174. 地下城游戏 -- 动规

174. 地下城游戏

class CalculateMinimumHP:
    """
    174. 地下城游戏
    https://leetcode.cn/problems/dungeon-game/
    """
    def solution(self, dungeon: List[List[int]]) -> int:
        # 我们想计算左上⻆到右下⻆所需的最⼩⽣命值
        m, n = len(dungeon), len(dungeon[0])
        self.memo = [[-1 for _ in range(n)] for _ in range(m)]
        return self.dp(dungeon, 0, 0)

    def dp(self, grid, i, j):
        """
        从 grid[i][j] 到达终点（右下⻆）所需的最少⽣命值
        :param grid:
        :param i:
        :param j:
        :return:
        """
        m, n = len(grid), len(grid[0])
        # base case
        if i == m - 1 and j == n - 1:
            return 1 if grid[i][j] >= 0 else -grid[i][j] + 1

        if i == m or j == n:
            return float('inf')

        if self.memo[i][j] != -1:
            return self.memo[i][j]

        res = min(self.dp(grid, i, j+1),
                  self.dp(grid, i+1, j)) - grid[i][j]

        self.memo[i][j] = 1 if res <= 0 else res
        return self.memo[i][j]