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:public class Solution {
public int uniquePathsWithObstacles(int[][] obstacleGrid) {
int[][] numberOfPaths = new int[obstacleGrid.length][obstacleGrid[0].length];
numberOfPaths[0][0] = obstacleGrid[0][0]==0 ? 1 : 0;
for (int i=0; i<obstacleGrid.length; i++)
{
for (int j=0; j<obstacleGrid[0].length; j++)
{
if (obstacleGrid[i][j]==0)
{
numberOfPaths[i][j] += i>0 ? numberOfPaths[i-1][j] : 0;
numberOfPaths[i][j] += j>0 ? numberOfPaths[i][j-1] : 0;
}
}
}
return numberOfPaths[obstacleGrid.length-1][obstacleGrid[0].length-1];
}
}
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