洛谷3703 [SDOI2017] 树点染色 【LCT】【线段树】

题目分析：

　　操作一很明显等价于LCT上的access操作，操作二是常识，操作三转化到dfs序上求最大值也是常识。access的时候顺便在线段树中把对应部分-1，把右子树的子树+1即可。

代码：

#include<bits/stdc++.h>
using namespace std;

const int maxn = 102000;

int num,n,m;

vector <int> g[maxn];

int f[maxn],dep[maxn],dfsin[maxn],dfsout[maxn];

class SegmentTree{
private:
    int data[maxn<<2],lazy[maxn<<2],maxx[maxn<<2];
    void push_down(int now){
    int L = (now<<1),R = (now<<1|1);
    data[L] += lazy[now]; maxx[L] += lazy[now]; lazy[L] += lazy[now];
    data[R] += lazy[now]; maxx[R] += lazy[now]; lazy[R] += lazy[now];
    lazy[now] = 0;
    }
public:
    void Add(int now,int tl,int tr,int l,int r,int d){
    if(lazy[now]&&tl!=tr) push_down(now);
    if(tl >= l && tr <= r){
        data[now] += d; lazy[now] += d;maxx[now] += d; return;
    }
    if(tl > r || tr < l) return;
    int mid = (tl+tr)/2;
    Add(now<<1,tl,mid,l,r,d);
    Add(now<<1|1,mid+1,tr,l,r,d);
    maxx[now] = max(maxx[now<<1],maxx[now<<1|1]);
    }
    int Query(int now,int tl,int tr,int l,int r){
    if(lazy[now]&&tl!=tr) push_down(now);
    if(tl >= l && tr <= r) return maxx[now];
    if(tl > r || tr < l) return 0;
    int mid = (tl+tr)/2;
    int ans = max(Query(now<<1,tl,mid,l,r),Query(now<<1|1,mid+1,tr,l,r));
    maxx[now] = max(maxx[now<<1],maxx[now<<1|1]);
    return ans;
    }
}T;

class LinkCutTree{
private:
    int ch[maxn][2],fa[maxn],data[maxn];
    stack <int> sta;
 
    int is_root(int now){return ch[fa[now]][0]!=now&&ch[fa[now]][1]!=now;}
    
    void r0(int now,int dr){
    int son = ch[now][dr],pa = fa[now],gp = fa[pa];
    int tag = is_root(pa);
    ch[pa][dr^1] = son; fa[son] = pa;
    ch[now][dr] = pa; fa[pa] = now; fa[now] = gp;
    if(tag == 1) return;
    if(ch[gp][0] == pa) ch[gp][0] = now;
    else ch[gp][1] = now;
    }

    void splay(int now){
    while(!is_root(now)){
        int pa = fa[now],gp = fa[pa];
        if(is_root(pa)){
        if(ch[pa][0] == now) r0(now,1);
        else r0(now,0);
        }else{
        if(ch[gp][0] == pa){
            if(ch[pa][0] == now) r0(pa,1),r0(now,1);
            else r0(now,0),r0(now,1);
        }else{
            if(ch[pa][0] == now) r0(now,1),r0(now,0);
            else r0(pa,0),r0(now,0);
        }
        }
    }
    }
public:
    void access(int now){
    int p = now,last = 0;
    while(p != 0){
        splay(p);
        int zz = ch[p][1]; while(ch[zz][0]) zz = ch[zz][0];
        if(zz)T.Add(1,1,n,dfsin[zz],dfsout[zz],1);
        int lt = p; while(ch[lt][0]) lt = ch[lt][0];
        T.Add(1,1,n,dfsin[lt],dfsout[lt],-1);
        ch[p][1] = last;
        last = p; p = fa[p];
    }
    T.Add(1,1,n,1,n,1);
    }
    void BuildLCT(){
    for(int i=1;i<=n;i++) data[i] = dep[i];
    for(int i=1;i<=n;i++) fa[i] = f[i];
    }
}LCT;

void read(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<n;i++){
    int u,v; scanf("%d%d",&u,&v);
    g[u].push_back(v); g[v].push_back(u);
    }
}

int RMQ[maxn<<1][20],app[maxn][2],euler[maxn<<1],nE;

void dfs(int now,int fa,int dp){
    f[now] = fa; dep[now] = dp;
    euler[++nE] = now; app[now][0] = app[now][1] = nE;
    dfsin[now] = dfsout[now] = ++num;
    T.Add(1,1,n,dfsin[now],dfsin[now],dp);
    for(int i=0;i<g[now].size();i++){
    int p = g[now][i];
    if(p == fa) continue;
    dfs(p,now,dp+1);
    dfsout[now] = dfsout[p];
    euler[++nE] = now; app[now][1] = nE;
    }
}

void BuildRMQ(){
    for(int i=1;i<=nE;i++) RMQ[i][0] = euler[i];
    for(int k=1;(1<<k)<=nE;k++){
    for(int i=1;i<=nE;i++){
        if(i+(1<<k-1) > nE) {RMQ[i][k] = RMQ[i][k-1];continue;}
        if(dep[RMQ[i][k-1]] < dep[RMQ[i+(1<<k-1)][k-1]]){
        RMQ[i][k] = RMQ[i][k-1];
        }else RMQ[i][k] = RMQ[i+(1<<k-1)][k-1];
    }
    }
}

int QueryLCA(int u,int v){
    int fst = min(app[u][0],app[v][0]),sec = max(app[u][1],app[v][1]);
    int len = sec-fst+1,k = 0;
    while((1<<k+1) <= len) k++;
    if(dep[RMQ[fst][k]] < dep[RMQ[sec-(1<<k)+1][k]]) return RMQ[fst][k];
    else return RMQ[sec-(1<<k)+1][k];
}

void init(){
    dfs(1,0,1);
    BuildRMQ();
    LCT.BuildLCT();
}

void getdist(){
    int u,v; scanf("%d%d",&u,&v);
    int lca = QueryLCA(u,v);
    u = dfsin[u],v = dfsin[v],lca = dfsin[lca];
    int ans = T.Query(1,1,n,u,u)+T.Query(1,1,n,v,v);
    ans = ans - 2*T.Query(1,1,n,lca,lca) + 1;
    printf("%d\n",ans);
}

void Query(){
    int u; scanf("%d",&u);
    int ans = T.Query(1,1,n,dfsin[u],dfsout[u]);
    printf("%d\n",ans);
}

void work(){
    for(int i=1;i<=m;i++){
    int cas; scanf("%d",&cas);
    if(cas == 1){int x;scanf("%d",&x);LCT.access(x);}
    else if(cas == 2) getdist();
    else if(cas == 3) Query();
    }
}

int main(){
    read();
    init();
    work();
    return 0;
}