HDU 6982(Road Discount-wqs二分)

Posted 2021-08-31 nike0good

给你一个无向图$n$个点$m$条边，每个边有一个代价$c_i$以及折扣价$d_i$，现在要求对每个$k(0\le k\le n-1)$，求恰取$k$条折扣价的最小生成树的代价是多少。
$n\le 1e3,m\le 2e5,c_i,d_i\le 1e3$

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \\
						For(j,m-1) cout<<a[i][j]<<' ';\\
						cout<<a[i][m]<<endl; \\
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
#define sqr(x) (x*x)
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 

#define MAXN (400000+10) 
int n, m, u[MAXN],v[MAXN],id[MAXN],w[MAXN],d[MAXN],c[MAXN];
bool b[MAXN<<1];
int iid[MAXN],t0=0;
class bingchaji
{
public:
	#define MAXN (1010)
	int father[MAXN],n,cnt;
	void mem(int _n)
	{
		n=cnt=_n;
		For(i,n) father[i]=i;
	}
	int getfather(int x) 
	{
		if (father[x]==x) return x;
		
		return father[x]=getfather(father[x]);
	}
	void unite(int x,int y)
	{
		x=getfather(x);
		y=getfather(y);
		if (x^y) {
			--cnt;
		
			father[x]=y;
		}
	}
	bool same(int x,int y)
	{
		return getfather(x)==getfather(y);
	}
}S;
bool cmp(int i,int j) {
	return w[i]<w[j]||w[i]==w[j]&&i<j;
}
int an[1010];
int M;
int work(int m,bool flag,int &p1) {
	if(!flag){
		For(i,m) id[i]=i;
		sort(id+1,id+1+m,cmp);
	}
	S.mem(n);
	int ans=0;
	For(p,m) {
		int i=id[p];
		if(!S.same(u[i],v[i])){
			S.unite(u[i],v[i]);
			
			p1+=i<=M;
			if(!flag)b[i]=1;
			ans+=w[i];
		}
	}
	return ans;
}
int main()
{
//	freopen("j.in","r",stdin);
//	freopen(".out","w",stdout);
	int T=read();
	For(kcase,T) {
		n=read(),m=read();
		For(i,m) u[i]=read(),v[i]=read(),c[i]=read(),d[i]=read(),b[i]=0;
		int p1=0;
		Rep(i,n) an[i]=INF;
		M=m;
		t0=0;
		
		For(i,m) w[i]=c[i];
		an[n-1]=work(m,0,p1); // no discount
		For(i,m) w[i]=d[i];
		an[0]=work(m,0,p1);
		M=0;
		For(i,m) if(b[i]) {
			++M;
			u[M]=u[i],v[M]=v[i];
			d[M]=d[i],c[M]=c[i];
		}
		m=M;
		For(i,M) u[i+M]=u[i],v[i+M]=v[i],w[i]=c[i],w[i+M]=d[i];
		For(i,M) iid[i]=i; sort(iid+1,iid+1+M,cmp);
		For(i,M) iid[i+M]=i+M; sort(iid+M+1,iid+1+2*M,cmp);
		
		int pr=0;
		Rep(mid,1002){
			For(i,m) w[i]=c[i],w[i+m]=d[i]+mid;
			
			int p1=1,p2=1;
			For(ttt,2*M) {
				if(p1>M) id[ttt]=iid[p2+M],++p2;
				else if(p2>M) id[ttt]=iid[p1],++p1;
				else {
					if(w[iid[p1]]>w[iid[p2+M]]) id[ttt]=iid[p2+M],++p2;
					else id[ttt]=iid[p1],++p1;
				}
			}
			
			
			p1=0;
			int ans=work(2*M,1,p1);
			ans-mid*(n-1-p1);
			
			gmin(an[p1],ans-mid*(n-1-p1))
			if(pr+1<p1) {
				Fork(j,pr+1,p1-1) gmin(an[j],ans-mid*(n-1-j))
			}
			pr=p1;
		}
		RepD(i,n-2) {
			gmin(an[i],an[i+1])
		}
		RepD(i,n-1) printf("%d\\n",an[i]);
	}
	return 0;
}