链接

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题解

做法一(TLE)：

维护每个点到最远的儿子的距离disxdis_xdisx
设yyy的左右儿子为a,ba,ba,b，那么以yyy为lcalcalca的最长链的长度就是disa+disbdis_a+dis_bdisa+disb

每次给一个叶子挂上两个孩子，都会影响到包含这个叶子结点的一条链的disdisdis和fff值，拿树剖+线段树维护一下就可以了

时间复杂度O(nlog2n)O(nlog^2n)O(nlog2n)

做法二(TLE)：
分析同上，拿lctlctlct去维护这个东西，时间复杂度O(nlogn)O(nlogn)O(nlogn)

都知道splaysplaysplay常数大，所以TTT掉也是没办法的事请

做法三(AC):

要用到一定的树的知识，直径的求法就是从任意一个点出发找到离这个点最远的点，假设这个最远的点是uuu，那么可以证明uuu肯定是直径的端点，再从uuu出发找最远点vvv，则路径(u,v)(u,v)(u,v)就是直径

考虑新加入的点xxx，如果新树的直径包含xxx，那么要么是(u,x)(u,x)(u,x)，要么是(v,x)(v,x)(v,x)，直接更新一下就好了

代码一(TLE)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define iinf 0x3f3f3f3f
#define linf (1ll<<60)
#define eps 1e-8
#define maxn 1000010
#define maxe 1000010
#define maxk 19
#define cl(x) memset(x,0,sizeof(x))
#define rep(_,__) for(_=1;_<=(__);_++)
#define em(x) emplace(x)
#define emb(x) emplace_back(x)
#define emf(x) emplace_front(x)
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
ll read(ll x=0)
{ll c, f(1);for(c=getchar();!isdigit(c);c=getchar())if(c=='-')f=-f;for(;isdigit(c);c=getchar())x=x*10+c-0x30;return f*x;
}
struct Graph
{int etot, head[maxn], to[maxe], next[maxe], w[maxe];void clear(int N){for(int i=1;i<=N;i++)head[i]=0;etot=0;}void adde(int a, int b, int c=0){to[++etot]=b;w[etot]=c;next[etot]=head[a];head[a]=etot;}
}G;
struct ShuLianPouFen
{int size[maxn], top[maxn], tid[maxn], tim, untid[maxn], deep[maxn], son[maxn], fa[maxn];void dfs1(Graph &G, int pos){int p, v;size[pos]=1;for(p=G.head[pos];p;p=G.next[p]){if((v=G.to[p])==fa[pos])continue;fa[v]=pos;deep[v]=deep[pos]+1;dfs1(G,v);if(size[v]>size[son[pos]])son[pos]=v;size[pos]+=size[v];}}void dfs2(Graph &G, int pos, int tp){int p, v;top[pos]=tp;tid[pos]=++tim;untid[tid[pos]]=pos;if(son[pos])dfs2(G,son[pos],tp);for(p=G.head[pos];p;p=G.next[p])if((v=G.to[p])!=fa[pos] and v!=son[pos])dfs2(G,v,v);}void run(Graph &G, int root){tim=0;deep[root]=1;dfs1(G,root);dfs2(G,root,root);}
}sp;
struct SegmentTree
