Areoplane chess
传送门1
传送门2
Hzz loves aeroplane chess very much. The chess map contains
There are also M flight lines on the chess map. The i-th flight line can help Hzz fly from 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
Then
The input end with
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
题意
数轴上有
分析
期望dp.(期望dp一般逆推)
定义
1. 对于可以直接飞的点,
2. 不能飞的点,
CODE
#include<cstdio>
#include<memory.h>
#define N 100005
#define FOR(i,a,b) for(int i=(a),i##_END_=(b);i<=i##_END_;i++)
#define ROF(i,a,b) for(int i=(a),i##_END_=(b);i>=i##_END_;i--)
double dp[N];
int fly[N];
int main() {
int n,m;
while(~scanf("%d%d",&n,&m)&&(n||m)) {
memset(fly,-1,sizeof fly);
FOR(i,1,m) {
int a,b;
scanf("%d%d",&a,&b);
fly[a]=b;
}
memset(dp,0,sizeof dp);
ROF(i,n-1,0) {
if(fly[i]==-1) {
FOR(j,i+1,i+6)dp[i]+=dp[j]/6.0;
dp[i]++;
} else dp[i]=dp[fly[i]];
}
printf("%.4lf\n",dp[0]);
}
return 0;
}