# 174. 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 -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.

Credits:
Special thanks to @stellari for adding this problem and creating all test cases.

1 (K) -3 3
0 -2 0
-3 -3 -3 (P)

``````class Solution {
public:
int calculateMinimumHP(vector<vector<int>>& dungeon) {
int m = dungeon.size(), n = dungeon[0].size();
vector<vector<int>> dp(m + 1, vector<int>(n + 1, INT_MAX));
dp[m][n - 1] = 1; dp[m - 1][n] = 1;
for (int i = m - 1; i >= 0; --i) {
for (int j = n - 1; j >= 0; --j) {
dp[i][j] = max(1, min(dp[i + 1][j], dp[i][j + 1]) - dungeon[i][j]);
}
}
return dp[0][0];
}
};
``````

``````class Solution {
public:
int calculateMinimumHP(vector<vector<int>>& dungeon) {
int m = dungeon.size(), n = dungeon[0].size();
vector<int> dp(n + 1, INT_MAX);
dp[n - 1] = 1;
for (int i = m - 1; i >= 0; --i) {
for (int j = n - 1; j >= 0; --j) {
dp[j] = max(1, min(dp[j], dp[j + 1]) - dungeon[i][j]);
}
}
return dp[0];
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/174

Unique Paths

Minimum Path Sum

Cherry Pickup

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

https://leetcode.com/problems/dungeon-game/discuss/52774/C++-DP-solution

https://leetcode.com/problems/dungeon-game/discuss/52843/6-lines-16-ms-C++-O(mn)-Time-O(n)-Space

https://leetcode.com/problems/dungeon-game/discuss/52790/My-AC-Java-Version-Suggestions-are-welcome

LeetCode All in One 题目讲解汇总(持续更新中…)

 微信打赏 Venmo 打赏
（欢迎加入博主的知识星球，博主将及时答疑解惑，并分享刷题经验与总结，试运营期间前五十位可享受半价优惠～）

×

Help us with donation