hdu 4405 Aeroplane chess

 

Aeroplane chess
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 915 Accepted Submission(s): 631


Problem Description
Hzz loves aeroplane chess very much. The chess map contains N+1 grids labeled from 0 to N. Hzz starts at grid 0. For each step he throws a dice(a dice have six faces with equal probability to face up and the numbers on the faces are 1,2,3,4,5,6). When Hzz is at grid i and the dice number is x, he will moves to grid i+x. Hzz finishes the game when i+x is equal to or greater than N.

There are also M flight lines on the chess map. The i-th flight line can help Hzz fly from grid Xi to Yi (0<Xi<Yi<=N) without throwing the dice. If there is another flight line from Yi, Hzz can take the flight line continuously. It is granted that there is no two or more flight lines start from the same grid.

Please help Hzz calculate the expected dice throwing times to finish the game.


Input
There are multiple test cases.
Each test case contains several lines.
The first line contains two integers N(1≤N≤100000) and M(0≤M≤1000).
Then M lines follow, each line contains two integers Xi,Yi(1≤Xi<Yi≤N).
The input end with N=0, M=0.


Output
For each test case in the input, you should output a line indicating the expected dice throwing times. Output should be rounded to 4 digits after decimal point.


Sample Input
2 0
8 3
2 4
4 5
7 8
0 0


Sample Output
1.1667
2.3441


Source
2012 ACM/ICPC Asia Regional Jinhua Online


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zhoujiaqi2010

//15MS    1884K    705 B    C++
//概率DP，简单题吧..由后往前推
#include<stdio.h>
#include<string.h>
double dp[1000005]; //dp[i]表示由位置i到终点最少步数 
int go[1000005]; //g[x]=y 代表 由位置x可以直接到y 
double Go(int x)
{
    while(go[x]) x=go[x];
    return dp[x]/6;
}
int main(void) 
{
    int n,m;
    int x,y;
    while(scanf("%d%d",&n,&m),n+m)
    {
        memset(dp,0,sizeof(dp));
        memset(go,0,sizeof(go));
        for(int i=0;i<m;i++){ 
            scanf("%d%d",&x,&y);
            go[x]=y;
        }
        for(int i=n-1;i>=0;i--){
            dp[i]=1;
            for(int j=1;j<=6;j++){
                if(go[i+j]) dp[i]+=Go(i+j);
                else dp[i]+=dp[i+j]/6;
            }
        }
        printf("%.4lf\n",dp[0]);    
    }
    return 0;
}