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.
\n\n\n
Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2021/08/02/lc-unique1.jpg\")
\n\nInput: grid = [[1,0,0,0],[0,0,0,0],[0,0,2,-1]]\nOutput: 2\nExplanation: We have the following two paths: \n1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2)\n2. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2)\n\n\n
Example 2:
\n![\"\"](\"https://assets.leetcode.com/uploads/2021/08/02/lc-unique2.jpg\")
\n\nInput: grid = [[1,0,0,0],[0,0,0,0],[0,0,0,2]]\nOutput: 4\nExplanation: We have the following four paths: \n1. (0,0),(0,1),(0,2),(0,3),(1,3),(1,2),(1,1),(1,0),(2,0),(2,1),(2,2),(2,3)\n2. (0,0),(0,1),(1,1),(1,0),(2,0),(2,1),(2,2),(1,2),(0,2),(0,3),(1,3),(2,3)\n3. (0,0),(1,0),(2,0),(2,1),(2,2),(1,2),(1,1),(0,1),(0,2),(0,3),(1,3),(2,3)\n4. (0,0),(1,0),(2,0),(2,1),(1,1),(0,1),(0,2),(0,3),(1,3),(1,2),(2,2),(2,3)\n\n\n
Example 3:
\n![\"\"](\"https://assets.leetcode.com/uploads/2021/08/02/lc-unique3-.jpg\")
\n\nInput: grid = [[0,1],[2,0]]\nOutput: 0\nExplanation: There is no path that walks over every empty square exactly once.\nNote that the starting and ending square can be anywhere in the grid.\n\n\n
\n
Constraints:
\n\nm == grid.lengthn == grid[i].length1 <= m, n <= 201 <= m * n <= 20-1 <= grid[i][j] <= 2Compiled with clang 11 using the latest C++ 17 standard.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
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