63. Unique Paths II

描述

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

Now consider if some obstacles are added to the grids. How many unique paths would there be?

例图

Example:

Input:
[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]
Output: 2
Explanation:
There is one obstacle in the middle of the 3x3 grid above.
There are two ways to reach the bottom-right corner:
1. Right -> Right -> Down -> Down
2. Down -> Down -> Right -> Right

解法

动态规划

class Solution:
    def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int:
        if not obstacleGrid or obstacleGrid[0][0]:
            return 0

        m = len(obstacleGrid)  # rows
        n = len(obstacleGrid[0])  # cols
        dp = [[0 for _ in range(n)] for _ in range(m)]

        for i in range(m):
            if obstacleGrid[i][0]:
                break
            dp[i][0] = 1

        for j in range(n):
            if obstacleGrid[0][j]:
                break
            dp[0][j] = 1

        for i in range(1, m):
            for j in range(1, n):
                if obstacleGrid[i][j]:
                    dp[i][j] = 0
                else:
                    dp[i][j] = dp[i-1][j] + dp[i][j-1]

        return dp[-1][-1]

引用