【LeetCode】Unique Paths II 解题报告

【题目】

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.

【解析】

题意：数组 A[m][n] ，从 A[0][0] 到 A[m-1][n-1] 有多少条路径，A[m][n] 中可能存在障碍，即A[i][j] = 1 时。

与 【LeetCode】Unique Paths 解题报告不同的是，数组中多了障碍，其实只要把障碍地方的解变为 0 就好。

【动态规划】

public class Solution {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        int rows = obstacleGrid.length;
        if (rows < 1) return 0;
        int cols = obstacleGrid[0].length;
        if (cols < 1) return 0;

        if (obstacleGrid[0][0] == 1 || obstacleGrid[rows - 1][cols - 1] == 1) return 0;

        int[] ans = new int[cols];
        ans[0] = 1;
        for (int j = 1; j < cols; j++) {
            if (obstacleGrid[0][j] == 0) {
                ans[j] = ans[j - 1];
            } else {
                ans[j] = 0;
            }
        }

        for (int i = 1; i < rows; i++) {
            if (obstacleGrid[i][0] == 1) {
                ans[0] = 0;
            }
            for (int j = 1; j < cols; j++) {
                if (obstacleGrid[i][j] == 1) {
                    ans[j] = 0;
                } else {
                    ans[j] += ans[j - 1];
                }
            }
        }

        return ans[cols - 1];
    }
}

题目比较怪异的地方是有一个测试用例为 [[1]] ，即起点和终点重合，而且是障碍。