【leetcode】Unique Paths I & II
2015-04-20 17:29
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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).
How many possible unique paths are there?
Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
解题:从左上角走到右下角,每次只能向下或者向右走一步,不管怎么走都需要m+n-2步才能走到,而这其中有m-1步是向下走,有n-1是向右走,只用从这m+n-2个位置中选择m-1个位置,则剩余的位置表示向右走。容易求得值是Cm-1m+n-2,利用杨辉三角即可。
II:
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.
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).
How many possible unique paths are there?
Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
解题:从左上角走到右下角,每次只能向下或者向右走一步,不管怎么走都需要m+n-2步才能走到,而这其中有m-1步是向下走,有n-1是向右走,只用从这m+n-2个位置中选择m-1个位置,则剩余的位置表示向右走。容易求得值是Cm-1m+n-2,利用杨辉三角即可。
class Solution { public: int uniquePaths(int m, int n) { vector<vector<int>>f(m,vector<int>(n)); for(int i=0;i<n;i++) f[0][i]=1; for(int i=0;i<m;i++) f[i][0]=1; for(int i=1;i<m;i++) for(int j=1;j<n;j++) f[i][j]=f[i-1][j]+f[i][j-1]; return f[m-1][n-1]; } };
II:
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.
class Solution { public: int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) { int row=obstacleGrid.size(); int col=obstacleGrid[0].size(); int *dp=new int[col]; if(obstacleGrid[0][0]!=0) dp[0]=0; else dp[0]=1; for(int i=1;i<col;i++) if(obstacleGrid[0][i]!=0) dp[i]=0; else dp[i]=dp[i-1]; for(int i=1;i<row;i++) for(int j=0;j<col;j++) if(obstacleGrid[i][j]!=0) dp[j]=0; else if(j>0) dp[j]=dp[j]+dp[j-1]; return dp[col-1]; } };
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