BZOJ4316: 小C的独立集

Posted 2020-08-30

传送门

圆方树预备知识。

首先搞出DFS树，然后设状态$f[node][OK][OKanc]$为别表示在当前点选/不限和环顶节点选/不选。

剩下的就是TreeDP常规的东西。

P.S.课件上说第一个状态设为父亲的，亲测没有设成自己来得方便

//BZOJ 4316
//by Cydiater
//2017.2.12
#include <iostream>
#include <queue>
#include <map>
#include <ctime>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <iomanip>
#include <cmath>
#include <bitset>
#include <set>
#include <vector>
using namespace std;
#define ll long long
#define up(i,j,n)	for(int i=j;i<=n;i++)
#define down(i,j,n)	for(int i=j;i>=n;i--)
#define cmax(a,b)	a=max(a,b)
#define cmin(a,b)	a=min(a,b)
#define Auto(i,node)	for(int i=LINK[node];i;i=e[i].next)
const int MAXN=2e5+5;
const int oo=0x3f3f3f3f;
inline int read(){
	char ch=getchar();int x=0,f=1;
	while(ch>‘9‘||ch<‘0‘){if(ch==‘-‘)f=-1;ch=getchar();}
	while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
	return x*f;
}
int LINK[MAXN],N,M,len=0,fa[MAXN],dep[MAXN],anc[MAXN],f[MAXN][2][2],fat[MAXN];
bool istop[MAXN];
struct edge{
	int y,next;
}e[MAXN];
namespace solution{
	inline void insert(int x,int y){e[++len].next=LINK[x];LINK[x]=len;e[len].y=y;}
	inline void Insert(int x,int y){insert(x,y);insert(y,x);}
	void DFS(int node,int father,int deep){
		dep[node]=deep+1;fa[node]=father;
		Auto(i,node)if(e[i].y!=father&&!dep[e[i].y])
			DFS(e[i].y,node,deep+1);
	}
	void Prepare(){
		N=read();M=read();
		up(i,1,M){
			int x=read(),y=read();
			Insert(x,y);
		}
		DFS(1,0,0);
		up(node,1,N)Auto(i,node){
			if(dep[e[i].y]<dep[node]&&e[i].y!=fa[node]){
				istop[e[i].y]=1;
				anc[node]=e[i].y;
				int tmp=node;
				while(tmp!=e[i].y){
					fat[tmp]=e[i].y;
					tmp=fa[tmp];
				}
			}
		}
	}
	int TreeDP(int node,int OK,int OKanc){
		if(f[node][OK][OKanc]!=-1)return f[node][OK][OKanc];
		f[node][OK][OKanc]=0;
		if(OK){
			if(anc[node]&&OKanc)return f[node][OK][OKanc];
			Auto(i,node)if(dep[e[i].y]==dep[node]+1){
				if(fat[e[i].y]==node&&istop[node])
					f[node][OK][OKanc]+=TreeDP(e[i].y,0,1);
				else f[node][OK][OKanc]+=TreeDP(e[i].y,0,OKanc);
			}
			f[node][OK][OKanc]++;
		}else{
			Auto(i,node)if(dep[e[i].y]==dep[node]+1){
				if(fat[e[i].y]==node&&istop[node]){
					f[node][OK][OKanc]+=max(TreeDP(e[i].y,0,0),TreeDP(e[i].y,1,0));
				}
				else f[node][OK][OKanc]+=max(TreeDP(e[i].y,0,OKanc),TreeDP(e[i].y,1,OKanc));
			}			
		}
		return f[node][OK][OKanc];
	}
}
int main(){
	//freopen("input.in","r",stdin);
	using namespace solution;
	Prepare();
	memset(f,-1,sizeof(f));
	cout<<max(TreeDP(1,1,1),TreeDP(1,0,0))<<endl;
	return 0;
}