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概率dp HDU 4405
Aeroplane chess
Time Limit:1000MS Memory Limit:32768KB 64bit IO Format:%I64d & %I64uAppoint description:
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.
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.
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
/************************************************************************* > File Name: t.cpp > Author: acvcla > Mail: acvcla@gmail.com > Created Time: 2014年10月21日 星期二 21时33分55秒 ************************************************************************/ #include<iostream> #include<algorithm> #include<cstdio> #include<vector> #include<cstring> #include<map> #include<queue> #include<stack> #include<string> #include<cstdlib> #include<ctime> #include<set> #include<math.h> using namespace std; typedef long long LL; const int maxn = 1e5 + 10; #define rep(i,a,b) for(int i=(a);i<=(b);i++) #define pb push_back double dp[maxn]; int y[maxn],n,m; int main(int argc, char const *argv[]) { while(~scanf("%d%d",&n,&m)){ if(!n&&!m){ return 0; } n++; memset(dp,0,sizeof dp); memset(y,0,sizeof(y)); int x,to; for(int i=1;i<=m;i++){ scanf("%d%d",&x,&to); y[x+1]=to+1; } for(int i=n-1;i>=1;i--){ double t=0; for(int j=1;j<=6;j++)t+=dp[i+j]/6; if(y[i]){ t=dp[y[i]]-1; } dp[i]=t+1; } printf("%.4f\n",dp[1]); } return 0; }
概率dp HDU 4405
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