[LeetCode] Problem 63 - Unique Paths II

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A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).

Now consider if some obstacles are added to the grids. How many unique paths would there be?

k5Fgjx.png

An obstacle and empty space is marked as 1 and 0 respectively in the grid.

Note

m and n will be at most 100.

Example

Input:
[
[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

Code

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// O(mn) runtime, O(mn) space – Dynamic programming
public int uniquePathsWithObstacles(int[][] obstacleGrid) {
    int m = obstacleGrid.length;
    int n = obstacleGrid[0].length;
    int[][] dp = new int[m][n];

    dp[0][0] = obstacleGrid[0][0] ^ 1;

    for (int i = 1; i < n; i++)
        dp[0][i] = obstacleGrid[0][i] == 1 ? 0 : dp[0][i-1];

    for (int i = 1; i < m; i++)
        dp[i][0] = obstacleGrid[i][0] == 1 ? 0 : dp[i-1][0];

    for (int i = 1; i < m; i++) {
        for (int j = 1; j < n; j++)
            dp[i][j] = obstacleGrid[i][j] == 1 ? 0 : dp[i-1][j] + dp[i][j-1];
    }

    return dp[m-1][n-1];
}