980. Unique Paths III

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. `1 <= grid.length * grid[0].length <= 20`

980. Unique Paths III
``````struct Solution;

impl Solution {
fn unique_paths_iii(mut grid: Vec<Vec<i32>>) -> i32 {
let mut res = 0;
let n = grid.len();
let m = grid[0].len();
let mut count = 0;
for i in 0..n {
for j in 0..m {
if grid[i][j] == 0 {
count += 1;
}
}
}
for i in 0..n {
for j in 0..m {
if grid[i][j] == 1 {
Self::dfs(i, j, count, &mut res, &mut grid, n, m);
}
}
}
res as i32
}

fn dfs(
i: usize,
j: usize,
left: usize,
all: &mut usize,
grid: &mut Vec<Vec<i32>>,
n: usize,
m: usize,
) {
match grid[i][j] {
2 => {
if left == 0 {
*all += 1;
}
}
1 => {
grid[i][j] = -1;
for (r, c) in Self::adj(i, j, n, m) {
Self::dfs(r, c, left, all, grid, n, m);
}
grid[i][j] = 1;
}

0 => {
grid[i][j] = -1;
for (r, c) in Self::adj(i, j, n, m) {
Self::dfs(r, c, left - 1, all, grid, n, m);
}
grid[i][j] = 0;
}

_ => {}
}
}

fn adj(i: usize, j: usize, n: usize, m: usize) -> Vec<(usize, usize)> {
let mut res = vec![];
if i > 0 {
res.push((i - 1, j));
}
if j > 0 {
res.push((i, j - 1));
}
if i + 1 < n {
res.push((i + 1, j));
}
if j + 1 < m {
res.push((i, j + 1));
}
res
}
}

#[test]
fn test() {
let grid = vec_vec_i32![[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, -1]];
let res = 2;
assert_eq!(Solution::unique_paths_iii(grid), res);
let grid = vec_vec_i32![[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2]];
let res = 4;
assert_eq!(Solution::unique_paths_iii(grid), res);
let grid = vec_vec_i32![[0, 1], [2, 0]];
let res = 0;
assert_eq!(Solution::unique_paths_iii(grid), res);
}
``````