{#define inf 0x3f3f3f3fint mx[maxn<<2], add[maxn<<2], L[maxn<<2], R[maxn<<2];void maketag_add(int o, int v){add[o]+=v;mx[o]+=v;}void pushdown(int o){if(L[o]==R[o])return;if(add[o]){maketag_add(o<<1,add[o]);maketag_add(o<<1|1,add[o]);add[o]=0;}}void pushup(int o){mx[o]=max(mx[o<<1],mx[o<<1|1]);}void build(int o, int l, int r){int mid(l+r>>1);L[o]=l, R[o]=r;add[o]=0;if(l==r){return;}build(o<<1,l,mid);build(o<<1|1,mid+1,r);pushup(o);}void segadd(int o, int l, int r, int v){int mid(L[o]+R[o]>>1);if(l<=L[o] and r>=R[o]){maketag_add(o,v);return;}pushdown(o);if(l<=mid)segadd(o<<1,l,r,v);if(r>mid)segadd(o<<1|1,l,r,v);pushup(o);}int segmax(int o, int l, int r){int mid(L[o]+R[o]>>1), ans(-inf);if(l<=L[o] and r>=R[o])return mx[o];pushdown(o);if(l<=mid)ans=max(ans,segmax(o<<1,l,r));if(r>mid)ans=max(ans,segmax(o<<1|1,l,r));return ans;}#undef inf
}dep, f;
struct Doubling_LCA
{int f[maxn][maxk+1], depth[maxn];void clear(int n){for(int i=1;i<=n;i++)depth[i]=0, cl(f[i]);}void dfs(Graph &G, int pos, int pre){for(auto k=1;(1<<k)<=depth[pos];k++)f[pos][k]=f[f[pos][k-1]][k-1];for(auto p(G.head[pos]);p;p=G.next[p])if(G.to[p]!=pre){f[G.to[p]][0]=pos;depth[G.to[p]]=depth[pos]+1;dfs(G,G.to[p],pos);}}void run(Graph &G, int root){depth[root]=1;dfs(G,root,0);}int q(int x, int y){if(depth[x]<depth[y])swap(x,y);for(auto k(maxk);~k;k--)if(depth[f[x][k]]>=depth[y])x=f[x][k];if(x==y)return x;for(auto k(maxk);~k;k--)if(f[x][k]!=f[y][k])x=f[x][k], y=f[y][k];return f[x][0];}int jp(int x, int b){for(auto k=0;k<=maxk;k++)if(b&(1<<k))x=f[x][k];return x;}
}db;
void add(SegmentTree &t, int x, int y, int v)
{int tx=sp.top[x];while(tx!=sp.top[y]){t.segadd(1,sp.tid[tx],sp.tid[x],v);x=sp.fa[tx], tx=sp.top[x];}t.segadd(1,sp.tid[y],sp.tid[x],v);
}
int v[maxn];
int main()
{int q, n=4, i, cnt;q=read();G.adde(1,2), G.adde(1,3), G.adde(1,4);rep(i,q){v[i]=read();G.adde(v[i],n+1);G.adde(v[i],n+2);n+=2;}sp.run(G,1);db.run(G,1);dep.build(1,1,n);f.build(1,1,n);dep.segadd(1,sp.tid[1],sp.tid[1],+2);dep.segadd(1,sp.tid[2],sp.tid[2],+2);dep.segadd(1,sp.tid[3],sp.tid[3],+2);dep.segadd(1,sp.tid[4],sp.tid[4],+2);cnt=4;rep(i,q){int x=v[i];for(int k=maxk;~k;k--)if(db.f[x][k]!=0 and dep.segmax(1,sp.tid[db.f[x][k]],sp.tid[db.f[x][k]])<sp.deep[v[i]]+1)x=db.f[x][k];add(dep,v[i],x,+1);add(dep,cnt+1,cnt+1,+sp.deep[cnt+1]);add(dep,cnt+2,cnt+2,+sp.deep[cnt+2]);add(f,v[i],x==1?1:sp.fa[x],+1);add(f,v[i],v[i],+1);int ans=f.segmax(1,2,n);int d2, d3, d4;d2=dep.segmax(1,sp.tid[2],sp.tid[2])-1;d3=dep.segmax(1,sp.tid[3],sp.tid[3])-1;d4=dep.segmax(1,sp.tid[4],sp.tid[4])-1;ans=max(ans,d2+d3), ans=max(ans,d3+d4), ans=max(ans,d2+d4);printf("%d\n",ans);cnt+=2;}return 0;
}

