Aeroplane chess
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 1499 Accepted Submission(s): 1022
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.
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.
題意:飛行棋,擲骰子決定走的點數,其中還有一些近路,不用花費點數就能通過,求走到n的期望。
思路:把邊記錄下來,邊兩邊的期望值相等,從後向前掃一遍。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <queue>
#include <map>
using namespace std;
const int mod=1e9+7;
const int N=100010;
double dp[N];
int edge[N];
int main(){
int n,m,a,b;
while(scanf("%d%d",&n,&m),n||m){
memset(dp,0,sizeof(dp));
memset(edge,0,sizeof(edge));
while(m--){
scanf("%d%d",&a,&b);
edge[a]=b;
}
double p=1.0/6;
for(int i=n-1;i>=0;i--){
if(edge[i]){
dp[i]=dp[edge[i]];
continue;
}
dp[i]=1;
for(int j=1;j<=6;j++){
dp[i]+=dp[i+j]*p;
}
}
printf("%.4lf\n",dp[0]);
}
return 0;
}