LintCode (114) Unique paths

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?

Have you met this question in a real interview? 

Yes

Example

1,1	1,2	1,3	1,4	1,5	1,6	1,7
2,1
3,1						3,7

Above is a 3 x 7 grid. How many possible unique paths are there?

Note

m and n will be at most 100.

Dp:

求解得数目，走table, matrix dp

f[i][j] 为 从0,0走到i,j的路径数

转化方程 f[i][j]= f[i-1][j]+f[i][j-1]

解： f[m-1][n-1]

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class Solution { public: /** * @param n, m: positive integer (1 <= n ,m <= 100) * @return an integer */ int uniquePaths(int m, int n) { // wirte your code here vector<vector<int>> tbl(m, vector<int>(n,1)); for(int i=1; i<m; i++){ for (int j=1; j<n; j++){ tbl[i][j]=tbl[i-1][j]+tbl[i][j-1]; } } return tbl[m-1][n-1]; } };