代码二(TLE)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define iinf 0x3f3f3f3f
#define linf (1ll<<60)
#define eps 1e-8
#define maxn 1000010
#define maxe 1000010
#define maxk 19
#define cl(x) memset(x,0,sizeof(x))
#define rep(_,__) for(_=1;_<=(__);_++)
#define em(x) emplace(x)
#define emb(x) emplace_back(x)
#define emf(x) emplace_front(x)
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
ll read(ll x=0)
{ll c, f(1);for(c=getchar();!isdigit(c);c=getchar())if(c=='-')f=-f;for(;isdigit(c);c=getchar())x=x*10+c-0x30;return f*x;
}
struct Graph
{int etot, head[maxn], to[maxe], next[maxe], w[maxe];void clear(int N){for(int i=1;i<=N;i++)head[i]=0;etot=0;}void adde(int a, int b, int c=0){to[++etot]=b;w[etot]=c;next[etot]=head[a];head[a]=etot;}
}G;
struct LinkCutTree
{int rev[maxn], f[maxn], ch[maxn][2], s[maxn], mx[maxn], add[maxn], v[maxn];int getwh(int x){if(f[x]==0)return -1;if(ch[f[x]][0]==x)return 0;if(ch[f[x]][1]==x)return 1;return -1;}bool isroot(int x){return getwh(x)==-1;}void maketag_rev(int x){if(x)rev[x]^=1;}void maketag_add(int x, int v){if(x)add[x]+=v;}void join(int x, int y, int wh){if(x)f[x]=y;if(y)ch[y][wh]=x;}void pushdown(int x){if(rev[x]){swap(ch[x][0],ch[x][1]);maketag_rev(ch[x][0]), maketag_rev(ch[x][1]);rev[x]=0;}if(add[x]){v[x]+=add[x];mx[x]+=add[x];maketag_add(ch[x][0],add[x]);maketag_add(ch[x][1],add[x]);add[x]=0;}}void pushup(int x){pushdown(ch[x][0]), pushdown(ch[x][1]);mx[x]=v[x];if(ch[x][0])mx[x]=max(mx[x],mx[ch[x][0]]);if(ch[x][1])mx[x]=max(mx[x],mx[ch[x][1]]);}void rotate(int x){int y=f[x], z=f[y];int c=getwh(x);if(!isroot(y))join(x,z,getwh(y));else f[x]=z;join(ch[x][!c],y,c);join(y,x,!c);pushup(y);pushup(x);}void splay(int x){int y, top(0);for(y=x;!isroot(y);y=f[y])s[++top]=y;s[++top]=y;for(;top;top--)pushdown(s[top]);while(!isroot(x)){y=f[x];if(isroot(y)){rotate(x);break;}if(getwh(x)^getwh(y))rotate(x);else rotate(y);rotate(x);}}void access(int x){int t=0;while(x){splay(x);ch[x][1]=t;pushup(x);t=x;x=f[x];}}void makeroot(int x){access(x);splay(x);maketag_rev(x);}void link(int x, int y){makeroot(x);f[x]=y;}void cut(int x, int y){makeroot(x); access(y);splay(y);if(ch[y][0]==x and ch[x][1]==0)f[x]=ch[y][0]=0;}int findroot(int x){access(x); splay(x);while(ch[x][0])pushdown(x), x=ch[x][0];splay(x);return x;}
}f, dep;
struct Doubling_LCA
{int f[maxn][maxk+1], depth[maxn];void clear(int n){for(int i=1;i<=n;i++)depth[i]=0, cl(f[i]);}void dfs(Graph &G, int pos, int pre){for(auto k=1;(1<<k)<=depth[pos];k++)f[pos][k]=f[f[pos][k-1]][k-1];for(auto p(G.head[pos]);p;p=G.next[p])if(G.to[p]!=pre){f[G.to[p]][0]=pos;depth[G.to[p]]=depth[pos]+1;dfs(G,G.to[p],pos);}}void run(Graph &G, int root){depth[root]=1;dfs(G,root,0);}int q(int x, int y){if(depth[x]<depth[y])swap(x,y);for(auto k(maxk);~k;k--)if(depth[f[x][k]]>=depth[y])x=f[x][k];if(x==y)return x;for(auto k(maxk);~k;k--)if(f[x][k]!=f[y][k])x=f[x][k], y=f[y][k];return f[x][0];}int jp(int x, int b){for(auto k=0;k<=maxk;k++)if(b&(1<<k))x=f[x][k];return x;}
}db;
void add(LinkCutTree &t, int x, int y, int v)
{t.makeroot(y);t.access(x);t.splay(x);t.maketag_add(x,v);
}
int qmax(LinkCutTree &t, int x, int y)
{t.makeroot(y);t.access(x);t.splay(x);return t.mx[x];
}
int v[maxn];
int main()
{int q, n=4, i, cnt, ans=0;q=read();G.adde(1,2), G.adde(1,3), G.adde(1,4);rep(i,q){v[i]=read();G.adde(v[i],n+1);G.adde(v[i],n+2);n+=2;}db.run(G,1);for(i=2;i<=4;i++)dep.v[i]=2;cnt=4;rep(i,q){int x=v[i];for(int k=maxk;~k;k--)if(db.f[x][k]>1){dep.splay(db.f[x][k]);if(dep.v[db.f[x][k]]<db.depth[v[i]]+1)x=db.f[x][k];}add(dep,v[i],x,+1);add(f,v[i],db.f[x][0]==1?x:db.f[x][0],+1);add(f,v[i],v[i],+1);ans=max(ans,qmax(f,v[i],db.f[x][0]==1?x:db.f[x][0]));dep.link(cnt+1,v[i]); dep.v[cnt+1]=dep.mx[cnt+1]=db.depth[cnt+1];dep.link(cnt+2,v[i]); dep.v[cnt+2]=dep.mx[cnt+1]=db.depth[cnt+2];f.link(cnt+1,v[i]);f.link(cnt+2,v[i]);int d2, d3, d4;d2=qmax(dep,2,2)-1;d3=qmax(dep,3,3)-1;d4=qmax(dep,4,4)-1;ans=max(ans,d2+d3), ans=max(ans,d3+d4), ans=max(ans,d2+d4);printf("%d\n",ans);cnt+=2;}return 0;
}

