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.
Solution:
Using dynamic programming:class Solution: # @param obstacleGrid, a list of lists of integers # @return an integer def uniquePathsWithObstacles(self, obstacleGrid): uniquePaths = [[]] uniquePaths[0].append(1 if obstacleGrid[0][0] == 0 else 0) for i in range(0,len(obstacleGrid)): uniquePaths.append([]) for j in range(0, len(obstacleGrid[0])): uniquePaths[i].append(0) if obstacleGrid[i][j] == 0: uniquePaths[i][j] += uniquePaths[i-1][j] if i>0 else 0 uniquePaths[i][j] += uniquePaths[i][j-1] if j>0 else 0 return uniquePaths[len(obstacleGrid)-1][len(obstacleGrid[0])-1]
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