LCA最近公共祖先

不会 准备研究一波！！！

 #include<bits/stdc++.h>
 const int maxn = ;
 using namespace std;
 vector<int> g[maxn];
 int par[][maxn], dep[maxn], n, m, ml;
 void dfs(int v, int p, int d)
 {
     par[][v] = p;
     dep[v] = d;
     for (int i = ; i < g[v].size(); ++i){
         if (g[v][i] != p) dfs(g[v][i], v, d + );
     }
     return ;
 }
 void init(int v)
 {
     dfs(v, -, );
     int sum = ;
     while (sum <= n) sum <<= , ++ml;
     for (int k = ; k < ml; ++k){
         for (int v = ; v <= n; ++v){
             if (par[k][v] == -) par[k + ][v] = -;
             else par[k + ][v] = par[k][par[k][v]];
         }
     }
     return ;
 }
 int lca(int u, int v)
 {
     if (dep[u] > dep[v]) swap(u, v);
     for (int k = ; k < ml; ++k){
         if (((dep[v] - dep[u]) >> k) & ) v = par[k][v];
     }
     if (u == v) return u;
     for (int k = ml; k >= ; --k){
         if (par[k][u] != par[k][v]) u = par[k][u], v = par[k][v];
     }
     return par[][u];
 }
 int main()
 {
     int s, u, v;
     scanf("%d %d %d", &n, &m, &s);
     int t = n;
     while (--t){
         scanf("%d %d", &u, &v);
         g[u].push_back(v);
         g[v].push_back(u);
     }
     init(s);
     while (m--){
         scanf("%d %d", &u, &v);
         printf("%d\n", lca(u, v));
     }
     return ;
 }

题目   https://www.luogu.org/problemnew/show/P3379

自己写的一个倍增LCA

 #include<iostream>
 #include<cstring>
 //#include<bits/stdc++.h>
 #include<math.h>
 #include<algorithm>
 #include<queue>
 #include<stack>
 #include<cstdio>
 #include<map>
 #include<set>
 #define  si(a)       scanf("%d",&a)
 #define  sl(a)       scanf("%lld",&a)
 #define  sii(a,b)    scanf("%d%d",&a,&b)
 #define  sll(a,b)    scanf("%lld%lld",&a,&b)
 #define  queues      priority_queue
 #define mod 998244353
 #define mem(a)  memset(a,0,sizeof(a));
 #define def(a) ((a)&(-a))
 #define fi  first
 #define se  second
 #define mp  make_pair
 #define  pb push_back
 typedef long long ll;
 //priority_queue<int,vector<int >,greater<int > >q;
 const ll INF=0x3f3f3f3f;
 //const double E=exp(1);
 //const double PI=acos(-1);
 using namespace std;
 int de[];
 int lg[];
 int f[][];
 vector<int>ss[];
 void get_lg()
 {lg[]=-;
     for(int i=;i<=;i++)
         lg[i]=lg[i>>]+;
 }
 void dfs(int p,int fa)
 {  de[p]=de[fa]+;
     f[p][]=fa;
     for(int i=;i<=lg[de[p]]+;i++)
         f[p][i]=f[f[p][i-]][i-];
     for(int i=;i<ss[p].size();i++)
     { int x=ss[p][i];
         if(x!=fa)
         {
             dfs(x,p);
         }
     }
 }
 int LCA(int a,int b)
  {   if(de[a]<de[b])swap(a,b);
     while(de[a]!=de[b])
     {
         a=f[a][lg[de[a]-de[b]]];
     }
    if(a==b)return a;
        for(int i=lg[de[a]];i>=;i--)
        {
            if(f[a][i]!=f[b][i])
             a=f[a][i],b=f[b][i];
        }
    return f[a][];
  }
  int main()
 {  ios::sync_with_stdio(false);
     int n,m,s;
     scanf("%d%d%d",&n,&m,&s);
     for(int i=;i<n;i++)
     {
         int a,b;
         scanf("%d%d",&a,&b);
         ss[a].pb(b);
         ss[b].pb(a);
     }
     get_lg();
     dfs(s,);
     for(int i=;i<=n;i++)
     {
         int a,b;
         scanf("%d%d",&a,&b);
         printf("%d\n",LCA(a,b));
     //    cout<<LCA(a,b)<<endl;
     }
 }

又有一个树链剖分求LCA

 #include<bits/stdc++.h>
 typedef long long ll;
 const int maxn=+;
 const int INF=0x3f3f3f3f;
 using namespace std;
 const ll MAX=
 int read(){int x=,f=;char s=getchar();for(; s>''||s<''; s=getchar()) if(s=='-') f=-;for(; s>=''&&s<=''; s=getchar()) x=x*+s-'';return x*f;}
 vector<int>q[maxn];
 int f[maxn];
 int d[maxn];
 int siz[maxn];
 int son[maxn];

 int top[maxn];
 int id[maxn];
 int rk[maxn];
 int dfs(int a,int fa)
 {
     f[a]=fa;
     d[a]=d[fa]+;
     siz[a]=;
     for(int i=; i<q[a].size(); i++)
     {
         int z=q[a][i];
         if(z!=fa)
         {
             dfs(z,a);
             siz[a]+=siz[z];
             if(!son[a]||siz[z]>siz[son[a]])
                 son[a]=z;
         }
     }
     return ;
 }
 int sum;
 void dfs1(int a,int b)
 {
     top[a]=b;
     if(!son[a])
         return ;
     dfs1(son[a],b);
     for(int i=; i<q[a].size(); i++)
     {
         int z=q[a][i];
         if(z!=f[a]&&z!=son[a])
             dfs1(z,z);
     }
 }
 int lca(int a,int b)
 {
     while(top[a]!=top[b])
     {
         d[top[a]]>d[top[b]]?a=f[top[a]]:b=f[top[b]];

     }
     return d[a]<d[b]?a:b;
 }
 int main()
 {
     ios::sync_with_stdio(false);
     int n,m,s;
     n=read();m=read();s=read();
     for(int i=; i<n; i++)
     {
         int a,b;
         a=read();
         b=read();
         q[a].pb(b);
         q[b].pb(a);
     }
     dfs(s,);
     dfs1(s,s);
     while(m--)
     {
         int a,b;
         a=read();
         b=read();
         cout<<lca(a,b)<<endl;
     }
 }