Unique-paths

题目描述

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.

import java.util.*;
public class Solution {
    public int uniquePaths(int m, int n) {
        int dp[][] = new int[m][n];
        for(int i = 0 ; i<m ; i++)
        {
            dp[i][0] = 1;
        }
        for(int j = 0; j<n ;j++)
        {
            dp[0][j] = 1;
        }
        for(int i = 1; i<m ; i++)
        {
            for(int j = 1; j<n; j++)
            {
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }
        return dp[m-1][n-1];
    }
}