On a 2-dimensional grid
, there are 4 types of squares:
1
represents the starting square. There is exactly one starting square.2
represents the ending square. There is exactly one ending square.0
represents empty squares we can walk over.-1
represents 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: [[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:
Input: [[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:
Input: [[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.
Note:
1 <= grid.length * grid[0].length <= 20
在二维网格 grid 上,有 4 种类型的方格:
- 1 表示起始方格。且只有一个起始方格。
- 2 表示结束方格,且只有一个结束方格。
- 0 表示我们可以走过的空方格。
- -1 表示我们无法跨越的障碍。
返回在四个方向(上、下、左、右)上行走时,从起始方格到结束方格的不同路径的数目,每一个无障碍方格都要通过一次。
- 这一题也可以按照第 79 题的思路来做。题目要求输出地图中从起点到终点的路径条数。注意路径要求必须走满所有空白的格子。
- 唯一需要注意的一点是,空白的格子并不是最后走的总步数,
总步数 = 空白格子数 + 1
,因为要走到终点,走到终点也算一步。