1102. Path With Maximum Minimum Value

Given a matrix of integers `A` with R rows and C columns, find the maximum score of a path starting at `[0,0]` and ending at `[R-1,C-1]`.

The score of a path is the minimum value in that path.  For example, the value of the path 8 →  4 →  5 →  9 is 4.

A path moves some number of times from one visited cell to any neighbouring unvisited cell in one of the 4 cardinal directions (north, east, west, south).

Example 1:

```Input: [[5,4,5],[1,2,6],[7,4,6]]
Output: 4
Explanation:
The path with the maximum score is highlighted in yellow.
```

Example 2:

```Input: [[2,2,1,2,2,2],[1,2,2,2,1,2]]
Output: 2```

Example 3:

```Input: [[3,4,6,3,4],[0,2,1,1,7],[8,8,3,2,7],[3,2,4,9,8],[4,1,2,0,0],[4,6,5,4,3]]
Output: 3```

Note:

1. `1 <= R, C <= 100`
2. `0 <= A[i][j] <= 10^9`

1102. Path With Maximum Minimum Value
``````struct Solution;
use std::collections::BinaryHeap;

impl Solution {
fn maximum_minimum_path(a: Vec<Vec<i32>>) -> i32 {
let n = a.len();
let m = a[0].len();
let mut visited: Vec<Vec<bool>> = vec![vec![false; m]; n];
let mut queue: BinaryHeap<(i32, usize, usize)> = BinaryHeap::new();
visited[0][0] = true;
queue.push((a[0][0], 0, 0));
let mut res = std::i32::MAX;
while let Some((x, i, j)) = queue.pop() {
res = res.min(x);
if i == n - 1 && j == m - 1 {
break;
}
if i > 0 && !visited[i - 1][j] {
visited[i - 1][j] = true;
queue.push((a[i - 1][j], i - 1, j));
}
if j > 0 && !visited[i][j - 1] {
visited[i][j - 1] = true;
queue.push((a[i][j - 1], i, j - 1));
}
if i + 1 < n && !visited[i + 1][j] {
visited[i + 1][j] = true;
queue.push((a[i + 1][j], i + 1, j));
}
if j + 1 < m && !visited[i][j + 1] {
visited[i][j + 1] = true;
queue.push((a[i][j + 1], i, j + 1));
}
}
res
}
}

#[test]
fn test() {
let a = vec_vec_i32![[5, 4, 5], [1, 2, 6], [7, 4, 6]];
let res = 4;
assert_eq!(Solution::maximum_minimum_path(a), res);
let a = vec_vec_i32![[2, 2, 1, 2, 2, 2], [1, 2, 2, 2, 1, 2]];
let res = 2;
assert_eq!(Solution::maximum_minimum_path(a), res);
let a = vec_vec_i32![
[3, 4, 6, 3, 4],
[0, 2, 1, 1, 7],
[8, 8, 3, 2, 7],
[3, 2, 4, 9, 8],
[4, 1, 2, 0, 0],
[4, 6, 5, 4, 3]
];
let res = 3;
assert_eq!(Solution::maximum_minimum_path(a), res);
}
``````