<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 {
    vector<array<int,2>> dir = {{0,1}, {1,0}};
    int f (vector<vector<int>> &grid, int row, int col){
        // priority_queue<array<int,3>, vector<array<int,3>>, greater<array<int,3>>> pq;
        priority_queue<array<int,4>> pq;//[currlowesthp][currhp][row][col]
        pq.push({grid[row][col], grid[row][col], row, col});
        int n = grid.size(), m = grid[0].size();
        vector<vector<int>> dist(n, vector<int> (m, -1e9));

        while (!pq.empty()){
            auto temp = pq.top();
            pq.pop();
            int r = temp[2], c = temp[3], maxi = temp[0], currHp = temp[1];
            if (r == n-1 && c == m-1){
                return maxi;
            }
            for (auto d : dir){
                int x = d[0] + r, y = d[1] + c;
                if (x<n && y<m){
                    if (dist[x][y] < grid[x][y] + currHp){
                        dist[x][y] = grid[x][y] + currHp;
                        pq.push({min(maxi, dist[x][y]), dist[x][y], x, y});
                    }
                }
            }
        }
        return -1;
    }
public:
    int calculateMinimumHP(vector<vector<int>>& dungeon) {
        int n = dungeon.size(), m = dungeon[0].size();
        vector<vector<int>> dp(n, vector<int>(m,-1));

        int ans = - 1 * f(dungeon, 0, 0) + 1;
        if (ans<=0) return 1;
        else return ans;
    }
};
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