leetcode题解63：不同路径 II

描述

该题来自于力扣第63题

分析

与力扣第62题唯一不同的地方，在于有障碍物，不难发现，到达i,j网格的步数，依然是相邻左方与上方的步数之和，不过如果有一个相邻的区域是障碍物，那么该方向就失效，那么设置达到障碍物的步数为0就可以。所以转移方程为
\[ dp[i][j] = \left\{ \begin{aligned} & 0 & i,j\text{是障碍物}\\ & dp[i][j-1] & i,j\text{不是障碍物且 } i == 0 \text{ and } j > 0 \\ & dp[i-1][j] & i,j\text{不是障碍物且 } j == 0 \text{ and } i > 0 \\ & dp[i-1][j] + dp[i][j-1] & others \end{aligned} \right. \]
注意初始化dp[0][0]=1

代码

python

class Solution:
    def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int:
        m = len(obstacleGrid)
        n = len(obstacleGrid[0])
        dp = [[0 for _ in range(n)] for _ in range(m)]
        for i in range(m):
            for j in range(n):
                if obstacleGrid[i][j] == 0:
                    if i == 0 and j == 0:
                        dp[i][j] = 1
                        continue
                    if i > 0:
                        dp[i][j] += dp[i-1][j]
                    if j > 0:
                        dp[i][j] += dp[i][j-1]
        return dp[m-1][n-1]