2015
04-16

# Activation

After 4 years’ waiting, the game "Chinese Paladin 5" finally comes out. Tomato is a crazy fan, and luckily he got the first release. Now he is at home, ready to begin his journey.
But before starting the game, he must first activate the product on the official site. There are too many passionate fans that the activation server cannot deal with all the requests at the same time, so all the players must wait in queue. Each time, the server deals with the request of the first player in the queue, and the result may be one of the following, each has a probability:
1. Activation failed: This happens with the probability of p1. The queue remains unchanged and the server will try to deal with the same request the next time.
2. Connection failed: This happens with the probability of p2. Something just happened and the first player in queue lost his connection with the server. The server will then remove his request from the queue. After that, the player will immediately connect to the server again and starts queuing at the tail of the queue.
3. Activation succeeded: This happens with the probability of p3. Congratulations, the player will leave the queue and enjoy the game himself.
4. Service unavailable: This happens with the probability of p4. Something just happened and the server is down. The website must shutdown the server at once. All the requests that are still in the queue will never be dealt.
Tomato thinks it sucks if the server is down while he is still waiting in the queue and there are no more than K-1 guys before him. And he wants to know the probability that this ugly thing happens.
To make it clear, we say three things may happen to Tomato: he succeeded activating the game; the server is down while he is in the queue and there are no more than K-1 guys before him; the server is down while he is in the queue and there are at least K guys before him.
Now you are to calculate the probability of the second thing.

There are no more than 40 test cases. Each case in one line, contains three integers and four real numbers: N, M (1 <= M <= N <= 2000), K (K >= 1), p1, p2, p3, p4 (0 <= p1, p2, p3, p4 <= 1, p1 + p2 + p3 + p4 = 1), indicating there are N guys in the queue (the positions are numbered from 1 to N), and at the beginning Tomato is at the Mth position, with the probability p1, p2, p3, p4 mentioned above.

There are no more than 40 test cases. Each case in one line, contains three integers and four real numbers: N, M (1 <= M <= N <= 2000), K (K >= 1), p1, p2, p3, p4 (0 <= p1, p2, p3, p4 <= 1, p1 + p2 + p3 + p4 = 1), indicating there are N guys in the queue (the positions are numbered from 1 to N), and at the beginning Tomato is at the Mth position, with the probability p1, p2, p3, p4 mentioned above.

2 2 1 0.1 0.2 0.3 0.4
3 2 1 0.4 0.3 0.2 0.1
4 2 3 0.16 0.16 0.16 0.52

0.30427
0.23280
0.90343

kuangbin题解写的很好，我就不赘余了。。

1、激活失败，留在队列中等待下一次激活（概率为p1)
2、失去连接，出队列，然后排在队列的最后（概率为p2）
3、激活成功，离开队列（概率为p3）
4、服务器瘫痪，服务器停止激活，所有人都无法激活了。

dp[n][m]就是所求
j==1:    dp[i][1]=p1*dp[i][1]+p2*dp[i][i]+p4;
2<=j<=k: dp[i][j]=p1*dp[i][j]+p2*dp[i][j-1]+p3*dp[i-1][j-1]+p4;
k<j<=i:  dp[i][j]=p1*dp[i][j]+p2*dp[i][j-1]+p3*dp[i-1][j-1];

j==1:    dp[i][1]=p*dp[i][i]+p41;
2<=j<=k: dp[i][j]=p*dp[i][j-1]+p31*dp[i-1][j-1]+p41;
k<j<=i:  dp[i][j]=p*dp[i][j-1]+p31*dp[i-1][j-1];

p=p2/(1-p1);
p31=p3/(1-p1)
p41=p4/(1-p1)

j==1:   dp[i][1]=p*dp[i][i]+c[1];
2<=j<=k:dp[i][j]=p*dp[i][j-1]+c[j];
k<j=i:  dp[i][j]=p*dp[i][j]+c[j];

#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
#include<queue>
#include<math.h>
using namespace std;
#define eps 1e-9
#define zero(x) ((fabs(x)<eps?0:x))
#define maxn 2200
double dp[maxn][maxn];
double c[maxn];
double p[maxn];
int main()
{
int n,m,k;
double p1,p2,p3,p4;
while(~scanf("%d%d%d%lf%lf%lf%lf",&n,&m,&k,&p1,&p2,&p3,&p4))
{
if(p4<eps)
{
puts("0.00000");
continue;
}
double p21=p2/(1-p1);
double p41=p4/(1-p1);
double p31=p3/(1-p1);
p[0]=1.0;
for(int i=1;i<=n;i++)p[i]=p[i-1]*p21;
dp[1][1]=p41/(1-p21);
for(int i=2;i<=n;i++)
{
double tmp=p[i-1]*p41;
for(int j=2;j<=k&&j<=i;j++)c[j]=p31*dp[i-1][j-1]+p41;
for(int j=k+1;j<=i;j++)c[j]=p31*dp[i-1][j-1];
for(int j=2;j<=i;j++)tmp+=p[i-j]*c[j];
dp[i][i]=tmp/(1-p[i]);
dp[i][1]=p21*dp[i][i]+p41;
for(int j=2;j<i;j++)dp[i][j]=p21*dp[i][j-1]+c[j];
}
printf("%.5f\n",dp[n][m]);
}
return 0;
}



1. 主要是有人看着,他们要坚持自己的清高,我大新疆有句话,三个回回在一起是三个回回,两个回回在一起是半个回回,一个回回那不是回回***大学的时候经常看见我回族舍友偷偷跑去吃回锅肉

2. 我还有个问题想请教一下，就是感觉对于新手来说，递归理解起来有些困难，不知有没有什么好的方法或者什么好的建议？

3. 在方法1里面：

//遍历所有的边，计算入度
for(int i=0; i<V; i++)
{
degree = 0;