有一個吸血鬼被困了，有n條路可以逃出去，每條路有一個難度c[],他初始的戰斗力是f，對於第i條路，若f > c[i]他花t[i]天就能出去，否則，他就停留一天，同時戰斗力增加c[i]然後再選一條路走出去，他走每條路的概率是相同的。問他逃出去的天數的期望。
設dp[i]表示在戰斗力為i時逃出去的期望值，那麼可推出狀態方程
dp[i] = 1/n * t[j]（c[j] > i），dp[i] = 1/n * (1+dp[ i+c[j] ] )( c[j] <= i)。
需要注意的是終態的確定。當f > Max時，這時的期望值為總時間的平均值便是終態了，但是i + c[j]有可能大於Max+1，所以終態應該是Max*2。初始化時就忘乘2了。
還有就是t[i]是整數。
Description
If thou doest well, shalt thou not be accepted? and if thou doest not well, sin lieth at the door. And unto thee shall be his desire, and thou shalt rule over him.
And Cain talked with Abel his brother: and it came to pass, when they were in the field, that Cain rose up against Abel his brother, and slew him.
And the LORD said unto Cain, Where is Abel thy brother? And he said, I know not: Am I my brother's keeper?
And he said, What hast thou done? the voice of thy brother's blood crieth unto me from the ground.
And now art thou cursed from the earth, which hath opened her mouth to receive thy brother's blood from thy hand;
When thou tillest the ground, it shall not henceforth yield unto thee her strength; a fugitive and a vagabond shalt thou be in the earth.
—— Bible Chapter 4
Now Cain is unexpectedly trapped in a cave with N paths. Due to LORD's punishment, all the paths are zigzag and dangerous. The difficulty of the ith path is ci.
Then we define f as the fighting capacity of Cain. Every day, Cain will be sent to one of the N paths randomly.
Suppose Cain is in front of the ith path. He can successfully take ti days to escape from the cave as long as his fighting capacity f is larger than ci. Otherwise, he has to keep trying day after day. However, if Cain failed to escape, his fighting capacity would increase ci as the result of actual combat. (A kindly reminder: Cain will never died.)www.Bkjia.com
As for ti, we can easily draw a conclusion that ti is closely related to ci. Let's use the following function to describe their relationship:
After D days, Cain finally escapes from the cave. Please output the expectation of D.
Input
The input consists of several cases. In each case, two positive integers N and f (n ≤ 100, f ≤ 10000) are given in the first line. The second line includes N positive integers ci (ci ≤ 10000, 1 ≤ i ≤ N)
Output
For each case, you should output the expectation(3 digits after the decimal point).
Sample Input
3 1 1 2 3
Sample Output
6.889
#include#include #include #include #include using namespace std; double dp[1000010]; int b[110]; double a=(1+sqrt(5))*0.5; int main() { int n,f; while(~scanf("%d %d",&n,&f)) { int Max=0; for(int i=1; i<=n; i++) { scanf("%d",&b[i]); Max=max(Max,b[i]); } memset(dp,0,sizeof(dp)); for(int i=2*Max; i>=f; i--) { dp[i]=0; for(int j=1; j<=n; j++) { if(i>b[j])dp[i]+=(int)(a*b[j]*b[j]); else dp[i]+=(1+dp[i+b[j]]); } dp[i]/=n; } printf("%.3lf\n",dp[f]); } return 0; }
