1. 程式人生 > >UVALive 2197 Paint the Roads(費用流)

UVALive 2197 Paint the Roads(費用流)

題意:n個點,m條邊,還有一個k,給出每條邊的資訊,讓你選擇一些邊,使得這些邊組成的圖裡面,每個點只屬於k個迴路上,問最小的費用

如果每個點都只在k個迴路上,那麼這些點的出度入度是相等的,都是等於k,所以對於每個點,拆點分別連源點匯點,容量為k,費用為0,然後邊就正常的連上,容量為1,費用為邊權,跑一遍費用流,若最後的流量等於k*n,就是答案,否則就是-1

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
const int maxn=110;
const int maxm=1e5+7;
const int inf=0x3f3f3f3f;
struct Node
{
	int to;
	int capa;
	int cost;
	int next;
}edge[maxm];
int cnt;
int source,sink;
int n,m,k;
int head[maxn];
int dis[maxn];
int rec[maxn];
int pre[maxn];
bool vis[maxn];
void init()
{
	cnt=0;
	memset(head,-1,sizeof(head));
	return;
}
void add(int u,int v,int capa,int cost)
{
	edge[cnt].to=v;
	edge[cnt].capa=capa;
	edge[cnt].cost=cost;
	edge[cnt].next=head[u];
	head[u]=cnt++;
	edge[cnt].to=u;
	edge[cnt].capa=0;
	edge[cnt].cost=-cost;
	edge[cnt].next=head[v];
	head[v]=cnt++;
	return;
}
bool spfa()
{
	memset(dis,inf,sizeof(dis));
	memset(pre,-1,sizeof(pre));
	memset(rec,-1,sizeof(rec));
	memset(vis,false,sizeof(vis));
	queue<int> que;
	que.push(source);
	dis[source]=0;
	vis[source]=true;
	while(!que.empty())
	{
		int node=que.front();
		que.pop();
		vis[node]=false;
		for(int i=head[node];~i;i=edge[i].next)
		{
			int v=edge[i].to;
			if(edge[i].capa>0&&dis[v]>dis[node]+edge[i].cost)
			{
				dis[v]=dis[node]+edge[i].cost;
				rec[v]=i;
				pre[v]=node;
				if(!vis[v])
				{
					vis[v]=true;
					que.push(v);
				}
			}
		}
	}
	return dis[sink]!=inf;
}
int mcmf()
{
	int maxflow=0;
	int mincost=0;
	while(spfa())
	{
		int node=sink;
		int minn=inf;
		while(node!=source)
		{
			minn=min(edge[rec[node]].capa,minn);
			node=pre[node];
		}
		maxflow+=minn;
		node=sink;
		while(node!=source)
		{
			mincost+=minn*edge[rec[node]].cost;
			edge[rec[node]].capa-=minn;
			edge[rec[node]^1].capa+=minn;
			node=pre[node];
		}
	}
	if(maxflow==k*n) return mincost;
	return -1;
}
int main()
{
	//freopen("in.txt","r",stdin);
	//freopen("out.txt","w",stdout);
	int test;
	scanf("%d",&test);
	while(test--)
	{
		init();
		scanf("%d%d%d",&n,&m,&k);
		source=0;
		sink=n*2+1;
		for(int i=1;i<=n;i++)
		{
			add(source,i,k,0);
			add(i+n,sink,k,0);
		}
		for(int i=0;i<m;i++)
		{
			int u,v,w;
			scanf("%d%d%d",&u,&v,&w);
			add(u+1,v+n+1,1,w);
		}
		printf("%d\n",mcmf());
	}
	return 0;
}