[BZOJ1977/BeiJing2010组队]次小生成树 Tree

Description

Input

Output

Sample Input
5 6
1 2 1
1 3 2
2 4 3
3 5 4
3 4 3
4 5 6

Sample Output
11

HINT

50% 的数据N≤2 000 M≤3 000；
80% 的数据N≤50 000 M≤100 000；
100% 的数据N≤100 000 M≤300 000 ，边权值非负且不超过 10^9 。

/*program from Wolfycz*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x7f7f7f7f
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
int x=0,f=1;char ch=getchar();
for (;ch<'0'||ch>'9';ch=getchar())	if (ch=='-')    f=-1;
for (;ch>='0'&&ch<='9';ch=getchar())	x=(x<<1)+(x<<3)+ch-'0';
return x*f;
}
inline void print(int x){
if (x>=10)	print(x/10);
putchar(x%10+'0');
}
const int N=1e5,M=3e5;
int v[N+10],dfn[N+10],ID[N+10];
int n,m;
struct S1{
#define ls (p<<1)
#define rs (p<<1|1)
struct node{
int f,g;
node(){f=g=-inf;}
void insert(int _f,int _g){f=_f,g=_g;}
}tree[(N<<2)+10];
friend node operator +(const node &x,const node &y){
node z;
z.f=max(x.f,y.f);
z.g=max(x.g,y.g);
if (x.f!=y.f)	z.g=max(z.g,min(x.f,y.f));
return z;
}
void build(int p,int l,int r){
if (l==r){
tree[p].insert(v[dfn[l]],-inf);
return;
}
int mid=(l+r)>>1;
build(ls,l,mid),build(rs,mid+1,r);
tree[p]=tree[ls]+tree[rs];
}
node Query(int p,int l,int r,int x,int y){
if (x<=l&&r<=y)	return tree[p];
int mid=(l+r)>>1; node res;
if (x<=mid)	res=res+Query(ls,l,mid,x,y);
if (y>mid)	res=res+Query(rs,mid+1,r,x,y);
return res;
}
}ST;//Segment Tree
struct S2{
int pre[(M<<1)+10],now[N+10],child[(M<<1)+10],val[(M<<1)+10];
int top[N+10],Rem[N+10],deep[N+10],size[N+10],fa[N+10];
int tot,Time;
void join(int x,int y,int z){pre[++tot]=now[x],now[x]=tot,child[tot]=y,val[tot]=z;}
void insert(int x,int y,int z){join(x,y,z),join(y,x,z);}
void build(int x){
deep[x]=deep[fa[x]]+1,size[x]=1;
for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
if (son==fa[x])	continue;
fa[son]=x,v[son]=val[p];
build(son),size[x]+=size[son];
if (size[Rem[x]]<size[son])	Rem[x]=son;
}
}
void dfs(int x){
if (!x)	return;
dfn[ID[x]=++Time]=x;
top[x]=Rem[fa[x]]==x?top[fa[x]]:x;
dfs(Rem[x]);
for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
if (son==fa[x]||son==Rem[x])	continue;
dfs(son);
}
}
int Get(int x,int y,int z){
S1::node res;
while (top[x]!=top[y]){
if (deep[top[x]]<deep[top[y]])	swap(x,y);
res=res+ST.Query(1,1,n,ID[top[x]],ID[x]);//+被重载了，在ST结构体里面
x=fa[top[x]];
}
if (x!=y){
if (deep[x]>deep[y])	swap(x,y);
res=res+ST.Query(1,1,n,ID[Rem[x]],ID[y]);
}
if (res.f==-inf&&res.g==-inf)	return inf;//开始没判，后面因为重边导致res两个信息都为-inf，于是炸int了。。。
return z-(z==res.f?res.g:res.f);
}
}HLD;//Heavy-Light Decomposition
struct S3{
int fa[N+10];
void init(){for (int i=1;i<=n;i++)	fa[i]=i;}
int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
}DSU;//Disjoint Set Union
struct S4{
int x,y,z,type;
S4(){type=0;}
bool operator <(const S4 &a)const{return z<a.z;}
}A[M+10];
int main(){
for (int i=1;i<=m;i++)	A[i].insert();
sort(A+1,A+1+m);
DSU.init();
ll MST=0;int Ans=inf;
for (int i=1;i<=m;i++){
int x=DSU.find(A[i].x),y=DSU.find(A[i].y);
if (x!=y)	DSU.fa[x]=y,HLD.insert(A[i].x,A[i].y,A[i].z),A[i].type=1,MST+=A[i].z;
}
HLD.build(1),HLD.dfs(1),ST.build(1,1,n);
for (int i=1;i<=m;i++){
if (A[i].type)	continue;
Ans=min(Ans,HLD.Get(A[i].x,A[i].y,A[i].z));
}
printf("%lld\n",MST+Ans);
return 0;
}


posted @ 2018-10-06 09:50  Wolfycz  阅读(142)  评论(0编辑  收藏  举报