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.

题目：机器人从左上角到右下角，每次只能往右或者下走一格，问有多少种走法？

思路：DP问题，构造一个m*n矩阵，用step[row][col]代表走到（i，j）节点的多种线路数，因为只能往右或者下移动，所以矩阵的第一行（只能往右移动）和第一列（只能往下移动）为1.其它节点的线路数为

 steps[i][j] = steps[i - 1][j] + steps[i][j - 1];

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