980. Unique Paths III

Hard

4.5K

170

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:**

Input:grid = [[1,0,0,0],[0,0,0,0],[0,0,2,-1]]Output:2Explanation: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:**

Input:grid = [[1,0,0,0],[0,0,0,0],[0,0,0,2]]Output:4Explanation: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:**

Input:grid = [[0,1],[2,0]]Output:0Explanation: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.

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