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.

思路：在只允许从左向右，从上到下移动的情况下，从mxn的矩阵（0,0）点，到（m-1，n-1）点，有多少路径。

public class Solution {      public int uniquePaths(int m, int n) {          int[][] array=new int[m][n];          for(int i=0; i<m;i++){              for(int j=0;j<n;j++){                  array[i][j]=1;              }          }          for(int i=1; i<m;i++){              for(int j=1;j<n;j++){                  array[i][j]=array[i-1][j]+array[i][j-1];              }          }          return array[m-1][n-1];      }  }