Solution to LeetCode 174 Dungeon Game.
LeetCode 174
Dungeon Game (Hard) [link]
The question asks for the minimum hp at K such that K can reach P. This is equivalent to ask the hp at K such that K has 1 hp at P. The recurrence relation of the minimum hp needed at (i.j).
dp[i][j] = min(dp[i+1][j], dp[i][j+1]) - dungeon[i][j]
Since dp[i][j] can be non-positive, we have to keep it above 1.
dp[i][j] = max(1, min(dp[i+1][j], dp[i][j+1]) - dungeon[i][j])
Base case: dp[m][n - 1] = dp[m - 1][n] = 1
Final answer: dp[0][0]
class Solution(object):
def calculateMinimumHP(self, dungeon):
"""
:type dungeon: List[List[int]]
:rtype: int
"""
m, n = len(dungeon), len(dungeon[0])
BIG = float('inf')
dp = [[BIG] * (n + 1) for _ in range(m + 1)]
dp[m][n - 1] = dp[m - 1][n] = 1
for i in range(m - 1, -1, -1):
for j in range(n - 1, -1, -1):
res = min(dp[i + 1][j], dp[i][j + 1]) - dungeon[i][j]
dp[i][j] = max(res, 1)
return dp[0][0]
