63. Unique Paths II

Problem Link

Description

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You are given an m x n integer array grid. There is a robot initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

An obstacle and space are marked as 1 or 0 respectively in grid. A path that the robot takes cannot include any square that is an obstacle.

Return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The testcases are generated so that the answer will be less than or equal to 2 * 109.

 

Example 1:

Input: obstacleGrid = [[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

Example 2:

Input: obstacleGrid = [[0,1],[0,0]]
Output: 1

 

Constraints:

• m == obstacleGrid.length
• n == obstacleGrid[i].length
• 1 <= m, n <= 100
• obstacleGrid[i][j] is 0 or 1.

Solution

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Python3

class Solution:
    def uniquePathsWithObstacles(self, grid: List[List[int]]) -> int:
        if grid[0][0] == 1 or grid[-1][-1] == 1: return 0
 
        rows, cols = len(grid), len(grid[0])
 
        @cache
        def go(x, y):
            if x == rows - 1 and y == cols - 1: return 1
 
            count = 0
 
            for dx, dy in [(x + 1, y), (x, y + 1)]:
                if dx < rows and dy < cols and grid[dx][dy] != 1:
                    count += go(dx, dy)
 
            return count
        
        return go(0, 0)