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Unique Paths II LC #63 Medium 2D DP · Obstacles
Problem

Same as Unique Paths, but the grid has obstacles. obstacleGrid[r][c]=1 means blocked. Return the number of unique paths avoiding obstacles. Robot moves only right or down.

Example 1
Input: [[0,0,0],[0,1,0],[0,0,0]]
Output: 2
Example 2
Input: [[0,1],[0,0]]
Output: 1
Constraints: dp[r][c]=0 if blocked else top+left
Try Examples
Custom:
Approach
2D DP with Obstacles — dp[r][c]=0 if blocked else top+left
Same as Unique Paths but obstacle cells force dp=0. Paths cannot pass through blocked cells.
Grid with Obstacles
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Variables
cell (r,c)
—
top
—
left
—
paths
—
Step Logic
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Algorithm
1
Obstacle cell: dp[c]=0 (no path through it)
2
Open cell: dp[r][c] = top + left (same as Unique Paths)
3
First row/col: propagate 0 after any obstacle
4
Answer = dp[m-1][n-1]
Time
O(m×n)
Space
O(n)
Why This Works

Obstacle cells cannot be reached, so dp=0. Open cells inherit top+left. A 0 propagates through adjacent cells that depend on it, correctly blocking all paths through the obstacle.