# Unique Paths II

## Question

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.
Note
m and n will be at most 100.

Example
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.


## 题解

### C++ initialization error

class Solution {
public:
/**
* @param obstacleGrid: A list of lists of integers
* @return: An integer
*/
int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
if(obstacleGrid.empty() || obstacleGrid[0].empty()) {
return 0;
}

const int M = obstacleGrid.size();
const int N = obstacleGrid[0].size();

vector<vector<int> > ret(M, vector<int>(N, 0));

for (int i = 0; i != M; ++i) {
if (0 == obstacleGrid[i][0]) {
ret[i][0] = 1;
}
}
for (int i = 0; i != N; ++i) {
if (0 == obstacleGrid[0][i]) {
ret[0][i] = 1;
}
}

for (int i = 1; i != M; ++i) {
for (int j = 1; j != N; ++j) {
if (obstacleGrid[i][j]) {
ret[i][j] = 0;
} else {
ret[i][j] = ret[i -1][j] + ret[i][j - 1];
}
}
}

return ret[M - 1][N - 1];
}
};


### C++

class Solution {
public:
/**
* @param obstacleGrid: A list of lists of integers
* @return: An integer
*/
int uniquePathsWithObstacles(vector<vector<int> > &obstacleGrid) {
if(obstacleGrid.empty() || obstacleGrid[0].empty()) {
return 0;
}

const int M = obstacleGrid.size();
const int N = obstacleGrid[0].size();

vector<vector<int> > ret(M, vector<int>(N, 0));

for (int i = 0; i != M; ++i) {
if (obstacleGrid[i][0]) {
break;
} else {
ret[i][0] = 1;
}
}
for (int i = 0; i != N; ++i) {
if (obstacleGrid[0][i]) {
break;
} else {
ret[0][i] = 1;
}
}

for (int i = 1; i != M; ++i) {
for (int j = 1; j != N; ++j) {
if (obstacleGrid[i][j]) {
ret[i][j] = 0;
} else {
ret[i][j] = ret[i -1][j] + ret[i][j - 1];
}
}
}

return ret[M - 1][N - 1];
}
};


### 源码分析

1. 异常处理
2. 初始化二维矩阵(全0阵)，尤其注意遇到障碍物时应break跳出当前循环
3. 递推路径数
4. 返回ret[M - 1][N - 1]