Unique Paths

题目描述：

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.

动态规划

public class Solution {
public int uniquePaths(int m, int n) {
int[][] area=new int[m]
;
area[0][0]=1;
for (int i = 1; i < n; i++) {
area[0][i]=1;
}
for (int i = 1; i < m; i++) {
area[i][0]=1;
}
for(int i=1;i<m;i++){
for(int j=1;j<n;j++) {
area[i][j]=area[i-1][j]+area[i][j-1];
}
}
return area[m-1][n-1];
}
}