uoj#217. 【UNR #1】奇怪的线段树（上下界最小流）

题目描述

n<=4000

题解

线段树性质：一次区间查找从左往右对应右子树->右子树->...->左子树->左子树

把[l,r]向r+1连边，r+1向[r+1,l']连边，跑上下界最小流即可

上下界最小流=上下界可行流-残量网络T->S最大流，可行流=T->S的inf边跑过的流量

染色树的叶子节点要经过至少一次，非叶子可以经过任意次，没有染色的点不能经过

code

#include <bits/stdc++.h>
#define fo(a,b,c) for (a=b; a<=c; a++)
#define fd(a,b,c) for (a=b; a>=c; a--)
#define min(a,b) (a<b?a:b)
#define max(a,b) (a>b?a:b)
#define inf 114514
#define ll long long
//#define file
using namespace std;

int a[2000001][3],tr[8001][2],d[8001],ls[30001],cur[30001],f[30001],g[30001];
int L[8001],R[8001],Tr[8001],A[8001],B[8001],n,i,j,k,l,t,tot,t1,t2,len,ans,S,T;
bool bz1[8001],bz2[8001];

void NEW(int x,int y,int z) {++len;a[len][0]=y;a[len][1]=ls[x];ls[x]=len;a[len][2]=z;}
void New(int x,int y,int z) {NEW(x,y,z),NEW(y,x,0);}
void pd(int Fa,int t)
{
	if (Tr[t] && (!tr[t][0] || !Tr[tr[t][0]] && !Tr[tr[t][1]]))
	{
		if (tr[Fa][0]==t) bz1[t]=1;
		else bz2[t]=1;
	}
	if (t>1) {if (tr[Fa][0]==t) A[++t1]=t; else B[++t2]=t;}
	
	if (!tr[t][0]) return;
	if (!Tr[t] && Tr[tr[t][0]]) {printf("OwO\n");exit(0);}
	if (!Tr[t] && Tr[tr[t][1]]) {printf("OwO\n");exit(0);}
	pd(t,tr[t][0]),pd(t,tr[t][1]);
}

int dfs(int t,int flow)
{
	int i,use=0,w;
	if (t==T) return flow;
	
	for (i=cur[t]; i; i=a[i][1])
	if (a[i][2] && f[t]==f[a[i][0]]+1)
	{
		cur[t]=i;
		
		w=dfs(a[i][0],min(flow-use,a[i][2]));
		a[i][2]-=w,a[i^1][2]+=w;
		use+=w;
		if (flow==use) return use;
	}
	
	cur[t]=ls[t];
	--g[f[t]];
	if (!g[f[t]]) {f[S]=T+1;return use;}
	++f[t],++g[f[t]];
	return use;
}

int main()
{
	#ifdef file
	freopen("uoj217.in","r",stdin);
	#endif
	
	scanf("%d",&n);
	t=tot=1;L[1]=1;R[1]=n;d[t]=1;
	fo(i,1,n*2-1)
	{
		scanf("%d",&j);Tr[d[t]]=j;
		if (L[d[t]]!=R[d[t]])
		{
			scanf("%d",&k);
			tr[d[t]][0]=++tot;L[tot]=L[d[t]];R[tot]=k;
			tr[d[t]][1]=++tot;L[tot]=k+1;R[tot]=R[d[t]];
			l=d[t],d[++t]=tr[l][0];
		}
		else
		{
			--t;
			while (t && tr[d[t]][1]==d[t+1]) --t;
			if (t) l=d[t],d[++t]=tr[l][1];
		}
	}
	pd(0,1);
	
	if (!Tr[1]) {printf("0\n");return 0;}
	if (Tr[1] && !Tr[tr[1][0]] && !Tr[tr[1][1]]) {printf("1\n");return 0;}
	S=(n+tot)*2+1;T=S+1;
	len=1;
	fo(i,1,n) New(i,i+n,inf);
	fo(i,1,t2)
	if (Tr[B[i]])
	{
		New(T,B[i]+n*2,inf);
		New(B[i]+n*2,B[i]+n*2+tot,inf);
		if (bz2[B[i]]) New(T+1,B[i]+n*2+tot,1),New(B[i]+n*2,T+2,1);
		New(B[i]+n*2+tot,S,inf);
		
		New(L[B[i]],B[i]+n*2,inf);
		if (R[B[i]]<n)
		New(B[i]+n*2+tot,R[B[i]]+1,inf);
	}
	fo(i,1,t1)
	if (Tr[A[i]])
	{
		New(T,A[i]+n*2,inf);
		New(A[i]+n*2,A[i]+n*2+tot,inf);
		if (bz1[A[i]]) New(T+1,A[i]+n*2+tot,1),New(A[i]+n*2,T+2,1);
		New(A[i]+n*2+tot,S,inf);
		
		New(L[A[i]]+n,A[i]+n*2,inf);
		if (R[A[i]]<n)
		New(A[i]+n*2+tot,R[A[i]]+n+1,inf);
	}
	
	New(S,T,inf);
	S+=2,T+=2;g[0]=T;
	while (f[S]<=T) dfs(S,inf);ans=a[len][2];
	memset(f,0,sizeof(f)),memset(g,0,sizeof(g)),memset(cur,0,sizeof(cur));
	S-=2,T-=2;g[0]=T;a[len][2]=a[len^1][2]=0;
	while (f[S]<=T) ans-=dfs(S,inf);
	
	printf("%d\n",ans);
	
	fclose(stdin);
	fclose(stdout);
	return 0;
}