Question:
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?
Solution:
public class Solution { public int uniquePaths(int m, int n) { //c(m-1,m+n-2) if(m==0||n==0) return 0; double sum=1; for(int i=n;i<=m+n-2;i++) sum=sum*i/(i-n+1); return (int)sum; } } 用dynamic programming......
int[][] ans=new int[m][n]; int i=0; int j=0; for(i=0;i<=m-1;i++) { for(j=0;j<=n-1;j++) { if(i==0||j==0) ans[i][j]=1; else ans[i][j]=ans[i-1][j]+ans[i][j-1]; } } return ans[i-1][j-1];
