BZOJ 1565 Luogu P2805 [NOI2009]植物大战僵尸 (Tarjan判环、最小割)

我: “立个flag 14点之前调完这题”

洛谷AC时间: 2019-06-24 14:00:16

实力打脸。。。

网络流板子从来写不对系列

题目链接: (BZOJ) https://www.lydsy.com/JudgeOnline/problem.php?id=1565

(luogu) https://www.luogu.org/problemnew/show/P2805

题解: 长得就那么像个最大权闭合子图啊。。。

\(i\)攻击\(j\)相当于如果想吃掉\(i\)必须吃掉\(j\), 另外如果吃掉\(i\)必须吃掉\(i\)右侧的点，最大权闭合子图。

但是可能有环，注意环并非要么全吃要么全不吃而是全都不能吃，所以用Tarjan提前判一下环，在环里的点和\(T\)连\(+\inf\)表示不能吃

时间复杂度\(O(MaxFlow(nm,(nm)^2))\).

代码

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;

const int N = 602;
const int M = 362400;
const int INF = 1e8;

namespace MaxFlow
{
	struct Edge
	{
		int v,w,nxt,rev;
	} e[(M<<1)+3];
	int fe[N+3];
	int te[N+3];
	int dep[N+3];
	int que[N+3];
	int n,en;
	void addedge(int u,int v,int w)
	{
		en++; e[en].v = v; e[en].w = w;
		e[en].nxt = fe[u]; fe[u] = en; e[en].rev = en+1;
		en++; e[en].v = u; e[en].w = 0;
		e[en].nxt = fe[v]; fe[v] = en; e[en].rev = en-1;
	}
	bool bfs()
	{
		for(int i=1; i<=n; i++) dep[i] = 0;
		int head = 1,tail = 1; que[tail] = 1; dep[1] = 1;
		while(head<=tail)
		{
			int u = que[head]; head++;
			for(int i=fe[u]; i; i=e[i].nxt)
			{
				if(dep[e[i].v]==0 && e[i].w>0)
				{
					dep[e[i].v] = dep[u]+1;
					tail++; que[tail] = e[i].v;
				}
			}
		}
		return dep[2]!=0;
	}
	int dfs(int u,int cur)
	{
		if(u==2) {return cur;}
		int rst = cur;
		for(int i=te[u]; i; i=e[i].nxt)
		{
			if(dep[e[i].v]==dep[u]+1 && e[i].w>0 && rst>0)
			{
				int flow = dfs(e[i].v,min(rst,e[i].w));
				if(flow>0)
				{
					e[i].w-=flow; e[e[i].rev].w += flow; rst-=flow;
					if(e[i].w>0) {te[u] = i;}
					if(rst==0) {return cur;}
				}
			}
		}
		if(cur==rst) {dep[u] = 0;}
		return cur-rst;
	}
	int dinic(int _n)
	{
		n = _n;
		int ret = 0;
		while(bfs())
		{
			for(int i=1; i<=n; i++) te[i] = fe[i];
			ret += dfs(1,INF);
		}
		return ret;
	}
}

namespace Tarjan
{
	struct Edge
	{
		int v,nxt;
	} e[M+3];
	int fe[N+3];
	int dfn[N+3],low[N+3],stk[N+3];
	bool instk[N+3];
	bool inscc[N+3];
	int n,en,cnt,tp;
	void addedge(int u,int v)
	{
		en++; e[en].v = v;
		e[en].nxt = fe[u]; fe[u] = en;
	}
	void dfs(int u)
	{
		cnt++; dfn[u] = low[u] = cnt; tp++; stk[tp] = u; instk[u] = true;
		for(int i=fe[u]; i; i=e[i].nxt)
		{
			if(!dfn[e[i].v])
			{
				dfs(e[i].v);
				low[u] = min(low[u],low[e[i].v]);
			}
			else if(instk[e[i].v])
			{
				low[u] = min(low[u],low[e[i].v]);
			}
		}
		if(low[u]>=dfn[u])
		{
			if(stk[tp]!=u) {inscc[u] = true;}
			while(stk[tp]!=u)
			{
				inscc[stk[tp]] = true;
				instk[stk[tp]] = false;
				stk[tp] = 0; tp--;
			}
			stk[tp] = 0; tp--; instk[u] = false;
		}
	}
	void work(int _n)
	{
		n = _n;
		for(int i=1; i<=n; i++)
		{
			if(!dfn[i]) {dfs(i);}
		}
	}
}

int n,m;

int getid(int x,int y) {return x*m+y+3;}

int main()
{
	scanf("%d%d",&n,&m); int ans = 0;
	for(int i=1; i<=n*m; i++)
	{
		int x; scanf("%d",&x);
		if(x>0) {MaxFlow::addedge(1,i+2,x); ans += x;}
		else if(x<0) {MaxFlow::addedge(i+2,2,-x);}
		scanf("%d",&x);
		while(x--)
		{
			int y,z; scanf("%d%d",&y,&z); int pos = getid(y,z);
			MaxFlow::addedge(pos,i+2,INF);
			Tarjan::addedge(pos-2,i);
		}
		if(i%m!=0)
		{
			MaxFlow::addedge(i+2,i+3,INF);
			Tarjan::addedge(i,i+1);
		}
	}
	Tarjan::work(n*m);
	for(int i=1; i<=n*m; i++)
	{
		if(Tarjan::inscc[i])
		{
			MaxFlow::addedge(i+2,2,INF);
		}
	}
	int tmp = MaxFlow::dinic(n*m+2);
	ans -= tmp;
	printf("%d\n",ans);
	return 0;
}