2870: 最长道路tree

链接

https://www.lydsy.com/JudgeOnline/problem.php?id=2870

思路

先把树转化为二叉树

再链分治

%%yyb

代码

#include <iostream>
#include <algorithm>
#include <cstring>
#include <utility>
#include <cstdio>
#include <vector>
#define ll long long
using namespace std;
const int N=4e5+7,inf=0x3f3f3f3f;
int read() {
    int x=0,f=1;char s=getchar();
    for(;s>'9'||s<'0';s=getchar()) if(s=='-') f=-1;
    for(;s>='0'&&s<='9';s=getchar()) x=x*10+s-'0';
    return x*f;
}
int n,sdgzy,w[N];
ll ans;
struct node {
    int v,nxt,w;
}e[N];
int head[N],mvp;
void Add(int u,int v,int q) {
    e[++mvp].v=v;
    e[mvp].w=q;
    e[mvp].nxt=head[u];
    head[u]=mvp;
}
vector<int> G[N];
void dfs(int u,int f) {
    for(int i=head[u];i;i=e[i].nxt) {
        int v=e[i].v;
        if(v==f) continue;
        G[u].push_back(v);
        dfs(v,u);
    }
}
void rebuild() {
    mvp=1,memset(head,0,sizeof(head));
    for(int i=1;i<=n;++i) {
        int tmp=G[i].size();
        if(tmp<=2) {
            for(int j=0;j<tmp;++j) Add(i,G[i][j],G[i][j]<=sdgzy),Add(G[i][j],i,G[i][j]<=sdgzy);
        } else {
            int a=++n,b=++n;w[a]=w[b]=w[i];
            Add(a,i,0),Add(i,a,0),Add(b,i,0),Add(i,b,0);
            for(int j=0;j<tmp;++j) {
                if(j&1) G[a].push_back(G[i][j]);
                else G[b].push_back(G[i][j]);
            }
        }
    }
}
bool vis[N];
int rt,rt_val,siz[N];
void get_rt(int u,int f,int tot) {
    siz[u]=1;
    for(int i=head[u];i;i=e[i].nxt) {
        int v=e[i].v;
        if(vis[i>>1]||v==f) continue;
        get_rt(v,u,tot);
        siz[u]+=siz[v];
        int tmp=max(siz[v],tot-siz[v]);
        if(tmp<rt_val) rt_val=tmp,rt=i;
    }
}
int top[2];
pair<int,int> SX[2][N];
void get_dis(int u,int f,int mi,int dep,int opt) {
    mi=min(mi,w[u]);
    SX[opt][++top[opt]]=make_pair(mi,dep);
    for(int i=head[u];i;i=e[i].nxt) {
        int v=e[i].v;
        if(vis[i>>1]||v==f) continue;
        get_dis(v,u,mi,dep+e[i].w,opt);
    }
}
bool cmp(pair<int,int> a,pair<int,int> b) {return a>b;}
void solve(int u,int tot) {
    rt_val=inf;
    get_rt(u,0,tot);
    if(rt_val >= inf) return;
    vis[rt>>1]=1;
    ll ls=e[rt].v,rs=e[rt^1].v;//bian fen zhi
    top[0]=top[1]=0;
    get_dis(ls,u,inf,0,0);
    get_dis(rs,u,inf,0,1);
    sort(SX[0]+1,SX[0]+1+top[0],cmp);
    sort(SX[1]+1,SX[1]+1+top[1],cmp);
    int ma=0;
    for(int i=1,j=1;i<=top[0];++i) {
        while(j<=top[1]&&SX[1][j].first>=SX[0][i].first) ma=max(ma,SX[1][j].second),j++;
        if(j-1<=top[1]&&SX[1][j-1].first>=SX[0][i].first)
        ans=max(ans,1LL*SX[0][i].first*(SX[0][i].second+ma+1+e[rt].w));//dian = bian + 1
        // if(j>top[1]) break;
    }
    ma=0;
    for(int i=1,j=1;i<=top[1];++i) {
        while(j<=top[0]&&SX[0][j].first>=SX[1][i].first) ma=max(ma,SX[0][j].second),j++;
        if(j-1<=top[0]&&SX[0][j-1].first>=SX[1][i].first)
            ans=max(ans,1LL*SX[1][i].first*(SX[1][i].second+ma+1+e[rt].w));
        // if(j>top[0]) break;
    }
    int a=siz[ls],b=tot-a;
    solve(ls,a);
    solve(rs,b);
}
int main() {
    // freopen("a.in","r",stdin);
    // freopen("a.out","w",stdout);
    n=read();sdgzy=n;
    for(int i=1;i<=n;++i) w[i]=read();
    for(int i=1;i<n;++i) {
        int x=read(),y=read();
        Add(x,y,0),Add(y,x,0);
    }
    dfs(1,0);
    rebuild();
    solve(1,n);
    cout<<ans<< "\n";
    return 0;
}