lca 欧拉序+rmq(st) 欧拉序+rmq(线段树) 离线dfs 倍增

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

1.欧拉序+rmq(st)

 /*

 在这里，对于一个数，选择最左边的

 选择任意一个都可以，[left_index,right_index]，深度都大于等于这个数的深度

 */

 #include <cstdio>

 #include <cstdlib>

 #include <cmath>

 #include <cstring>

 #include <time.h>

 #include <string>

 #include <set>

 #include <map>

 #include <list>

 #include <stack>

 #include <queue>

 #include <vector>

 #include <bitset>

 #include <ext/rope>

 #include <algorithm>

 #include <iostream>

 using namespace std;

 #define ll long long

 #define minv 1e-6

 #define inf 1e9

 #define pi 3.1415926536

 #define E  2.7182818284

 const ll mod=1e9+;//

 const int maxn=5e5+;

 struct node

 {

     int d;

     node *next;

 }*e[maxn];

 int s=;

 ///每条边走两遍，n-1条边，走2(n-1)个点

 int a[maxn<<],b[maxn<<],f[maxn<<][],lef[maxn],er[];

 bool vis[maxn]={};

 void dfs(int d,int dep)

 {

     node* p=e[d];

     vis[d]=;

     s++;

     lef[d]=s;

     a[s]=d;

     b[s]=dep;

     while (p)

     {

         if (!vis[p->d])

         {

             dfs(p->d,dep+);

             s++;

             a[s]=d;

             b[s]=dep;

         }

         p=p->next;

     }

 }

 int main()

 {

     int n,q,root,x,y,i,j,k,m,d;

     node *p;

     scanf("%d%d%d",&n,&q,&root);

     for (i=;i<n;i++)

     {

         scanf("%d%d",&x,&y);

         p=(node*) malloc (sizeof(node));

         p->d=y;

         p->next=e[x];

         e[x]=p;

         p=(node*) malloc (sizeof(node));

         p->d=x;

         p->next=e[y];

         e[y]=p;

     }

     dfs(root,);

     m=log(s)/log();

     er[]=;

     for (i=;i<=m;i++)

         er[i]=er[i-]<<;

     for (i=;i<=s;i++)

         f[i][]=i;

 //        f[i][0]=b[i];

     for (i=;i<=m;i++)   //2^i

         for (j=,k=j+er[i-];j<=s-er[i]+;j++,k++)  //-er[i]+1

             if (b[ f[j][i-] ] < b[ f[k][i-] ])

                 f[j][i]=f[j][i-];

             else

                 f[j][i]=f[k][i-];

 //            f[j][i]=min(f[j][i-1],f[j+er[i-1]][i-1]);

     while (q--)

     {

         scanf("%d%d",&x,&y);

         x=lef[x];

         y=lef[y];

         if (x>y)

             swap(x,y);

         d=log(y-x+)/log();

         j=y-er[d]+;

         if (b[ f[x][d] ] < b[ f[j][d] ])    //+1

             printf("%d\n",a[ f[x][d] ]);

         else

             printf("%d\n",a[ f[j][d] ]);

 //        printf("%d\n",min(f[x][d],f[y-er[d]+1][d]));

     }

     return ;

 }

 /*

 8 100 1

 1 2

 1 3

 2 4

 2 5

 3 6

 5 7

 6 8

 5 7

 5

 2 3

 1

 3 2

 1

 1 8

 1

 2 8

 1

 4 5

 2

 5 4

 2

 */

2.欧拉序+线段树

 /*

 在这里，对于一个数，选择最左边的

 选择任意一个都可以，[left_index,right_index]，深度都大于等于这个数的深度

 */

 #include <cstdio>

 #include <cstdlib>

 #include <cmath>

 #include <cstring>

 #include <time.h>

 #include <string>

 #include <set>

 #include <map>

 #include <list>

 #include <stack>

 #include <queue>

 #include <vector>

 #include <bitset>

 #include <ext/rope>

 #include <algorithm>

 #include <iostream>

 using namespace std;

 #define ll long long

 #define minv 1e-6

 #define inf 1e9

 #define pi 3.1415926536

 #define E  2.7182818284

 const ll mod=1e9+;//

 const int maxn=5e5+;

 struct node

 {

     int d;

     node *next;

