Find Minimum Time to Reach Last Room II
<p>There is a dungeon with <code>n x m</code> rooms arranged as a grid.</p>

<p>You are given a 2D array <code>moveTime</code> of size <code>n x m</code>, where <code>moveTime[i][j]</code> represents the <strong>minimum</strong> time in seconds when you can <strong>start moving</strong> to that room. You start from the room <code>(0, 0)</code> at time <code>t = 0</code> and can move to an <strong>adjacent</strong> room. Moving between <strong>adjacent</strong> rooms takes one second for one move and two seconds for the next, <strong>alternating</strong> between the two.</p>

<p>Return the <strong>minimum</strong> time to reach the room <code>(n - 1, m - 1)</code>.</p>

<p>Two rooms are <strong>adjacent</strong> if they share a common wall, either <em>horizontally</em> or <em>vertically</em>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">moveTime = [[0,4],[4,4]]</span></p>

<p><strong>Output:</strong> 7</p>

<p><strong>Explanation:</strong></p>

<p>The minimum time required is 7 seconds.</p>

<ul>
	<li>At time <code>t == 4</code>, move from room <code>(0, 0)</code> to room <code>(1, 0)</code> in one second.</li>
	<li>At time <code>t == 5</code>, move from room <code>(1, 0)</code> to room <code>(1, 1)</code> in two seconds.</li>
</ul>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">moveTime = [[0,0,0,0],[0,0,0,0]]</span></p>

<p><strong>Output:</strong> 6</p>

<p><strong>Explanation:</strong></p>

<p>The minimum time required is 6 seconds.</p>

<ul>
	<li>At time <code>t == 0</code>, move from room <code>(0, 0)</code> to room <code>(1, 0)</code> in one second.</li>
	<li>At time <code>t == 1</code>, move from room <code>(1, 0)</code> to room <code>(1, 1)</code> in two seconds.</li>
	<li>At time <code>t == 3</code>, move from room <code>(1, 1)</code> to room <code>(1, 2)</code> in one second.</li>
	<li>At time <code>t == 4</code>, move from room <code>(1, 2)</code> to room <code>(1, 3)</code> in two seconds.</li>
</ul>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">moveTime = [[0,1],[1,2]]</span></p>

<p><strong>Output:</strong> 4</p>
</div>

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

<ul>
	<li><code>2 &lt;= n == moveTime.length &lt;= 750</code></li>
	<li><code>2 &lt;= m == moveTime[i].length &lt;= 750</code></li>
	<li><code>0 &lt;= moveTime[i][j] &lt;= 10<sup>9</sup></code></li>
</ul>
Graph; Array; Matrix; Shortest Path; Heap (Priority Queue)
class Solution {
    public int minTimeToReach(int[][] moveTime) {
        int n = moveTime.length;
        int m = moveTime[0].length;
        int[][] dist = new int[n][m];
        for (var row : dist) {
            Arrays.fill(row, Integer.MAX_VALUE);
        }
        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) {
            int[] p = pq.poll();
            int d = p[0], i = p[1], j = p[2];

            if (i == n - 1 && j == m - 1) {
                return d;
            }
            if (d > dist[i][j]) {
                continue;
            }

            for (int k = 0; k < 4; k++) {
                int x = i + dirs[k];
                int y = j + dirs[k + 1];
                if (x >= 0 && x < n && y >= 0 && y < m) {
                    int t = Math.max(moveTime[x][y], dist[i][j]) + (i + j) % 2 + 1;
                    if (dist[x][y] > t) {
                        dist[x][y] = t;
                        pq.offer(new int[] {t, x, y});
                    }
                }
            }
        }
    }
}
