HDU 1548 A strange lift(递归模拟标记)

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本文介绍了一个有趣的算法问题——奇怪电梯挑战。任务是在限定楼层内找到从A层到达B层所需的最少按钮按压次数，电梯每层可上升或下降特定层数。文章通过递归深度优先搜索算法解决此问题。

A strange lift

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 18738 Accepted Submission(s): 6932

Problem Description

There is a strange lift.The lift can stop can at every floor as you want, and there is a number Ki(0 <= Ki <= N) on every floor.The lift have just two buttons: up and down.When you at floor i,if you press the button "UP" , you will go up Ki floor,i.e,you will go to the i+Ki th floor,as the same, if you press the button "DOWN" , you will go down Ki floor,i.e,you will go to the i-Ki th floor. Of course, the lift can't go up high than N,and can't go down lower than 1. For example, there is a buliding with 5 floors, and k1 = 3, k2 = 3,k3 = 1,k4 = 2, k5 = 5.Begining from the 1 st floor,you can press the button "UP", and you'll go up to the 4 th floor,and if you press the button "DOWN", the lift can't do it, because it can't go down to the -2 th floor,as you know ,the -2 th floor isn't exist.
Here comes the problem: when you are on floor A,and you want to go to floor B,how many times at least he has to press the button "UP" or "DOWN"?

Input

The input consists of several test cases.,Each test case contains two lines.
The first line contains three integers N ,A,B( 1 <= N,A,B <= 200) which describe above,The second line consist N integers k1,k2,....kn.
A single 0 indicate the end of the input.

Output

For each case of the input output a interger, the least times you have to press the button when you on floor A,and you want to go to floor B.If you can't reach floor B,printf "-1".

Sample Input

5 1 5
3 3 1 2 5
0

Sample Output

3

/*
题目意思是：有N层电梯，输入A B 要你从A到B
第i层电梯可以升降ki层，但是不能小于1或大于n；问能否到B
思路：数组标记，从第一层枚举上或下，回朔，若都不行，则无解 
*/
#include<iostream>
#include <string.h>
using namespace std;
const int N=200+5;
const int INF=1000000000;
bool book[N];
int k[N];
int a,b,n,re;
void dfs(int now,int sum){
	if(now==b)
	{
		if(re>sum)
		  re=sum;
		return;
	}
	if(re<=sum)
	   return;
	int ne;
	ne=now+k[now];
	if(ne<=n){
		if(book[ne]==0){
		  book[ne]=1;
		  dfs(ne,sum+1);
		  book[ne]=0;
		}		
	}	  
	ne=now-k[now];
	if(ne>=1){
		if(book[ne]==0){
				book[ne]=1;
		dfs(ne,sum+1);
		book[ne]=0;
		}	
	}
}
int main()
{  
    while(cin>>n){
    	if(n==0)
    	 break;
    	cin>>a>>b;
    	memset(book,0,sizeof(book));
    	for(int i=1;i<=n;i++)
    	     cin>>k[i];
    	re=INF;
    	book[a]=1;
    	dfs(a,0);
    	if(re!=INF)
    	  cout<<re<<endl;
    	else
    	  cout<<-1<<endl;
	}
	return 0;
}