climbing-stairs &unique-paths

1.You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

2.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?

思路：动态规划

1.

public class Solution {    public int climbStairs(int n) {        if(n<=0)            return 0;        if(n==1)            return 1;        int d[]=new int[n];        d[0]=1;d[1]=2;        for(int i=2;i<n;i++){            d[i]=d[i-1]+d[i-2];        }        return d[n-1];    }}

2.

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