Dungeon Game — LeetCode 174 Python Solution

The problem

The demons had captured the princess 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.

Example

Input

dungeon = [[-2,-3,3],[-5,-10,1],[10,30,-5]]

Output

7

Explanation

The initial health of the knight must be at least 7 if he follows the optimal path: RIGHT-> RIGHT -> DOWN -> DOWN.

Python solution

class Solution:
    def calculateMinimumHP(self, dungeon: List[List[int]]) -> int:
        m, n = len(dungeon), len(dungeon[0])
        dp = [[inf] * (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):
                dp[i][j] = max(1, min(dp[i + 1][j], dp[i][j + 1]) - dungeon[i][j])
        return dp[0][0]

Complexity

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 174. Dungeon Game is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.

The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.

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