A strange lift

                          A strange lift

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

题目大意：乘坐电梯，给定电梯层数N和起始层数A,B，在每一层给定一个数字a[i]，该数字表示可以在该层上升或下降a[i]层，问最少按几次可以到达目标层？若不能到达输出-1.

思路：把每一层看做一个点，即可抽象成一个图，就成了求单元最短路问题，Dijkstra即可解决。

code：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int INF = 1<<30;

int N,A,B;
int map[205][205];
int a[205];
int dis[205],f[205];

void dijkstra(int A,int B)
{
    int min,k;
    memset(f,0,sizeof(f));
    for(int i=1;i<=N;i++)
        dis[i] = map[A][i];
    f[A] = 1;
    dis[A] = 0;
    for(int i=2;i<=N;i++)
    {
        min = INF;
        for(int j=1;j<=N;j++)
         if(!f[j] && min > dis[j])
         {
            k = j;
            min = dis[j];
         }
        if(min == INF) break;
        f[k] = 1;
        for(int j=1;j<=N;j++)
         if(dis[j] > dis[k] + map[k][j] && !f[j])
           dis[j] = dis[k] + map[k][j];
    }
}

int main()
{
    while(~scanf("%d",&N) && N)
    {
        scanf("%d%d",&A,&B);
        for(int i=1;i<=N;i++)
          for(int j=1;j<=N;j++)
            map[i][j] = INF;
        for(int i=1;i<=N;i++)
        {
            scanf("%d",&a[i]);
            if(i+a[i] <= N) map[i][i+a[i]] = 1;
            if(i-a[i] >= 0) map[i][i-a[i]] = 1;
        }
        dijkstra(A,B);
        if(dis[B] != INF) printf("%d\n",dis[B]);
        else printf("-1\n");
    }
    return 0;
}