LeetCode | 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?

//二维动态规划问题，参考http://blog.csdn.net/do_smile/article/details/45191653
public class Solution {
    public int uniquePaths(int m, int n) {
        
        if(m<=1 || n<=1) return 1;
        
        //状态变量，dp[i][j]表示达到点(i,j)的路径数目
        int[][] dp = new int[m+1][n+1];    //下标从0开始，m*n维数组
        for(int i=0; i<=n; i++)
            dp[0][i] = 1;
        for(int i=0; i<=n; i++)    //为多维数组的第0、1行，第0、1列均赋值为1
            dp[1][i] = 1;
        for(int i=0; i<=m; i++)
            dp[i][0] = 1;
        for(int i=0; i<=m; i++)
            dp[i][1] = 1;
        
        //状态转移方程：要达到某个点，只有两种到达方式，从左侧到达或从上侧到达
        //dp[i][j] = dp[i-1][j] + dp[i][j-1] , ( i>=2 && j>=2 )
        for(int i=2; i<=m; i++){
            for(int j=2; j<=n; j++)
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
        }
        
        return dp[m][n];
    }
}