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?

題意：走格子，只能向右下方，每次一個格子，問有多少種不同的走法。

思路：利用動態規劃的做法，列出m*n的矩陣，然后每次都加1，具體思路如下圖：

思路圖

具體代碼(java):

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