LeetCode 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?
Note: m and n will be at most 100.

题意：走格子，只能向右下方，每次一个格子，问有多少种不同的走法。

思路：利用动态规划的做法，列出m*n的矩阵，然后每次都加1，具体思路如下图：

思路图

具体代码(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];  
    }