在线算法ST算法

自学过程参考链接

https://blog.csdn.net/liangzhaoyang1/article/details/52549822

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<string>
#include<queue>
#include<algorithm>
#include<map>
using namespace std;

const int N = 500100;

struct node
{
    int v,next;
}t[N * 2];

int tot,cnt,n,m,s,x,y;
int head[2 * N],rmq[2 * N],dp[2 * N][22];
int F[2 * N],P[2 * N];

void add(int u,int v)
{
    t[tot].v = v;
    t[tot].next = head[u];
    head[u] = tot++;
}

void dfs(int x,int fa,int dep)
{
    F[++cnt] = x;
    rmq[cnt] = dep;
    P[x] = cnt;
    for(int i = head[x];i != -1; i = t[i].next)
    {
        if(t[i].v == fa) continue;
        dfs(t[i].v,x,dep + 1);
        F[++cnt] = x;
        rmq[cnt] = dep;
    }
}

void init(int n)
{
    for(int i = 1;i <= n; ++i) dp[i][0] = i;
    int k = trunc(log2(n));
    for(int j = 1;j <= k; ++j)
        for(int i = 1;i + (1 << j) - 1 <= n; ++i)
        {
            if(rmq[dp[i][j - 1]] < rmq[dp[i + (1 << (j - 1))][j - 1]])
                dp[i][j] = dp[i][j - 1];
            else dp[i][j] = dp[i + (1 << (j - 1))][j - 1];
        }
}

int lca(int a,int b)
{
    if(a > b) swap(a,b);
    int k = trunc(log2(b - a + 1));
    return rmq[dp[a][k]] <= rmq[dp[b - (1 << k) + 1][k]] ?
            dp[a][k]:dp[b - (1 << k) + 1][k];
}

int main()
{
    scanf("%d%d%d",&n,&m,&s);
    tot = 0;
    memset(head,-1,sizeof(head));
    for(int i = 1;i < n; ++i)
    {
        scanf("%d%d",&x,&y);
        add(x,y);
        add(y,x);
    }
    cnt = 0;
    dfs(s,s,0);
    init(2 * n - 1);
    for(int i = 0;i < m; ++i)
    {
        scanf("%d%d",&x,&y);
        printf("%d\n",F[lca(P[x],P[y])]);
    }
    return 0;
}

倍增法