# 【leetcode】Dungeon Game

# 地址

https://leetcode.com/problems/dungeon-game/

# 题目

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 | -10 | 1 |

10 | 30 | -5 (P) |

**Note:**

- 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.

# 思路

倒着dp，从终点向起点dp。

dp[i][j]：表示从（i,j)走到终点所需要的最小生命值。

显然：dp[i][j]=max(1, min(dp[i+1][j], dp[i][j+1]) - x[i][j])

# 代码

1 | class Solution { |