[leedcode 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.

public class Solution {

    public int uniquePaths(int m, int n) {

        //动态规划思想：构造一个二维数组,flag[i][j]代表到第i行，第j列共有flag[i][j]种走法，因为只能下行和右行，则

        //flag[i][j]=flag[i-1][j]+flag[i][j-1];

        //需要注意的是，在第0行，以及第0列，需要初始化为1；

        int flag[][]=new int[m][n];

        for(int i=0;i<m;i++){

            flag[i][0]=1;

            for(int j=0;j<n;j++){

                if(i==0)flag[0][j]=1;

                else if(i>0&&j>0)flag[i][j]=flag[i-1][j]+flag[i][j-1];

            }

        }

        return flag[m-1][n-1];

    }

}