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.

題意：從start位置開始，只能向下或者向右，有多少條路徑可以達到Finish。

思路：用動態規劃的思路，例如最後要達到Finish的位置，有兩個位置可以達到，那把這兩個位置的數目加起來就是總的條數。這樣往上推倒即可。

public int uniquePaths(int m, int n) {
        int[][] a = new int[m][n];  
        for (int i = 0; i < m; i++) {  
            a[i][0] = 1;  
        }  
        for (int i = 0; i < n; i++) {  
            a[0][i] = 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];
    }
 

種一棵樹最好的時間是十年前，其次是現在！