# 0980. Unique Paths III

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

## Description

You are given an `m x n` integer array `grid` where `grid[i][j]` could be:

* `1` representing the starting square. There is exactly one starting square.
* `2` representing the ending square. There is exactly one ending square.
* `0` representing empty squares we can walk over.
* `-1` representing obstacles that we cannot walk over.

Return *the number of 4-directional walks from the starting square to the ending square, that walk over every non-obstacle square exactly once*.

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/08/02/lc-unique1.jpg)

```
**Input:** grid = [[1,0,0,0],[0,0,0,0],[0,0,2,-1]]
**Output:** 2
**Explanation:** We have the following two paths: 
1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2)
2. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2)
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2021/08/02/lc-unique2.jpg)

```
**Input:** grid = [[1,0,0,0],[0,0,0,0],[0,0,0,2]]
**Output:** 4
**Explanation:** We have the following four paths: 
1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2),(2,3)
2. (0,0),(0,1),(1,1),(1,0),(2,0),(2,1),(2,2),(1,2),(0,2),(0,3),(1,3),(2,3)
3. (0,0),(1,0),(2,0),(2,1),(2,2),(1,2),(1,1),(0,1),(0,2),(0,3),(1,3),(2,3)
4. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2),(2,3)
```

**Example 3:**

![](https://assets.leetcode.com/uploads/2021/08/02/lc-unique3-.jpg)

```
**Input:** grid = [[0,1],[2,0]]
**Output:** 0
**Explanation:** There is no path that walks over every empty square exactly once.
Note that the starting and ending square can be anywhere in the grid.
```

**Constraints:**

* `m == grid.length`
* `n == grid[i].length`
* `1 <= m, n <= 20`
* `1 <= m * n <= 20`
* `-1 <= grid[i][j] <= 2`
* There is exactly one starting cell and one ending cell.

## ac

```java
```


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