bzoj1006 [HNOI2008]神奇的国度 弦图最大势染色

Description

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给定一张弦图，给每一对相邻点染上不同颜色，求最少颜色数

Solution

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跟我念，xian图~

关于弦图和最大势算法可以看论文
显然给出的图是弦图，根据结论我们找出完美消除序列然后贪心取mex就可以了

Code

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#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#define rep(i,st,ed) for (int i=st;i<=ed;++i)
#define drp(i,st,ed) for (int i=st;i>=ed;--i)
#define fill(x,t) memset(x,t,sizeof(x))
#define fi first
#define se second

typedef std:: pair <int,int> pair;
const int N=200005;
const int E=2000005;

struct edge {int x,y,next;} e[E];

int label[N],col[N],ls[N],q[N],edCnt,n;

bool vis[N],used[N];

int read() {
	int x=0,v=1; char ch=getchar();
	for (;ch<'0'||ch>'9';v=(ch=='-')?(-1):(v),ch=getchar());
	for (;ch<='9'&&ch>='0';x=x*10+ch-'0',ch=getchar());
	return x*v;
}

void add_edge(int x,int y) {
	e[++edCnt]=(edge) {x,y,ls[x]}; ls[x]=edCnt;
	e[++edCnt]=(edge) {y,x,ls[y]}; ls[y]=edCnt;
}

void MCS() {
	std:: priority_queue <pair> heap;
	rep(i,1,n) heap.push(pair(0,i));
	drp(i,n,1) {
		while (vis[heap.top().se]) heap.pop();
		int x=heap.top().se; heap.pop();
		vis[x]=1; q[i]=x;
		for (int j=ls[x];j;j=e[j].next) {
			if (!vis[e[j].y]) heap.push(pair(++label[e[j].y],e[j].y));
		}
	}
}

void color() {
	int ans=0;
	drp(i,n,1) {
		fill(used,0);
		int x=q[i];
		for (int j=ls[x];j;j=e[j].next) {
			used[col[e[j].y]]=1;
		}
		for (col[x]=1;used[col[x]];col[x]++);
		ans=std:: max(ans,col[x]);
	}
	printf("%d\n", ans);
}

int main(void) {
	freopen("data.in","r",stdin);
	freopen("myp.out","w",stdout);
	n=read(); int m=read();
	rep(i,1,m) {
		int x=read(),y=read();
		add_edge(x,y);
	}
	MCS(); color();
	return 0;
}