62. 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?
Above is a 3 x 7 grid. How many possible unique paths are there?

这是一道简单的动态规划题目：
定义一个二维数组sol[m][n]，最后数值为 sol[m-1][n-1],然后初始化数组，sol[0][i]=1,sol[i][0]=1，递推关系为sol[i][j]=sol[i-1][j]+sol[i][j-1]。
代码见下：

private static int uniquePaths(int m, int n) {        if(m<0||n<0) return -1;        if(m==0||n==0) return 1;        int[][] sol=new int[m][n];        for (int i = 0; i < m; i++) {            sol[i][0]=1;        }        for (int i = 0; i<n; i++) {            sol[0][i]=1;        }        for (int i = 1; i < m; i++) {            for (int j = 1; j < n; j++) {                sol[i][j]=sol[i-1][j]+sol[i][j-1];            }        }               return sol[m-1][n-1];    }