# Dungeon Game

The demons had captured the princess (P) and imprisoned her in the bottom-right corner of a dungeon. The dungeon consists of M x N rooms laid out in a 2D grid. Our valiant knight (K) was initially positioned in the top-left room and must fight his way through the dungeon to rescue the princess.

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

Some of the rooms are guarded by demons, so the knight loses health (negative integers) upon entering these rooms; other rooms are either empty (0's) or contain magic orbs that increase the knight's health (positive integers).

In order to reach the princess as quickly as possible, the knight decides to move only rightward or downward in each step.

Write a function to determine the knight's minimum initial health so that he is able to rescue the princess.

For example, given the dungeon below, the initial health of the knight must be at least 7 if he follows the optimal path `RIGHT-> RIGHT -> DOWN -> DOWN`.

``-2 (K)-3 3-5-10110 30 -5 (P)``

Notes:

The knight's health has no upper bound. 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.

## 动态规划

### 注意

• 由于最下面一行和最右面一列比较特殊，只有一种逆推方法，所以我们要先单独处理一下。

• 最右下角那个节点没有待逆推的节点，所以我们假设其逆推节点的血量为1。

### 代码

``public class Solution {public int calculateMinimumHP(int[][] dungeon) {if(dungeon == null || dungeon.length == 0) return 1;int m = dungeon.length;int n = dungeon[0].length;int[][] health = new int[m][n];health[m - 1][n - 1] = Math.max(1 - dungeon[m - 1][n - 1], 1);// 逆推最后一列的血量for(int i = m - 2; i >= 0; i--){health[i][n - 1] = Math.max(health[i + 1][n - 1] - dungeon[i][n - 1], 1);}// 逆推最后一行的血量for(int j = n - 2; j >= 0; j--){health[m - 1][j] = Math.max(health[m - 1][j + 1] - dungeon[m - 1][j], 1);}// 对于每个节点，从其下方和右方逆推回来for(int i = m - 2; i >= 0; i--){for(int j = n - 2; j >= 0; j--){int down = Math.max(health[i + 1][j] - dungeon[i][j], 1);int right = Math.max(health[i][j + 1] - dungeon[i][j], 1);health[i][j] = Math.min(down, right);}}return health[0][0];}}``

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