模板 最近公共祖先 LCA

洛谷 P3379

倍增算法

\(dep_u\) 求u的深度 , 最低为1

\(fa_{u,i}\)为u向上跳\(2^i\)层的祖先结点 , i = 0,1,2,3...

代码

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

inline int read() {
    int ans = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-')f = -1;
        ch = getchar();
    }
    while (ch <= '9' && ch >= '0') {
        ans = ans * 10 + ch - '0';
        ch = getchar();
    }
    return ans * f;
}
const int N = 5e5+10;
int fa[N][20];
int dep[N];
vector<int> v[N];
void dfs(int u,int father) {
    dep[u] = dep[father] +1;
    fa[u][0] = father;
    for (int i = 1; i<= 19; i++) {
        fa[u][i] =  fa[fa[u][i-1]][i-1];
    }
    for (auto e: v[u]) {
        if (e==father) continue;
        dfs(e,u);
    }
}
int lca(int u,int v) {
    if (dep[u] <dep[v])swap(u,v);
    for (int i = 19; i>= 0; i--) {
        if (dep[fa[u][i]] >= dep[v]) {
            u = fa[u][i];
        }
    }
    if (u==v) return u;
    for (int i = 19 ; i>= 0; i--) {
        if (fa[u][i]!= fa[v][i]) {
            u = fa[u][i],v = fa[v][i];
        }
    }
    return fa[u][0];
}
signed main() {
    int n=read(),m=read(),s=read();
    for (int i = 1; i< n;i++) {
        int x=read(),y=read();
        v[y].push_back(x);
        v[x].push_back(y);
    }
    dfs(s,0);
    for (int i = 1;i<=m;i++) {
        int a=read(),b=read();
        cout<<lca(a,b)<<"\n";
    }
    return 0;
}