Unique Paths II

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.

分析

这题与"Unique Paths"的解法相同，需注意的是若某个位置有障碍则到达该位置的走法为0，状态转移方程变为a[j] = obstacleGrid[j][i] ? 0 : a[j-1] + a[j];

代码

class Solution {public:    int uniquePathsWithObstacles(vector<vector<int> >& obstacleGrid) {        int m = obstacleGrid.size();        int n = obstacleGrid[0].size();        int i,j;        vector<int> a(m);a[0] = obstacleGrid[0][0] ? 0 : 1;        for (i = 1;i < m;i++)        a[i] = obstacleGrid[i][0] ? 0 : a[i-1];        for (i = 1;i < n;i++)        {        a[0] = obstacleGrid[0][i] ? 0 : a[0];        for (j = 1;j < m;j++)        a[j] = obstacleGrid[j][i] ? 0 : a[j-1] + a[j];}return a[m-1];    }};