1,0],[0,0,0]]
</strong><strong>Output: 2
</strong><strong>Explanation: There is one obstacle in the middle of the 3x3 grid above.
</strong>There are two ways to reach the bottom-right corner:
1. Right -> Right -> Down -> Down
2. Down -> Down -> Right -> Right
</code></pre>

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/11/04/robot2.jpg)

<pre><code><strong>Input: obstacleGrid = [[0,1],[0,0]]
</strong><strong>Output: 1
</strong></code></pre>

&#x20;

**Constraints:**

* `m == obstacleGrid.length`
* `n == obstacleGrid[i].length`
* `1 <= m, n <= 100`
* `obstacleGrid[i][j]` is `0` or `1`.

## Intuition

```
If there is an obstacle, 

Dont write any condition

else similar to PAths1
```

### Links

<https://leetcode.com/problems/unique-paths-ii/description/>

### Video Links

<https://www.youtube.com/watch?v=TmhpgXScLyY&ab_channel=takeUforward>

### Approach 1:

```
Memoization
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    int path(vector<vector<int>>& arr, int i, int j, vector<vector<int>> &dp){
        if(i==0 and j==0)
            return arr[0][0] == 0 ? 1 : 0;

        if(i<0 or j<0)
            return 0;

        if(dp[i][j] != -1)
            return dp[i][j];

        int l = 0, r = 0;

        if(arr[i][j] == 0){
            if( i>0 and arr[i-1][j] == 0)
                l = path(arr,i-1,j,dp);

            if(j>0 and arr[i][j-1] == 0)
                r = path(arr,i,j-1,dp);
        }
        return dp[i][j] = l+r;

    }

    int uniquePathsWithObstacles(vector<vector<int>>& arr) {
        int m = arr.size();
        int n = arr[0].size();

        vector<vector<int>> dp(m,vector<int>(n,-1));

        return path(arr,m-1,n-1,dp);
    }
};
```

{% endcode %}

### Approach 2:

```
Tabulation
```

{% code title="C++" lineNumbers="true" %}

```cpp
class Solution {
public:
    int uniquePathsWithObstacles(vector<vector<int>>& arr) {
        int m = arr.size();
        int n = arr[0].size();

        vector<vector<int>> dp(m,vector<int>(n,-1));
        dp[0][0] = arr[0][0] == 0 ? 1 : 0;

        for(int i=0; i<m; i++) {
            for(int j=0; j<n; j++) {
                if(i==0 and j==0)   continue;

                int l = 0, r = 0;

                if(arr[i][j] == 0){
                    if(i>0 and arr[i-1][j] == 0)
                        l = dp[i-1][j];

                    if(j>0 and arr[i][j-1] == 0)
                        r = dp[i][j-1];
                }
                dp[i][j] = l+r;
            }
        }
        

        return dp[m-1][n-1];
    }
};
```

{% endcode %}

### Approach 3:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 4:

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Similar Problems

###


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://coding-9.gitbook.io/untitled/dynamic-programming/dp-on-grids/63.-unique-paths-ii.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.