[Luogu] 模板题-最近公共祖先

树链剖分版本：

#include<cstdio>
#include<iostream>
#define maxn 1000000
using namespace std;

int siz[maxn],fa[maxn],depth[maxn],son[maxn],top[maxn],n,m,s;

struct edge{
    int from,v;
}e[maxn];
int tot,first[maxn];
void insert(int u,int v){
    tot++; e[tot].from = first[u]; e[tot].v = v; first[u] = tot;
}

void dfs(int now){
    siz[now] = 1;
    for(int i = first[now];i;i = e[i].from){
        int v = e[i].v;
        if(v != fa[now]){
            fa[v] = now;
            depth[v] = depth[now]+1;
            dfs(v);
            siz[now] += siz[v];
            if(!son[now] || siz[v] > siz[son[now]])
                son[now] = v;
        }
    }
}

void dfs2(int now,int t){
    top[now] = t;
    if(!son[now]) return;
    dfs2(son[now],t);
    for(int i = first[now];i;i = e[i].from){
        int v = e[i].v;
        if(v != fa[now] && v != son[now])
            dfs2(v,v);
    }
}

int LCA(int u,int v){
    if(depth[top[u]] < depth[top[v]]) swap(u,v);
    while(top[u] != top[v]){
        u = fa[top[u]];
        if(depth[top[u]] < depth[top[v]]) swap(u,v);
    }if(depth[u] < depth[v]) swap(u,v);
    return v;
}

int main(){
    scanf("%d%d%d",&n,&m,&s);
    
    for(int i = 1;i < n;i++){
        int x,y; scanf("%d%d",&x,&y);
        insert(x,y); insert(y,x);
    }depth[s] = 1; dfs(s); dfs2(s,s);
    
    while(m--){
        int u,v;
        scanf("%d%d",&u,&v);
        printf("%d
",LCA(u,v));
    }
    
    return 0;
}

Tarjan版本：

#include<cstdio>
#include<iostream>
#include<algorithm>
#define maxn 500005
using namespace std;

struct edge{
    int from,u,v,ans,order;
}e[maxn*2+5],e1[maxn*2+5];

int pre[maxn];
int find(int x){
    if(!pre[x]) return x;
    else{
        pre[x] = find(pre[x]);
        return pre[x];
    }
}

bool book[maxn];
int tot,tot1,first1[maxn],first[maxn],n,m,s;
void insert(int u,int v){
    tot++;
    e[tot].from = first[u];
    e[tot].v = v;
    e[tot].u = u;
    first[u] = tot;
}

void insert1(int u,int v,int i){
    tot1++;
    e1[tot1].order = i;
    e1[tot1].from = first1[u];
    e1[tot1].u = u;
    e1[tot1].v = v;
    first1[u] = tot1;
}

bool cmp(const edge &a,const edge &b){
    return a.order < b.order;
}

void Tarjan(int now,int father){
    for(int i = first[now];i;i = e[i].from){
        int v = e[i].v;
        if(v == father) continue;
        Tarjan(v,now);
        pre[find(v)] = find(now);
        book[v] = true;
    }
    
    for(int i = first1[now];i;i = e1[i].from){
        int v = e1[i].v;
        if(v == father) continue;
        if(book[v]){
            e1[i].ans = find(v);
        }
    }
}

int main(){
    scanf("%d%d%d",&n,&m,&s);
    for(int i = 1;i < n;i++){
        int a,b;
        scanf("%d%d",&a,&b);
        insert(a,b);
        insert(b,a);
    }
    
    for(int i = 1;i <= m;i++){
        int a,b;
        scanf("%d%d",&a,&b);
        insert1(a,b,i);
        insert1(b,a,i);
    }
    
    Tarjan(s,-1);
    
    sort(e1+1,e1+1+tot1,cmp);
    
    for(int i = 1;i <= tot1;i+=2){
        if(!e1[i].ans) printf("%d
",e1[i+1].ans);
        else printf("%d
",e1[i].ans);
    }
    
    return 0;
}