 }*e[maxn];

 int s=;

 ///每条边走两遍，n-1条边，走2(n-1)个点

 int a[maxn<<],b[maxn<<],lef[maxn],f[maxn<<];

 bool vis[maxn]={};

 int num=;

 void dfs(int d,int dep)

 {

     node* p=e[d];

     vis[d]=;

     s++;

     lef[d]=s;

     a[s]=d;

     b[s]=dep;

     while (p)

     {

         if (!vis[p->d])

         {

             dfs(p->d,dep+);

             s++;

             a[s]=d;

             b[s]=dep;

         }

         p=p->next;

     }

 }

 void build(int index,int l,int r)

 {

     if (l==r)

         f[index]=++num;

     else

     {

         int m=(l+r)>>;

         build(index<<,l,m);

         build(index<<|,m+,r);

         if (b[f[index<<]]<b[f[index<<|]])

             f[index]=f[index<<];

         else

             f[index]=f[index<<|];

     }

 }

 int query(int index,int l,int r,int x,int y)

 {

     if (x<=l && r<=y)

         return f[index];

     if (r<x || l>y)

         return ;

     int m=(l+r)>>;

     int p=query(index<<,l,m,x,y);

     int q=query(index<<|,m+,r,x,y);

     if (b[p]<b[q])

         return p;

     else

         return q;

 }

 int main()

 {

     int n,q,root,x,y,i,j,m,d;

     node *p;

     scanf("%d%d%d",&n,&q,&root);

     for (i=;i<n;i++)

     {

         scanf("%d%d",&x,&y);

         p=(node*) malloc (sizeof(node));

         p->d=y;

         p->next=e[x];

         e[x]=p;

         p=(node*) malloc (sizeof(node));

         p->d=x;

         p->next=e[y];

         e[y]=p;

     }

     dfs(root,);

     b[]=n+;

     build(,,s);

     while (q--)

     {

         scanf("%d%d",&x,&y);

         x=lef[x];

         y=lef[y];

         if (x>y)

             swap(x,y);

         printf("%d\n",a[query(,,s,x,y)]);

     }

     return ;

 }

3.离线dfs

 #include <cstdio>

 #include <cstdlib>

 #include <cmath>

 #include <cstring>

 #include <time.h>

 #include <string>

 #include <set>

 #include <map>

 #include <list>

 #include <stack>

 #include <queue>

 #include <vector>

 #include <bitset>

 #include <ext/rope>

 #include <algorithm>

 #include <iostream>

 using namespace std;

 #define ll long long

 #define minv 1e-6

 #define inf 1e9

 #define pi 3.1415926536

 #define E  2.7182818284

 const ll mod=1e9+;//

 const int maxn=5e5+;

 struct node

 {

     int d;

     node *next;

 }*e[maxn];

 struct rec

 {

     int d,index;

     rec *next;

 }*ask[maxn];

 bool vis[maxn]={};

 int r[maxn],fa[maxn];

 int getfather(int d)

 {

     if (fa[d]==d)

         return d;

     fa[d]=getfather(fa[d]);

     return fa[d];

 }

 void merge(int x,int y)

 {

     int s=getfather(x);

     int t=getfather(y);

     fa[t]=s;

 }

 void dfs(int d)

 {

     node *p;

     rec *v;

     vis[d]=;

     p=e[d];

     while (p)

     {

         if (!vis[p->d])

         {

             dfs(p->d);

             merge(d,p->d);

         }

         p=p->next;

     }

     v=ask[d];

     while (v)

     {

         if (vis[v->d])

             r[v->index]=getfather(v->d);

         v=v->next;

     }

 }

 int main()

 {

     node *p;

     rec *v;

     int n,q,root,x,y,i;

     scanf("%d%d%d",&n,&q,&root);

     for (i=;i<n;i++)

     {

         scanf("%d%d",&x,&y);

         p=(node*) malloc (sizeof(node));

         p->d=y;

         p->next=e[x];

         e[x]=p;

         p=(node*) malloc (sizeof(node));

         p->d=x;

         p->next=e[y];

         e[y]=p;

     }

     for (i=;i<=q;i++)

