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Distinct Paths II

Medium Acceptance 50.00% Points 30.00

You are given an n x n integer array grid. There is a scholar initially located at the top-left corner (i.e., grid[0][0]). The scholar tries to move to the bottom-right corner (i.e., grid[n - 1][n - 1]). The scholar 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 scholar takes cannot include any square that is an obstacle.

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

Examples
Example 1

Example 1

Input: Grid = [[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

Hints
Hint 1
Expected Time Complexity: O(n^2)
Hint 2
Expected Auxiliary Space: O(n^2)
Constraints
  • 1 <= n <= 100
  • grid[i][j] is 0 or 1
Companies
Amazon Microsoft Google
Topics
Array Recursion Dynamic Programming + 1 more
Solution.cs C#JavaPythonC++Javascript

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