Create 174_Dungeon_Game.md

Author: koji

174_Dungeon_Game.md

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+## 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.
+
+
+https://leetcode.com/problems/dungeon-game/
+
+
+```python
+def calculateMinimumHP(self, dungeon: List[List[int]]) -> int:
+ 
+ m = len(dungeon)
+ n = len(dungeon[0])
+ 
+ dungeon[-1][-1] = max(1, 1-dungeon[-1][-1])
+ 
+ for c in range(n-2, -1, -1):
+ dungeon[m-1][c] = max(1, dungeon[m-1][c+1] - dungeon[m-1][c])
+ 
+ for r in range(m-2, -1, -1):
+ dungeon[r][n-1] = max(1, dungeon[r+1][n-1] - dungeon[r][n-1])
+ 
+ 
+ for r in range(m-2, -1, -1):
+ for c in range(n-2, -1, -1):
+ dungeon[r][c] = max(1, min(dungeon[r+1][c]-dungeon[r][c], dungeon[r][c+1]-dungeon[r][c]))
+ 
+ return dungeon[0][0]
+```
+
+
+```
+Runtime: 68 ms, faster than 92.22% of Python3 online submissions for Dungeon Game.
+Memory Usage: 15.2 MB, less than 68.46% of Python3 online submissions for Dungeon Game.
+```