<p>The demons had captured the princess and imprisoned her in <strong>the bottom-right corner</strong> of a <code>dungeon</code>. The <code>dungeon</code> consists of <code>m x n</code> rooms laid out in a 2D grid. Our valiant knight was initially positioned in <strong>the top-left room</strong> and must fight his way through <code>dungeon</code> to rescue the princess.</p>

<p>The knight has an initial health point represented by a positive integer. If at any point his health point drops to <code>0</code> or below, he dies immediately.</p>

<p>Some of the rooms are guarded by demons (represented by negative integers), so the knight loses health upon entering these rooms; other rooms are either empty (represented as 0) or contain magic orbs that increase the knight&#39;s health (represented by positive integers).</p>

<p>To reach the princess as quickly as possible, the knight decides to move only <strong>rightward</strong> or <strong>downward</strong> in each step.</p>

<p>Return <em>the knight&#39;s minimum initial health so that he can rescue the princess</em>.</p>

<p><strong>Note</strong> that any room can contain threats or power-ups, even the first room the knight enters and the bottom-right room where the princess is imprisoned.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/13/dungeon-grid-1.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> dungeon = [[-2,-3,3],[-5,-10,1],[10,30,-5]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> The initial health of the knight must be at least 7 if he follows the optimal path: RIGHT-&gt; RIGHT -&gt; DOWN -&gt; DOWN.
</pre>

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

<pre>
<strong>Input:</strong> dungeon = [[0]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>m == dungeon.length</code></li>
	<li><code>n == dungeon[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>-1000 &lt;= dungeon[i][j] &lt;= 1000</code></li>
</ul>

class Solution {
public:
    typedef tuple<int, int, int> tp;
    int calculateMinimumHP(vector<vector<int>>& dun) {
        int m = dun.size(), n = dun[0].size();
        priority_queue<tp> pq;
        pq.push({dun[0][0], 0, 0});
        vector<vector<int>> dist(m, vector<int>(n, INT_MIN));
        dist[0][0] = dun[0][0];
        int w, i, j;
        int dir[2][2] = {{0, 1}, {1, 0}};
        while (!pq.empty()) {
            tie(w, i, j) = pq.top(); pq.pop();
            if (i == m - 1 && j == n - 1) 
                return max(1, -w + 1);
            for (auto& d : dir) {
                int x = i + d[0], y = j + d[1];
                if (x < m && y < n && dist[x][y] < dist[i][j] + dun[x][y]) {
                    dist[x][y] = dist[i][j] + dun[x][y];
                    pq.push({min(w, dist[i][j] + dun[x][y]), x, y});
                }
            }
        }
        return -1;
    }
};
13000