1368. Minimum Cost to Make at Least One Valid Path in a Grid

Given a m x n grid. Each cell of the grid has a sign pointing to the next cell you should visit if you are currently in this cell. The sign of grid[i][j] can be:
  • 1 which means go to the cell to the right. (i.e go from grid[i][j] to grid[i][j + 1])
  • 2 which means go to the cell to the left. (i.e go from grid[i][j] to grid[i][j - 1])
  • 3 which means go to the lower cell. (i.e go from grid[i][j] to grid[i + 1][j])
  • 4 which means go to the upper cell. (i.e go from grid[i][j] to grid[i - 1][j])

Notice that there could be some invalid signs on the cells of the grid which points outside the grid.

You will initially start at the upper left cell (0,0). A valid path in the grid is a path which starts from the upper left cell (0,0) and ends at the bottom-right cell (m - 1, n - 1) following the signs on the grid. The valid path doesn't have to be the shortest.

You can modify the sign on a cell with cost = 1. You can modify the sign on a cell one time only.

Return the minimum cost to make the grid have at least one valid path.

 

Example 1:

Input: grid = [[1,1,1,1],[2,2,2,2],[1,1,1,1],[2,2,2,2]]
Output: 3
Explanation: You will start at point (0, 0).
The path to (3, 3) is as follows. (0, 0) --> (0, 1) --> (0, 2) --> (0, 3) change the arrow to down with cost = 1 --> (1, 3) --> (1, 2) --> (1, 1) --> (1, 0) change the arrow to down with cost = 1 --> (2, 0) --> (2, 1) --> (2, 2) --> (2, 3) change the arrow to down with cost = 1 --> (3, 3)
The total cost = 3.

Example 2:

Input: grid = [[1,1,3],[3,2,2],[1,1,4]]
Output: 0
Explanation: You can follow the path from (0, 0) to (2, 2).

Example 3:

Input: grid = [[1,2],[4,3]]
Output: 1

Example 4:

Input: grid = [[2,2,2],[2,2,2]]
Output: 3

Example 5:

Input: grid = [[4]]
Output: 0

 

Constraints:

  • m == grid.length
  • n == grid[i].length
  • 1 <= m, n <= 100

Rust Solution

struct Solution;

use std::collections::VecDeque;

impl Solution {
    fn min_cost(grid: Vec<Vec<i32>>) -> i32 {
        let n = grid.len();
        let m = grid[0].len();
        let mut dist = vec![vec![std::i32::MAX; m]; n];
        let mut queue: VecDeque<(usize, usize, i32)> = VecDeque::new();
        dist[0][0] = 0;
        queue.push_back((0, 0, 0));
        while let Some((i, j, d)) = queue.pop_front() {
            let right = Self::cost(i, j, d, 1, &grid);
            let left = Self::cost(i, j, d, 2, &grid);
            let down = Self::cost(i, j, d, 3, &grid);
            let up = Self::cost(i, j, d, 4, &grid);
            if i > 0 && up < dist[i - 1][j] {
                dist[i - 1][j] = up;
                queue.push_back((i - 1, j, up));
            }
            if j > 0 && left < dist[i][j - 1] {
                dist[i][j - 1] = left;
                queue.push_back((i, j - 1, left));
            }
            if i + 1 < n && down < dist[i + 1][j] {
                dist[i + 1][j] = down;
                queue.push_back((i + 1, j, down));
            }
            if j + 1 < m && right < dist[i][j + 1] {
                dist[i][j + 1] = right;
                queue.push_back((i, j + 1, right));
            }
        }
        dist[n - 1][m - 1]
    }

    fn cost(i: usize, j: usize, cost: i32, dir: i32, grid: &[Vec<i32>]) -> i32 {
        if dir == grid[i][j] {
            cost
        } else {
            cost + 1
        }
    }
}

#[test]
fn test() {
    let grid = vec_vec_i32![[1, 1, 1, 1], [2, 2, 2, 2], [1, 1, 1, 1], [2, 2, 2, 2]];
    let res = 3;
    assert_eq!(Solution::min_cost(grid), res);
    let grid = vec_vec_i32![[1, 1, 3], [3, 2, 2], [1, 1, 4]];
    let res = 0;
    assert_eq!(Solution::min_cost(grid), res);
    let grid = vec_vec_i32![[2, 2, 2], [2, 2, 2]];
    let res = 3;
    assert_eq!(Solution::min_cost(grid), res);
    let grid = vec_vec_i32![[4]];
    let res = 0;
    assert_eq!(Solution::min_cost(grid), res);
}

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