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
function shortestPath(grid: number[][], k: number): number {
    const m = grid.length;
    const n = grid[0].length;
    if (k >= m + n - 3) {
        return m + n - 2;
    }

    let q: Point[] = [[0, 0, k]];
    const vis = Array.from({ length: m }, () =>
        Array.from({ length: n }, () => Array.from({ length: k + 1 }, () => false)),
    );
    vis[0][0][k] = true;
    const dirs = [0, 1, 0, -1, 0];
    let ans = 0;

    while (q.length) {
        const nextQ: Point[] = [];
        ++ans;

        for (const [i, j, k] of q) {
            for (let d = 0; d < 4; ++d) {
                const [x, y] = [i + dirs[d], j + dirs[d + 1]];
                if (x === m - 1 && y === n - 1) {
                    return ans;
                }
                const v = grid[x]?.[y];
                if (v === 0 && !vis[x][y][k]) {
                    nextQ.push([x, y, k]);
                    vis[x][y][k] = true;
                } else if (v === 1 && k > 0 && !vis[x][y][k - 1]) {
                    nextQ.push([x, y, k - 1]);
                    vis[x][y][k - 1] = true;
                }
            }
        }
        q = nextQ;
    }
    return -1;
}

type Point = [number, number, number];
