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.

解题思路：刚开始受思维影响，以为这题是求“Start" 到 "Finish" 走的步子数量，后来才发现是路径的多少，这就简单多了，如果只有一行或者一列，那就只有一条路径到达，也就是说，在第一行和第一列上的路径都是1，而其他的地方路径数量等于正上方格子的路径数量加上正左方的格子的路径数量。

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