网络流

目录

• 最大流
• 最小费用最大流

最大流

【模板】网络最大流(洛谷)

dinic

int head[MAXN],tot = 1;
struct edge
{
	int v,nxt;LL w;
}e[MAXM << 1];
void Add_Edge(int x,int y,LL z)
{
	e[++tot].v = y;
	e[tot].w = z;
	e[tot].nxt = head[x];
	head[x] = tot;
}
int d[MAXN];
bool bfs(int s,int t)
{
	for(int i = 1;i <= n;++ i) d[i] = -1;
	d[s] = 0;
	queue<int> q; q.push(s);
	while(!q.empty())
	{
		int p = q.front(); q.pop();
		for(int i = head[p]; i ;i = e[i].nxt)
			if(d[e[i].v] == -1 && e[i].w > 0)
			{
				d[e[i].v] = d[p] + 1;
				q.push(e[i].v);
			}
	}
	return d[t] != -1;
}
int cur[MAXN];
LL dfs(int x,LL flow,int t)
{
	if(x == t) return flow;
	LL ret = 0;
	for(int &i = cur[x]; i ;i = e[i].nxt)
	{
		if(d[x] + 1 == d[e[i].v] && e[i].w > 0)
		{
			LL dz = dfs(e[i].v,Min(flow-ret,e[i].w),t);//记得是flow-ret而不是flow!!!(货物变多可还行 
			e[i].w -= dz; e[i^1].w += dz;
			if((ret += dz) == flow) break;
		}
	}
	if(!ret) d[x] = -1;
	return ret;
}
LL dinic(int s,int t)
{
	LL ret = 0;
	while(bfs(s,t))
	{
		for(int i = 1;i <= n;++ i) cur[i] = head[i];
		ret += dfs(s,INF,t);
	}
	return ret;
}

int main()
{
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	n = Read(); m = Read(); s = Read(); t = Read();
	for(int i = 1,u,v,w;i <= m;++ i)
	{
		u = Read(),v = Read(),w = Read();
		Add_Edge(u,v,w);
		Add_Edge(v,u,0);
	}
	Put(dinic(s,t));
	return 0;
}

最小费用最大流

【模板】最小费用最大流(洛谷)

int head[MAXN],tot = 1;//tot初值一定要是1啊啊啊啊啊啊啊啊啊 
struct edge
{
	int v,w,c,nxt;
}e[MAXM << 1];
void Add_Edge(int u,int v,int w,int c)
{
	e[++tot].v = v;
	e[tot].w = w;
	e[tot].c = c;
	e[tot].nxt = head[u];
	head[u] = tot;
}

int pre[2][MAXN],dis[MAXN],flow[MAXN],maxflow,maxcost;
bool vis[MAXN];
bool bfs(int s,int t)
{
	for(int i = 1;i <= n;++ i) dis[i] = INF;
	queue<int> q; q.push(s);
	flow[s] = INF; dis[s] = 0; 
	while(!q.empty())
	{
		int p = q.front(); q.pop();
		vis[p]= 0;
		for(int i = head[p]; i ;i = e[i].nxt)
		{
			if(dis[p] + e[i].c < dis[e[i].v] && e[i].w > 0)
			{
				dis[e[i].v] = dis[p] + e[i].c;
				pre[0][e[i].v] = p;
				pre[1][e[i].v] = i;
				flow[e[i].v] = Min(flow[p],e[i].w);
				if(!vis[e[i].v])
				{
					vis[e[i].v] = 1;
					q.push(e[i].v);
				}
			}
		}
	}
	return dis[t] != INF;
}
void MCMF(int s,int t)
{
	while(bfs(s,t))
	{
		maxflow += flow[t];
		maxcost += flow[t] * dis[t];
		for(int now = t;now != s;now = pre[0][now])
		{
			e[pre[1][now]].w -= flow[t];
			e[pre[1][now]^1].w += flow[t];
		}
	}
}

int main()
{
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	n = Read(); m = Read(); s = Read(); t = Read();
	for(int i = 1,u,v,w,c;i <= m;++ i)
	{
		u = Read(); v = Read(); w = Read(); c = Read();
		Add_Edge(u,v,w,c);
		Add_Edge(v,u,0,-c);
	}
	MCMF(s,t);
	Put(maxflow,' '),Put(maxcost);
	return 0;
}