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?

使用动态规划的求解方式。

1. 对于第一行，路径只为1；
2. 对于第一列，路径只为1；
3. 对于i行j列，有两种达到方式：
   1. 从上方达到；
   2. 从下方达到。

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

~Thanks~
By 海天游草~~~2017.4.26