<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:
    vector<pair<int,int>> dir={{1,0},{0,1}};
    int calculateMinimumHP(vector<vector<int>>& dungeon) {
        int n=dungeon.size();
        int m=dungeon[0].size();

        priority_queue<pair<int,pair<int,int>>> pq;
        vector<vector<int>> dist(n,vector<int>(m,INT_MIN));
        pq.push({dungeon[0][0],{0,0}});
        dist[0][0]=dungeon[0][0];

        while(!pq.empty()){
            int minDis=pq.top().first;
            int x=pq.top().second.first;
            int y=pq.top().second.second;
            pq.pop();
            // cout<<minDis<<endl;

            if(x==n-1 && y==m-1){
                // for(int i=0;i<n;i++){
                //     for(int j=0;j<m;j++) cout<<dist[i][j];
                //     cout<<endl;
                // }
                if(minDis>=0) return 1;
                return abs(minDis)+1;   
            }

            for(auto it : dir){
                int nx=x+it.first;
                int ny=y+it.second;

                if(nx>=0 && nx<n && ny>=0 && ny<m && dist[nx][ny]<dist[x][y]+dungeon[nx][ny]){
                    dist[nx][ny]=dist[x][y]+dungeon[nx][ny];
                    pq.push({min(minDis,dist[nx][ny]),{nx,ny}});
                }
            }   
        }

        return -1;
    }
};
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