     {

         scanf("%d%d",&x,&y);

         v=(rec*) malloc (sizeof(rec));

         v->d=y;

         v->index=i;

         v->next=ask[x];

         ask[x]=v;

         v=(rec*) malloc (sizeof(rec));

         v->d=x;

         v->index=i;

         v->next=ask[y];

         ask[y]=v;

     }

     for (i=;i<=n;i++)

         fa[i]=i;

     dfs(root);

     for (i=;i<=q;i++)

         printf("%d\n",r[i]);

     return ;

 }

4.倍增

 #include <cstdio>

 #include <cstdlib>

 #include <cmath>

 #include <cstring>

 #include <time.h>

 #include <string>

 #include <set>

 #include <map>

 #include <list>

 #include <stack>

 #include <queue>

 #include <vector>

 #include <bitset>

 #include <ext/rope>

 #include <algorithm>

 #include <iostream>

 using namespace std;

 #define ll long long

 #define minv 1e-6

 #define inf 1e9

 #define pi 3.1415926536

 #define nl 2.7182818284

 const ll mod=1e9+;//

 const int maxn=5e5+;

 struct node

 {

     int d;

     node *next;

 }*e[maxn];

 bool vis[maxn]={};

 int q[maxn],dep[maxn],f[maxn][];

 int main()

 {

     node *p;

     int n,Q,root,head,tail,x,y,d,dd,i,j,k;

     scanf("%d%d%d",&n,&Q,&root);

     for (i=;i<n;i++)

     {

         scanf("%d%d",&x,&y);

         p=new node();

         p->d=y;

         p->next=e[x];

         e[x]=p;

         p=new node();

         p->d=x;

         p->next=e[y];

         e[y]=p;

     }

     head=,tail=;

     vis[root]=;

     q[]=root;

     dep[root]=;

     while (head<tail)

     {

         head++;

         d=q[head];

         p=e[d];

         while (p)

         {

             dd=p->d;

             if (!vis[dd])

             {

                 tail++;

                 q[tail]=dd;

                 vis[dd]=;

                 dep[dd]=dep[d]+;

                 //f[dd][]=d;

                 j=d;

                 k=;

                 while (j)

                 {

                     f[dd][k]=j;

                     j=f[j][k];

                     k++;

                 }

             }

             p=p->next;

         }

     }

     while (Q--)

     {

         scanf("%d%d",&x,&y);

         if (dep[x]<dep[y])

             swap(x,y);

         i=dep[x]-dep[y];

         j=;

         while (i)

         {

             if (i & )

                 x=f[x][j];

             i>>=;

             j++;

         }

         if (dep[x]==)

             k=;

         else

             k=log(dep[x]+minv)/log()+;

         i=(<<k);

         while (k)

         {

             k--;

             i>>=;

             if (dep[x]>=i && f[x][k]!=f[y][k])

             {

                 x=f[x][k];

                 y=f[y][k];

             }

         }

         if (x!=y)

             x=f[x][];

         printf("%d\n",x);

     }

     return ;

 }

 /*

 5 100 1

 1 2

 2 3

 3 4

 4 5

 1 5

 3 4

 2 4

 2 5

 7 100 1

 1 2

 2 3

 2 4

 4 5

 4 6

 1 7

 5 7

 3 7

 5 1

 2 6

 3 6

 10 100 1

 1 2

 2 3

 3 4

 4 5

 5 6

 6 7

 7 8

 8 9

 9 10

 1 10

 2 10

 3 10

 4 10

 5 9

 7 8

 10 100 1

 1 2

 2 3

 3 4

 3 5

 5 6

 5 7

 2 8

 8 9

 9 10

 6 10

 4 10

 3 1

 6 7

 3 10

 2 10

 3 7

 6 7

 4 7

 10 100 1

 1 2

 1 3

 1 4

 3 5

 3 6

 3 7

 7 8

 7 9

 7 10

 15 100 1

 1 2

 2 3

 3 4

 4 5

 5 6

 6 7

 7 8

 8 9

 9 10

 10 11

 11 12

 12 13

 13 14

 14 15

 1 15

 2 15

 2 14

 3 14

 3 13

 4 13

 4 12

 12 100 1

 1 2

 2 3

 3 4

 4 5

 5 6

 1 7

 7 8

 8 9

 9 10

 10 11

 11 12

 6 12

 4 7

 8 12

 1 6

 */