POJ 2987 Firing

Posted 2020-10-02 自为

tags:

篇首语：本文由小常识网(cha138.com)小编为大家整理，主要介绍了POJ 2987 Firing相关的知识，希望对你有一定的参考价值。

Time Limit: 5000MS		Memory Limit: 131072K
Total Submissions: 10804		Accepted: 3263

Description

You’ve finally got mad at “the world’s most stupid” employees of yours and decided to do some firings. You’re now simply too mad to give response to questions like “Don’t you think it is an even more stupid decision to have signed them?”, yet calm enough to consider the potential profit and loss from firing a good portion of them. While getting rid of an employee will save your wage and bonus expenditure on him, termination of a contract before expiration costs you funds for compensation. If you fire an employee, you also fire all his underlings and the underlings of his underlings and those underlings’ underlings’ underlings… An employee may serve in several departments and his (direct or indirect) underlings in one department may be his boss in another department. Is your firing plan ready now?

Input

The input starts with two integers n (0 < n ≤ 5000) and m (0 ≤ m ≤ 60000) on the same line. Next follows n + m lines. The first n lines of these give the net profit/loss from firing the i-th employee individually b_i (|b_i| ≤ 10⁷, 1 ≤ i ≤ n). The remaining m lines each contain two integers i and j (1 ≤ i, j ≤ n) meaning the i-th employee has the j-th employee as his direct underling.

Output

Output two integers separated by a single space: the minimum number of employees to fire to achieve the maximum profit, and the maximum profit.

Sample Input

5 5
8
-9
-20
12
-10
1 2
2 5
1 4
3 4
4 5

Sample Output

2 2

Hint

As of the situation described by the sample input, firing employees 4 and 5 will produce a net profit of 2, which is maximum.

Source

POJ Monthly--2006.08.27, frkstyc

 

这道题的性质和上一道题差不多，

都是最大闭合权图，

不同的地方在于

1.m的取值与权值无关，这样的话我们让读入的x,y之前的边为INF就好

2.需要求人数，我们重新DFS一遍残余网络，如果这条边还有流量的话，说明需要裁掉这个人，至于为什么，https://wenku.baidu.com/view/986baf00b52acfc789ebc9a9.html

注意几个问题：

1.不要全开long long会超时

2.输出的数不要写反了

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 #include<cmath>
  5 #include<queue>
  6 #define lli long long int 
  7 using namespace std;
  8 const int MAXN=2000001;
  9 const int INF = 1e8;
 10 inline void read(int &n)
 11 {
 12     char c=‘+‘;int x=0;bool flag=0;
 13     while(c<‘0‘||c>‘9‘){c=getchar();if(c==‘-‘)flag=1;}
 14     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-48;c=getchar();}
 15     n=flag==1?-x:x;
 16 }
 17 int n,m,s,t;
 18 struct node
 19 {
 20     int u,v,flow,nxt;
 21 }edge[MAXN];
 22 int head[MAXN];
 23 int cur[MAXN];
 24 int num=0;
 25 int deep[MAXN];
 26 lli tot=0;
 27 bool vis[MAXN];
 28 lli out;
 29 void add_edge(int x,int y,int z)
 30 {
 31     edge[num].u=x;
 32     edge[num].v=y;
 33     edge[num].flow=z;
 34     edge[num].nxt=head[x];
 35     head[x]=num++;
 36 }
 37 void add(int x,int y,int z)
 38 {
 39     add_edge(x,y,z);
 40     add_edge(y,x,0);
 41 }
 42 bool BFS()
 43 {
 44     memset(deep,0,sizeof(deep));
 45     deep[s]=1;
 46     queue<int>q;
 47     q.push(s);
 48     while(q.size()!=0)
 49     {
 50         int p=q.front();
 51         q.pop();
 52         for(int i=head[p];i!=-1;i=edge[i].nxt)
 53             if(!deep[edge[i].v]&&edge[i].flow)
 54                 deep[edge[i].v]=deep[edge[i].u]+1,
 55                 q.push(edge[i].v);
 56     }
 57     return deep[t];
 58     
 59 }
 60 lli DFS(int now,int nowflow)
 61 {
 62     if(now==t||nowflow<=0)
 63         return nowflow;
 64     lli totflow=0;
 65     for(int &i=cur[now];i!=-1;i=edge[i].nxt)
 66     {
 67         if(deep[edge[i].v]==deep[edge[i].u]+1&&edge[i].flow)
 68         {
 69             int canflow=DFS(edge[i].v,min(nowflow,edge[i].flow));
 70             edge[i].flow-=canflow;
 71             edge[i^1].flow+=canflow;
 72             totflow+=canflow;
 73             nowflow-=canflow;
 74             if(nowflow<=0)
 75                 break;
 76         }
 77     
 78     }
 79     return totflow;
 80 }
 81 void Dinic()
 82 {
 83     lli ans=0;
 84     while(BFS())
 85     {
 86         memcpy(cur,head,MAXN);
 87         ans+=DFS(s,1e8);
 88     }
 89     out=tot-ans;
 90 }
 91 int find_pep(int now)
 92 {
 93     vis[now]=1;
 94     for(int i=head[now];i!=-1;i=edge[i].nxt)
 95         if(!vis[edge[i].v]&&edge[i].flow)
 96             find_pep(edge[i].v);
 97 }
 98 int main()
 99 {
100     //freopen("a.in","r",stdin);
101     //freopen("c.out","w",stdout);
102     while(~scanf("%d%d",&n,&m))
103     {
104         memset(head,-1,sizeof(head));
105         num=0;
106         s=0,t=n+1;
107         tot=0;
108         for(int i=1;i<=n;i++)
109         {
110             int a;read(a);
111             if(a>0)    tot+=a,add(s,i,a);
112             if(a<0) add(i,t,-a);
113         }
114         for(int i=1;i<=m;i++)
115         {
116             int x,y;read(x);read(y);
117             add(x,y,INF);
118         }
119         Dinic();
120         memset(vis,0,sizeof(vis));
121         int ans=0;
122         find_pep(s);
123         for(int i=1;i<=n;i++)
124             ans+=vis[i];
125         //cout<<ans<<" "<<out<<endl;
126         printf("%d %I64d\n",ans,out);
127     }
128     return  0;
129 }