63. Unique Paths II

Posted 2021-12-22 flyljz

Medium

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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?

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 1:

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
这个题状态于62像是，但是有1的地方是障碍点不能通过
class Solution 
public:
int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) 
int m=obstacleGrid.size();
int n=obstacleGrid[0].size();
vector<vector<int> >dp (m,vector<int>(n));
for(int i=0;i<m;i++)

if(obstacleGrid[i][0]==1)
break;
else
dp[i][0]=1;

for(int j=0;j<n;j++)

if(obstacleGrid[0][j]==1)
break;
else
dp[0][j]=1;

for(int i=1;i<m;i++)
for(int j=1;j<n;j++)

if(obstacleGrid[i][j]==1)
dp[i][j]=0;
else
dp[i][j]=dp[i-1][j]+dp[i][j-1];

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


;
但是这里会报错

Line 27: Char 23: runtime error: signed integer overflow: 1053165744 + 1579748616 cannot be represented in type ‘int‘ (solution.cpp)

int类型精度不够，我们把dp容器的int 换成long就ac了

class Solution
public:
int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid)
int m=obstacleGrid.size();
int n=obstacleGrid[0].size();
vector<vector<long> >dp (m,vector<long>(n));
for(int i=0;i<m;i++)

if(obstacleGrid[i][0]==1)
break;
else
dp[i][0]=1;

for(int j=0;j<n;j++)

if(obstacleGrid[0][j]==1)
break;
else
dp[0][j]=1;

for(int i=1;i<m;i++)
for(int j=1;j<n;j++)

if(obstacleGrid[i][j]==1)
dp[i][j]=0;
else
dp[i][j]=dp[i-1][j]+dp[i][j-1];

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


;