代码三（AC）

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define iinf 0x3f3f3f3f
#define linf (1ll<<60)
#define eps 1e-8
#define maxn 1000010
#define maxe 1000010
#define maxk 19
#define cl(x) memset(x,0,sizeof(x))
#define rep(_,__) for(_=1;_<=(__);_++)
#define em(x) emplace(x)
#define emb(x) emplace_back(x)
#define emf(x) emplace_front(x)
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
ll read(ll x=0)
{ll c, f(1);for(c=getchar();!isdigit(c);c=getchar())if(c=='-')f=-f;for(;isdigit(c);c=getchar())x=x*10+c-0x30;return f*x;
}
struct Graph
{int etot, head[maxn], to[maxe], next[maxe], w[maxe];void clear(int N){for(int i=1;i<=N;i++)head[i]=0;etot=0;}void adde(int a, int b, int c=0){to[++etot]=b;w[etot]=c;next[etot]=head[a];head[a]=etot;}
}G;
struct Doubling_LCA
{int f[maxn][maxk+1], depth[maxn];void clear(int n){for(int i=1;i<=n;i++)depth[i]=0, cl(f[i]);}void dfs(Graph &G, int pos, int pre){for(auto k=1;(1<<k)<=depth[pos];k++)f[pos][k]=f[f[pos][k-1]][k-1];for(auto p(G.head[pos]);p;p=G.next[p])if(G.to[p]!=pre){f[G.to[p]][0]=pos;depth[G.to[p]]=depth[pos]+1;dfs(G,G.to[p],pos);}}void run(Graph &G, int root){depth[root]=1;dfs(G,root,0);}int q(int x, int y){if(depth[x]<depth[y])swap(x,y);for(auto k(maxk);~k;k--)if(depth[f[x][k]]>=depth[y])x=f[x][k];if(x==y)return x;for(auto k(maxk);~k;k--)if(f[x][k]!=f[y][k])x=f[x][k], y=f[y][k];return f[x][0];}int jp(int x, int b){for(auto k=0;k<=maxk;k++)if(b&(1<<k))x=f[x][k];return x;}
}db;
int v[maxn];
int qdis(int x, int y)
{int lca=db.q(x,y);return db.depth[x]+db.depth[y]-2*db.depth[lca];
}
int main()
{int q, n=4, i, cnt, ans=2, a, b;q=read();G.adde(1,2), G.adde(1,3), G.adde(1,4);rep(i,q){v[i]=read();G.adde(v[i],n+1);G.adde(v[i],n+2);n+=2;}db.run(G,1);a=2,b=3;cnt=4;rep(i,q){int p=qdis(a,cnt+1)>qdis(b,cnt+1)?a:b;if(qdis(p,cnt+1)>ans)ans=qdis(p,cnt+1), a=p, b=cnt+1;printf("%d\n",ans);cnt+=2;}return 0;
}

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cf379F. New Year Tree

链接

题解

代码一(TLE)

代码二(TLE)

代码三（AC）

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