【BZOJ2625】[Neerc2009]Inspection

Description

You are in charge of a team that inspects a new ski resort. A ski resort is situated on several mountains and consists of a number of slopes. Slopes are connected with each other, forking and joining. A map of the ski resort is represented as an acyclic directed graph. Nodes of the graph represent different points in ski resort and edges of the graph represent slopes between the points, with the direction of edges going downwards.?
Your team has to inspect each slope of the ski resort. Ski lifts on this resort are not open yet, but you have a helicopter. In one fiight the helicopter can drop one person into any point of the resort. From the drop off point the person can ski down the slopes, inspecting each slope as they ski. It is fine to inspect the same slope multiple times, but you have to minimize the usage of the helicopter. So, you have to figure out how to inspect all the slopes with the fewest number of helicopter flights. 給張有向無環圖，問至少多少條路徑能夠覆蓋所有的邊（可以重復

Input

The first line of the input file contains a single integer number n (2 <= n <= 100) - the number of points in the ski resort. The following n lines of the input file describe each point of the ski resort numbered from 1 to n. Each line starts with a single integer number mi (0 <= mi < n for i from 1 to n) and is followed by mi integer numbers aij separated by spaces. All aij are distinct for each i and each aij (1 <= aij <= n, aij??i) represents a slope going downwards from point i to point aij . Each point in the resort has at least one slope connected to it.

Output

On the first line of the output file write a single integer number k - the minimal number of helicopter flights that are needed to inspect all slopes. Then write k lines that describe inspection routes for each helicopter flight. Each route shall start with single integer number from 1 to n - the number of the drop off point for the helicopter flight, followed by the numbers of points that will be visited during inspection in the corresponding order as the slopes are inspected going downwards. Numbers on a line shall be separated by spaces. You can write routes in any order.

Sample Input

8
1 3
1 7
2 4 5
1 8
1 8
0
2 6 5
0

Sample Output

4

題解：經典的最小鏈覆蓋問題。

采用有上下界的網絡流的思路，將每個點拆成兩個，從出點向入點連一條(0,inf)的邊，對于每條邊(a,b)從a的出點向b的入點連一條(1,inf)的邊。然后先跑可行流再反著跑最大流。但是發現一個性質，第一遍跑可行流時一定能夠滿流，所以我們直接跑第二遍即可，具體連邊方法：

1.S->每個點的出點，每個點的入點->T 容量inf
2.每個點的入點->出點 容量inf
3.對于(a,b)，a的出點->b的入點 容量inf，a的出點->S，b的入點->T 容量1

ans=m-從T到S的最大流

#include <cstdio> #include <cstring> #include <iostream> #include <queue> using namespace std; const int inf=1<<30; int n,m,S,T,cnt,ans; int to[100000],next[100000],val[100000],head[1000],d[1000],m1[1000],m2[1000]; queue<int> q; int rd() {int ret=0,f=1; char gc=getchar();while(gc<'0'||gc>'9') {if(gc=='-') f=-f; gc=getchar();}while(gc>='0'&&gc<='9') ret=ret*10+gc-'0',gc=getchar();return ret*f; } void add(int a,int b,int c,int d) {to[cnt]=b,val[cnt]=c,next[cnt]=head[a],head[a]=cnt++;to[cnt]=a,val[cnt]=d,next[cnt]=head[b],head[b]=cnt++; } int dfs(int x,int mf) {if(x==T) return mf;int i,k,temp=mf;for(i=head[x];i!=-1;i=next[i]){if(d[to[i]]==d[x]+1&&val[i]){k=dfs(to[i],min(temp,val[i]));if(!k) d[to[i]]=0;val[i]-=k,val[i^1]+=k,temp-=k;if(!temp) break;}}return mf-temp; } int bfs() {while(!q.empty()) q.pop();memset(d,0,sizeof(d));int i,u;q.push(S),d[S]=1;while(!q.empty()){u=q.front(),q.pop();for(i=head[u];i!=-1;i=next[i]){if(!d[to[i]]&&val[i]){d[to[i]]=d[u]+1;if(to[i]==T) return 1;q.push(to[i]);}}}return 0; } int main() {n=rd(),S=0,T=2*n+1;int i,a,b;memset(head,-1,sizeof(head));for(i=1;i<=n;i++){a=rd(),m1[i]=a,ans+=a;while(a--) b=rd(),add(i,b+n,inf,0),m2[b]++;}for(i=1;i<=n;i++) add(S,i,inf,m1[i]),add(i+n,T,inf,m2[i]),add(i+n,i,inf,0);swap(S,T);while(bfs()) ans-=dfs(S,inf);printf("%d",ans);return 0; }

轉載于:https://www.cnblogs.com/CQzhangyu/p/7297651.html

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