[二分图 费用流] BZOJ 4514 [Sdoi2016]数字配对

不会有奇环，那么就建二分图

然后跑最大费用流，直到费用小于零为止，处理下零头

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cstring>
#define cl(x) memset(x,0,sizeof(x))
#define oo 1LL<<60
#define V G[p].v
using namespace std;
typedef long long ll;

inline char nc()
{
	static char buf[100000],*p1=buf,*p2=buf;
	if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }
	return *p1++;
}

inline void read(int &x)
{
	char c=nc(),b=1;
	for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;
	for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;
}

const int N=205;

struct edge{
	int u,v,f; ll w;
	int next;
};

edge G[N*N*10];
int head[N],inum=1;

inline void add(int u,int v,ll w,int f,int p){
	G[p].u=u; G[p].v=v; G[p].w=w; G[p].f=f; G[p].next=head[u]; head[u]=p;
}

inline void link(int u,int v,ll w,int f){
	add(u,v,w,f,++inum); add(v,u,-w,0,++inum);
}

int S,T;

const int ND=1000000;
int Q[ND],l,r;
int ins[N],pre[N];
ll dis[N];

ll Mincost,last,Flow; 

inline bool SPFA()
{
	l=r=-1; cl(ins); cl(Q); cl(pre); for (int i=1;i<=T;i++) dis[i]=-oo;
	Q[(++r)%ND]=S; ins[S]=1; dis[S]=0;
	while (l!=r)
	{
		int u=Q[(++l)%ND]; ins[u]=0;
		for (int p=head[u];p;p=G[p].next)
			if (G[p].f && dis[V]<dis[u]+G[p].w)
			{
				dis[V]=dis[u]+G[p].w; pre[V]=p;
				if (!ins[V])
					Q[(++r)%ND]=V,ins[V]=1;
			}
	}
	if (dis[T]==-oo) return 0;
	ll flow=1<<30,cost=dis[T];
	for (int p=pre[T];p;p=pre[G[p].u]) flow=min(flow,(ll)G[p].f);
	last=Mincost;
	Mincost+=flow*cost;
	if (Mincost<0)
	{
		Flow+=last/-cost;
		printf("%lld\n",Flow);
		exit(0);
	}
	Flow+=flow;
	for (int p=pre[T];p;p=pre[G[p].u])
		G[p].f-=flow,G[p^1].f+=flow;
	return 1;
}

int n;
int a[N],b[N],c[N];

const int maxn=100000;
int prime[maxn+5],vst[maxn+5],pnum;

inline void Pre()
{
	for (int i=2;i<=maxn;i++)
		if (!vst[i])
		{
			prime[++pnum]=i;
			for (int j=i+i;j<=maxn;j+=i) vst[j]=1;
		}
}

inline bool Jud(int x){
	if (x==1) return 0;
	for (int i=1;i<=pnum && (ll)prime[i]*prime[i]<=x;i++)
		if (x%prime[i]==0)
			return 0;
	return 1;
}

int tag[N][N];
int clr[N];

void dfs(int u,int c){
	clr[u]=c;
	for (int i=1;i<=n;i++)
		if (i!=u && clr[i]==-1 && tag[i][u])
				dfs(i,c^1);
}

int main()
{
	freopen("t.in","r",stdin);
	freopen("t.out","w",stdout);
	Pre();
	read(n);
	for (int i=1;i<=n;i++) read(a[i]);
	for (int i=1;i<=n;i++) read(b[i]);
	for (int i=1;i<=n;i++) read(c[i]);
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			if ((a[i]%a[j]==0 && Jud(a[i]/a[j])) || (a[j]%a[i]==0 && Jud(a[j]/a[i])))
				tag[i][j]=1;
	memset(clr,-1,sizeof(clr));
	for (int i=1;i<=n;i++)
		if (clr[i]==-1)
			dfs(i,0);
	S=n+1; T=n+2;
	for (int i=1;i<=n;i++)
		if (!clr[i])
			link(S,i,0,b[i]);
		else
			link(i,T,0,b[i]);
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			if (!clr[i] && clr[j] && tag[i][j])
				link(i,j,(ll)c[i]*c[j],1<<30);
	while (SPFA());
	printf("%lld\n",Flow);
	return 0;
}