LCA 倍增||树链剖分

方法1:倍增

1498ms

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=5e5+;
inline int read(){
    char c=getchar();int x=,f=;
    while(c<''||c>''){if(c=='-')f=-;c=getchar();}
    while(c>=''&&c<=''){x=x*+c-'';c=getchar();}
    return x*f;
}
int n,q,root,a,b;
struct edge{
    int v,ne;
}e[N<<];
int cnt=,h[N];
inline void ins(int u,int v){
    cnt++;
    e[cnt].v=v;e[cnt].ne=h[u];h[u]=cnt;
    cnt++;
    e[cnt].v=u;e[cnt].ne=h[v];h[v]=cnt;
}
int fa[N][],deep[N],vis[N];
void dfs(int u){
    vis[u]=;
    for(int j=;(<<j)<=deep[u];j++)
        fa[u][j]=fa[fa[u][j-]][j-];
    for(int i=h[u];i;i=e[i].ne){
        int v=e[i].v;
        if(vis[v]) continue;
        deep[v]=deep[u]+;
        fa[v][]=u;
        dfs(v);
    }
}
int lca(int x,int y){
    if(deep[x]<deep[y]) swap(x,y);
    int bin=deep[x]-deep[y];
    for(int i=;i<=;i++)
        if((<<i)&bin) x=fa[x][i];//,printf("x %d\n",i);

    for(int i=;i>=;i--)
        if(fa[x][i]!=fa[y][i]){
            x=fa[x][i];
            y=fa[y][i];
        }
    if(x==y) return x;
    else return fa[x][];
}
int main(int argc, const char * argv[]) {
    n=read();q=read();root=read();
    for(int i=;i<=n-;i++) a=read(),b=read(),ins(a,b);
    dfs(root);
    for(int i=;i<=q;i++){
        a=read();b=read();
        printf("%d\n",lca(a,b));
    }
    return ;
}

方法2:树链剖分

1314ms

让链首深度大的走到重链的父节点直到在一条重链上，返回深度小的节点

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=5e5+;
inline int read(){
    char c=getchar();int x=,f=;
    while(c<''||c>''){if(c=='-')f=-;c=getchar();}
    while(c>=''&&c<=''){x=x*+c-'';c=getchar();}
    return x*f;
}
int n,q,root,a,b;
struct edge{
    int v,ne;
}e[N<<];
int cnt=,h[N];
inline void ins(int u,int v){
    cnt++;
    e[cnt].v=v;e[cnt].ne=h[u];h[u]=cnt;
    cnt++;
    e[cnt].v=u;e[cnt].ne=h[v];h[v]=cnt;
}
int fa[N],deep[N],mx[N],size[N];
void dfs(int u){
    size[u]++;
    for(int i=h[u];i;i=e[i].ne){
        int v=e[i].v;
        if(v==fa[u]) continue;
        fa[v]=u;deep[v]=deep[u]+;
        dfs(v);
        size[u]+=size[v];
        if(size[v]>size[mx[u]]) mx[u]=v;
    }
}
int tid[N],top[N],tot;
void dfs(int u,int anc){
    if(!u) return;
    tid[u]=++tot;top[u]=anc;
    dfs(mx[u],anc);
    for(int i=h[u];i;i=e[i].ne){
        int v=e[i].v;
        if(v!=fa[u]&&v!=mx[u]) dfs(v,v);
    }
}
int lca(int x,int y){
    while(top[x]!=top[y]){
        if(deep[top[x]]<deep[top[y]]) swap(x,y);
        x=fa[top[x]];
    }
    if(deep[x]>deep[y]) swap(x,y);
    return x;
}
int main(int argc, const char * argv[]) {
    n=read();q=read();root=read();
    for(int i=;i<=n-;i++) a=read(),b=read(),ins(a,b);
    dfs(root);
    dfs(root,root);
    for(int i=;i<=q;i++){
        a=read();b=read();
        printf("%d\n",lca(a,b));
    }
    return ;
}