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：本题是一个dp题，因为机器人只能从上或者右到达当前位置，根据此规律，可以得出递推式

dp[i][j]=dp[i-1][j]+dp[i][j-1]

代码如下(已通过leetcode)

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];
   }
}