Unique Paths II

Question

https://leetcode.com/problems/unique-paths-ii/?tab=Description

Follow up for "Unique Paths":

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

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

For example, There is one obstacle in the middle of a 3x3 grid as illustrated below.

[
  [0,0,0],
  [0,1,0],
  [0,0,0]
]

The total number of unique paths is 2.

Note: m and n will be at most 100.

Tags

• array
• dynamic programming

Analysis

This problem is very similar to the previous one (Unique Paths I). Thus, we will follow almost the same algorithms: start from the right-bottom position and use the same recursive equation.

The only difference is that we need to set the value to 0 directly if the corresponding position has obstacle according to the obstacleGrid table.

Code:

class Solution(object):
    def uniquePathsWithObstacles(self, obstacleGrid):
        """
        :type obstacleGrid: List[List[int]]
        :rtype: int
        """
        if obstacleGrid == []:
            return 0
        height = len(obstacleGrid)
        width = len(obstacleGrid[0])
        dp = [[0] * (width + 1) for _ in range(height + 1)]
        for i in range(height - 1, -1, -1):
            for j in range(width - 1, -1, -1):
                if i == height - 1 and j == width - 1:
                    dp[i][j] = 1 - obstacleGrid[i][j]
                    continue
                if obstacleGrid[i][j] == 1:
                    dp[i][j] = 0
                else:
                    dp[i][j] = dp[i][j + 1] + dp[i + 1][j]
        return dp[0][0]