Shortest Path in a Grid with Obstacles Elimination
<p>You are given an <code>m x n</code> integer matrix <code>grid</code> where each cell is either <code>0</code> (empty) or <code>1</code> (obstacle). You can move up, down, left, or right from and to an empty cell in <strong>one step</strong>.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1200-1299/1293.Shortest%20Path%20in%20a%20Grid%20with%20Obstacles%20Elimination/images/short1-grid.jpg" style="width: 244px; height: 405px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,0],[1,1,0],[0,0,0],[0,1,1],[0,0,0]], k = 1
<strong>Output:</strong> 6
<strong>Explanation:</strong> 
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) -&gt; (0,1) -&gt; (0,2) -&gt; (1,2) -&gt; (2,2) -&gt; <strong>(3,2)</strong> -&gt; (4,2).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1200-1299/1293.Shortest%20Path%20in%20a%20Grid%20with%20Obstacles%20Elimination/images/short2-grid.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1],[1,1,1],[1,0,0]], k = 1
<strong>Output:</strong> -1
<strong>Explanation:</strong> We need to eliminate at least two obstacles to find such a walk.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 40</code></li>
	<li><code>1 &lt;= k &lt;= m * n</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> <strong>or</strong> <code>1</code>.</li>
	<li><code>grid[0][0] == grid[m - 1][n - 1] == 0</code></li>
</ul>
Breadth-First Search; Array; Matrix
class Solution {
    public int shortestPath(int[][] grid, int k) {
        int m = grid.length;
        int n = grid[0].length;
        if (k >= m + n - 3) {
            return m + n - 2;
        }
        Deque<int[]> q = new ArrayDeque<>();
        q.offer(new int[] {0, 0, k});
        boolean[][][] vis = new boolean[m][n][k + 1];
        vis[0][0][k] = true;
        int ans = 0;
        int[] dirs = {-1, 0, 1, 0, -1};
        while (!q.isEmpty()) {
            ++ans;
            for (int i = q.size(); i > 0; --i) {
                int[] p = q.poll();
                k = p[2];
                for (int j = 0; j < 4; ++j) {
                    int x = p[0] + dirs[j];
                    int y = p[1] + dirs[j + 1];
                    if (x >= 0 && x < m && y >= 0 && y < n) {
                        if (x == m - 1 && y == n - 1) {
                            return ans;
                        }
                        if (grid[x][y] == 0 && !vis[x][y][k]) {
                            q.offer(new int[] {x, y, k});
                            vis[x][y][k] = true;
                        } else if (grid[x][y] == 1 && k > 0 && !vis[x][y][k - 1]) {
                            q.offer(new int[] {x, y, k - 1});
                            vis[x][y][k - 1] = true;
                        }
                    }
                }
            }
        }
        return -1;
    }
}