【模板】LCA

CODE1： DFS序+RMQ

Time cost：1106ms

// luogu-judger-enable-o2
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#define ms(a,b) memset(a,b,sizeof a)
#define rep(i,a,n) for(int i = a;i <= n;i++)
#define per(i,n,a) for(int i = n;i >= a;i--)
#define inf 2147483647
using namespace std;
typedef long long ll;
ll read() {
    ll as = 0,fu = 1;
    char c = getchar();
    while(c < '0' || c > '9') {
        if(c == '-') fu = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9') {
        as = as * 10 + c - '0';
        c = getchar();
    }
    return as * fu;
}
const int N = 1000005;
//head
int n,m,s,ans;
int head[N],nxt[N],mo[N],cnt;
void add(int x,int y) {
    mo[++cnt] = y;
    nxt[cnt] = head[x];
    head[x] = cnt;
}

int dfn[N],idx;
int a[N<<1],top;
int dep[N];
void dfs(int x,int f,int d) {
    dep[x] = d;
    a[++top] = x;
    dfn[x] = top;
    for(int i = head[x];i;i = nxt[i]) {
        int sn = mo[i];
        if(sn == f) continue;
        dfs(sn,x,d+1);
        a[++top] = x;
    }
}


int st[25][N],pos[25][N];
void initst() {
    rep(i,1,top) st[0][i] = dep[a[i]],pos[0][i] = a[i];
    int r = log2(top);
    rep(i,1,r+1) {
        rep(j,1,top+1-(1<<i)) {
            if(st[i-1][j] <= st[i-1][j+(1<<i-1)]) {
                pos[i][j] = pos[i-1][j];
                st[i][j] = st[i-1][j];
            } else {
                pos[i][j] = pos[i-1][j+(1<<i-1)];
                st[i][j] = st[i-1][j+(1<<i-1)];
            }
        }
    }
}

int query(int l,int r) {
    if(r < l) swap(l,r);
    int len = log2(r-l+1);
    if(st[len][l] < st[len][r+1-(1<<len)]) ans = pos[len][l];
    else ans = pos[len][r+1-(1<<len)];
    return ans;
}

int main() {
    n = read();
    m = read();
    s = read();
    rep(i,2,n) {
        int x = read();
        int y = read();
        add(y,x),add(x,y);
    }
    dfs(s,0,0);
    initst();
    while(m--) {
        int x = read();
        int y = read();
        printf("%d\n",query(dfn[x],dfn[y]));
    }
    return 0;
}

CODE2: 树上倍增

Time cost：1157ms

// luogu-judger-enable-o2
#include<cstdio>
#include<iostream>
#include<cmath>
#include<algorithm>
#define rep(i,a,n) for(int i = a;i <= n;i++)
#define per(i,n,a) for(int i = n;i >= a;i--)
using namespace std;
typedef long long LL;
int read() {
    int ans = 0;
    char ch = getchar(),last=' ';
    while(ch < '0' || ch > '9') {
        last = ch;
        ch = getchar();
    }
    while(ch >= '0' && ch <= '9') {
        ans = ans * 10 + ch - '0';
        ch = getchar();
    }
    if(last == '-')
        ans = -ans;
    return ans;
}
const int N = 500005;
//head

int n,m,k;

struct edge {
    int nxt;//ÓëiÏàÁ¬µÄÉÏÒ»Ìõ±ß
    int mo;//Ä¿µÄµØ
} p[N<<1];

int head[N],dep[N],fa[21][N],cnt;
int lg[N];

void add(int x,int y) {
    p[++cnt].mo = y;
    p[cnt].nxt = head[x];
    head[x] = cnt;
}

void dfs(int u,int pa) {
    dep[u] = dep[pa] + 1;
    fa[0][u] = pa;    
    for(int i = 1; 1<<i <= dep[u]; i++) 
    fa[i][u] = fa[i-1][fa[i-1][u]];
    for(int i = head[u]; i; i = p[i].nxt) {
        int sn = p[i].mo;
        if(sn == pa) continue;
        dfs(sn,u);
    }
    return;
}

int LCA(int x,int y) {
    if(dep[x] < dep[y]) swap(x,y); //x±ÈyÉî 
    while(dep[x] > dep[y]) //±£Ö¤x,yͬһ²ã
        x = fa[ lg[dep[x]-dep[y]] - 1][x];
    if(x == y) return y;
    per(i,lg[dep[x]],0) //Ìøµ½LCAµÄÁ½¸ö¶ù×Ó´¦ 
        if(fa[i][x] != fa[i][y]) {
            x = fa[i][x];
            y = fa[i][y];
        }
    return fa[0][x];
}

int main() { 
    n = read();
    m = read();
    k = read();
    rep(i,1,n-1) {
        int x = read();
        int y = read();
        add(x,y),add(y,x);
    }
    dfs(k,0);
    rep(i,1,n) lg[i] = lg[i-1] + (1<<lg[i-1] == i);
    while(m--) {
        int x = read();
        int y = read();
        printf("%d\n",LCA(x,y));
    }
    return 0;
}

CODE3: 树剖

Time cost：1013ms

// luogu-judger-enable-o2
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cmath>
#define rep(i,a,n) for(int i = a;i <= n;i++)
#define per(i,n,a) for(int i = n;i >= a;i--)
#define ls t<<1
#define rs t<<1|1
using namespace std;
typedef long long ll;
int read() {
    int as = 0,fu = 1;
    char c = getchar();
    while(c < '0' || c > '9') {
        if(c == '-') fu = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9') {
        as = as * 10 + c - '0';
        c = getchar();
    }
    return as * fu;
}
const int N = 1000005;
//head

int n,T,s,mod;
int cnt,cur,head[N],nxt[N],mo[N];
int pa[N],mson[N],top[N],sz[N],dep[N];

void addline(int x,int y) {
    mo[++cnt] = y;
    nxt[cnt] = head[x];
    head[x] = cnt;
    mo[++cnt] = x;
    nxt[cnt] = head[y];
    head[y] = cnt;
    return;
}

void dfs1(int x,int fa,int d) {
    dep[x] = d;
    pa[x] = fa;
    sz[x] = 1;
    int maxson = -1;
    for(int i = head[x]; i; i = nxt[i]) {
        int sn = mo[i];
        if(sn == fa) continue;
        dfs1(sn,x,d+1);
        sz[x] += sz[sn];
        if(sz[sn] > maxson) {
            mson[x] = sn;
            maxson = sz[sn];
        }
    }
}
void dfs2(int x,int topx) {
    top[x] = topx;
    if(mson[x] == 0) return;
    dfs2(mson[x],topx);
    for(int i = head[x]; i; i = nxt[i]) {
        int sn = mo[i];
        if(sn == mson[x] || sn == pa[x]) continue;
        dfs2(sn,sn);
    }
    return;
}
void LCA(int x,int y) {
    while(top[x] != top[y]) {
        if(dep[top[x]] < dep[top[y]]) swap(x,y);
        x = pa[top[x]];
    }
    dep[x] > dep[y] ? printf("%d\n",y) : printf("%d\n",x) ;
    return;
}

int main() {
    n = read();
    T = read();
    s = read();
    rep(i,2,n) addline(read(),read());
    dfs1(s,0,0);
    dfs2(s,s);
    while(T--) {
        int x = read();
        int y = read();
        LCA(x,y);
    }
    return 0;
}