63. Unique Paths II 类别:动态规划 难度:medium
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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
.思路:
这题的思路与 62 Unique Paths 大致相同。 唯一的不同在于,如果某个方格有障碍,那么记录每个方格路径数的数组 res[] 在该单元内被置为 0 。
方格左上角和右下角只要有一个为障碍,那么结果都是 0.
程序:
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,0)); for(int i = n - 1;i >= 0&&obstacleGrid[m - 1][i] != 1;i--) dp[m - 1][i] = 1; for(int i = m - 1;i >= 0&&obstacleGrid[i][n - 1] != 1;i--) dp[i][n - 1] = 1; for(int i = m - 2;i >= 0;i--) { for(int j = n - 2;j >= 0;j--) { if(obstacleGrid[i][j] == 1) dp[i][j] = 0; else dp[i][j] = dp[i + 1][j] + dp[i][j + 1]; } } return dp[0][0]; }};
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