Minimum Time to Visit a Cell In a Grid
<p>You are given a <code>m x n</code> matrix <code>grid</code> consisting of <b>non-negative</b> integers where <code>grid[row][col]</code> represents the <strong>minimum</strong> time required to be able to visit the cell <code>(row, col)</code>, which means you can visit the cell <code>(row, col)</code> only when the time you visit it is greater than or equal to <code>grid[row][col]</code>.</p>

<p>You are standing in the <strong>top-left</strong> cell of the matrix in the <code>0<sup>th</sup></code> second, and you must move to <strong>any</strong> adjacent cell in the four directions: up, down, left, and right. Each move you make takes 1 second.</p>

<p>Return <em>the <strong>minimum</strong> time required in which you can visit the bottom-right cell of the matrix</em>. If you cannot visit the bottom-right cell, then return <code>-1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2500-2599/2577.Minimum%20Time%20to%20Visit%20a%20Cell%20In%20a%20Grid/images/yetgriddrawio-8.png" /></p>

<pre>
<strong>Input:</strong> grid = [[0,1,3,2],[5,1,2,5],[4,3,8,6]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> One of the paths that we can take is the following:
- at t = 0, we are on the cell (0,0).
- at t = 1, we move to the cell (0,1). It is possible because grid[0][1] &lt;= 1.
- at t = 2, we move to the cell (1,1). It is possible because grid[1][1] &lt;= 2.
- at t = 3, we move to the cell (1,2). It is possible because grid[1][2] &lt;= 3.
- at t = 4, we move to the cell (1,1). It is possible because grid[1][1] &lt;= 4.
- at t = 5, we move to the cell (1,2). It is possible because grid[1][2] &lt;= 5.
- at t = 6, we move to the cell (1,3). It is possible because grid[1][3] &lt;= 6.
- at t = 7, we move to the cell (2,3). It is possible because grid[2][3] &lt;= 7.
The final time is 7. It can be shown that it is the minimum time possible.
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2500-2599/2577.Minimum%20Time%20to%20Visit%20a%20Cell%20In%20a%20Grid/images/yetgriddrawio-9.png" style="width: 151px; height: 151px;" /></p>

<pre>
<strong>Input:</strong> grid = [[0,2,4],[3,2,1],[1,0,4]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There is no path from the top left to the bottom-right cell.
</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>2 &lt;= m, n &lt;= 1000</code></li>
	<li><code>4 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>
	<li><code>grid[0][0] == 0</code></li>
</ul>

<p>&nbsp;</p>
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Breadth-First Search; Graph; Array; Matrix; Shortest Path; Heap (Priority Queue)
class Solution {
    public int minimumTime(int[][] grid) {
        if (grid[0][1] > 1 && grid[1][0] > 1) {
            return -1;
        }
        int m = grid.length, n = grid[0].length;
        int[][] dist = new int[m][n];
        for (var e : dist) {
            Arrays.fill(e, 1 << 30);
        }
        dist[0][0] = 0;
        PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[0] - b[0]);
        pq.offer(new int[] {0, 0, 0});
        int[] dirs = {-1, 0, 1, 0, -1};
        while (true) {
            var p = pq.poll();
            int i = p[1], j = p[2];
            if (i == m - 1 && j == n - 1) {
                return p[0];
            }
            for (int k = 0; k < 4; ++k) {
                int x = i + dirs[k], y = j + dirs[k + 1];
                if (x >= 0 && x < m && y >= 0 && y < n) {
                    int nt = p[0] + 1;
                    if (nt < grid[x][y]) {
                        nt = grid[x][y] + (grid[x][y] - nt) % 2;
                    }
                    if (nt < dist[x][y]) {
                        dist[x][y] = nt;
                        pq.offer(new int[] {nt, x, y});
                    }
                }
            }
        }
    }
}