leetcode 174. 地下城游戏

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题目链接:leetcode

思路：

  • 使用动态规划，knight的生命值最少为1
  • 初始条件，dp[-1][-1] = max(1-dungeon[-1][-1],1);
    dp[i][-1] = max(dp[i+1][-1]-dungeon[i][-1],1)
    dp[-1][j] = max(dp[-1][j+1] -dungeon[-1][j],1)
  • 转移方程，dp[i][j] = max(min(dp[i+1][j],dp[i][j+1])-dungeon[i][j],1)
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class Solution(object):
    def calculateMinimumHP(self, dungeon):
        """
        :type dungeon: List[List[int]]
        :rtype: int
        """
        #dp[i][j] 
        if not dungeon or not dungeon[0]:return 0
        m,n = len(dungeon),len(dungeon[0])
        dp = [[0]*n for _ in range(m)]
        dp[-1][-1] = max(1-dungeon[-1][-1],1)
        for i in range(m-2,-1,-1):
            dp[i][n-1] = max(dp[i+1][n-1]-dungeon[i][n-1],1)
        
        for j in range(n-2,-1,-1):
            dp[m-1][j] = max(dp[m-1][j+1] -dungeon[m-1][j],1)
            
        for i in range(m-2,-1,-1):
            for j in range(n-2,-1,-1):
                dp[i][j] = max(min(dp[i+1][j],dp[i][j+1])-dungeon[i][j],1)
        return dp[0][0]