package UniquePaths;

/**

* User: Danyang

* Date: 1/19/2015

* Time: 20:29

* 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?

*/

public class Solution {

/**

* DP

* f[i][j] = f[i-1][j] + f[i][j-1]

* @param m

* @param n

* @return

*/

public int uniquePaths(int m, int n) {

int [][] f = new int[m+1][n+1];

f[0][1] = 1;

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

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

f[i][j] = f[i-1][j]+f[i][j-1];

return f[m][n];

}

}