1293. Shortest Path in a Grid with Obstacles Elimination

Given a m * n grid, where each cell is either 0 (empty) or 1 (obstacle). In one step, you can move up, down, left or right from and to an empty cell.

Return the minimum number of steps to walk from the upper left corner (0, 0) to the lower right corner (m-1, n-1) given that you can eliminate at most k obstacles. If it is not possible to find such walk return -1.

 

Example 1:

Input: 
grid = 
[[0,0,0],
 [1,1,0],
 [0,0,0],
 [0,1,1],
 [0,0,0]], 
k = 1
Output: 6
Explanation: 
The shortest path without eliminating any obstacle is 10. 
The shortest path with one obstacle elimination at position (3,2) is 6. Such path is (0,0) -> (0,1) -> (0,2) -> (1,2) -> (2,2) -> (3,2) -> (4,2).

 

Example 2:

Input: 
grid = 
[[0,1,1],
 [1,1,1],
 [1,0,0]], 
k = 1
Output: -1
Explanation: 
We need to eliminate at least two obstacles to find such a walk.

 

Constraints:

  • grid.length == m
  • grid[0].length == n
  • 1 <= m, n <= 40
  • 1 <= k <= m*n
  • grid[i][j] == 0 or 1
  • grid[0][0] == grid[m-1][n-1] == 0

Rust Solution

struct Solution;

use std::collections::HashSet;
use std::collections::VecDeque;

impl Solution {
    fn shortest_path(grid: Vec<Vec<i32>>, k: i32) -> i32 {
        let n = grid.len();
        let m = grid[0].len();
        let mut queue: VecDeque<(usize, usize, i32, i32)> = VecDeque::new();
        let mut visited: HashSet<(usize, usize, i32)> = HashSet::new();
        queue.push_back((0, 0, k, 0));
        visited.insert((0, 0, k));
        while let Some((i, j, left, step)) = queue.pop_front() {
            if i == n - 1 && j == m - 1 {
                return step;
            }
            let nstep = step + 1;
            for &(di, dj) in &[(-1, 0), (1, 0), (0, -1), (0, 1)] {
                let ni = i as i32 + di;
                let nj = j as i32 + dj;
                if 0 <= ni && ni < n as i32 && 0 <= nj && nj < m as i32 {
                    let ni = ni as usize;
                    let nj = nj as usize;
                    let nleft = left - grid[ni][nj];
                    if nleft >= 0 && visited.insert((ni, nj, nleft)) {
                        queue.push_back((ni, nj, nleft, nstep));
                    }
                }
            }
        }
        -1
    }
}

#[test]
fn test() {
    let grid = vec_vec_i32![[0, 0, 0], [1, 1, 0], [0, 0, 0], [0, 1, 1], [0, 0, 0]];
    let k = 1;
    let res = 6;
    assert_eq!(Solution::shortest_path(grid, k), res);
    let grid = vec_vec_i32![[0, 1, 1], [1, 1, 1], [1, 0, 0]];
    let k = 1;
    let res = -1;
    assert_eq!(Solution::shortest_path(grid, k), res);
}

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