<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:
    int m, n;
    int calculateMinimumHP(vector<vector<int>>& grid) {
        m = grid.size(); n = grid[0].size();
        int left = 1, right = 1000 * (m+n) + 1, ans = right;
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if (isGood(grid, mid)) {
                ans = mid;
                right = mid - 1;
            } else left = mid + 1;
        }
        return ans;
    }
    bool isGood(vector<vector<int>>& grid, int initHealth) {
        vector<vector<int>> dp(m, vector<int>(n, 0));
        dp[0][0] = initHealth + grid[0][0];
        for (int r = 0; r < m; ++r) {
            for (int c = 0; c < n; ++c) {
                if (r > 0 && dp[r-1][c] > 0)
                    dp[r][c] = max(dp[r][c], dp[r-1][c] + grid[r][c]);
                if (c > 0 && dp[r][c-1] > 0)
                    dp[r][c] = max(dp[r][c], dp[r][c-1] + grid[r][c]);
            }
        }
        return dp[m-1][n-1] > 0;
    }
};
14800