C07【模板】P3690 动态树（Link Cut Tree）
视频链接：265【模板】P3690 动态树（Link Cut Tree）_哔哩哔哩_bilibili
Luogu P3690 【模板】动态树（Link Cut Tree）
#include <iostream> #include <cstring> #include <algorithm> using namespace std; #define N 100010 #define fa(x) tr[x].fa #define lc(x) tr[x].ch[0] #define rc(x) tr[x].ch[1] #define notroot(x) lc(fa(x))==x||rc(fa(x))==x int n,m; struct node{ //splay的信息 int ch[2],fa,v,sum; int tag; //翻转懒标记 }tr[N]; void pushup(int x){ //上传 tr[x].sum=tr[lc(x)].sum^tr[x].v^tr[rc(x)].sum; } void pushdown(int x){ //下传 if(tr[x].tag){ swap(lc(x),rc(x)); tr[lc(x)].tag^=1; tr[rc(x)].tag^=1; tr[x].tag=0; } } void pushall(int x){ //递归下传 if(notroot(x)) pushall(fa(x)); pushdown(x); } void rotate(int x){ //旋转x int y=fa(x),z=fa(y),k=rc(y)==x; //y的右儿是x if(notroot(y)) tr[z].ch[rc(z)==y]=x; fa(x)=z; //z的儿是x,x的父是z tr[y].ch[k]=tr[x].ch[k^1]; fa(tr[x].ch[k^1])=y; //y的儿是x的异儿,x的异儿的父是y tr[x].ch[k^1]=y; fa(y)=x; //x的异儿是y,y的父是x pushup(y); pushup(x); //自底向上pushup } void splay(int x){ //x伸展到根 pushall(x); //递归下传 while(notroot(x)){ //折线转xx,直线转yx int y=fa(x),z=fa(y); if(notroot(y)) (rc(y)==x)^(rc(z)==y)?rotate(x):rotate(y); rotate(x); } } void access(int x){ //打通x到树根的路 for(int y=0; x;){ splay(x); //x转到当前splay的根 rc(x)=y; //x的右儿指向下面splay的根 pushup(x); //更新x的sum y=x,x=fa(x); //存x,x爬到上面的splay } } void makeroot(int x){ //换根 access(x); //通路 splay(x); //伸展 tr[x].tag^=1; //翻转懒标记 } void split(int x,int y){ //分离x到y的路径 makeroot(x); //x换根 access(y); //y通路 splay(y); //y伸展 } void output(int x,int y){ //输出 split(x,y); //分离 printf("%d\n",tr[y].sum); } int findroot(int x){ //找根 access(x); splay(x); while(lc(x)) pushdown(x),x=lc(x); splay(x); //防止卡链 return x; } void link(int x,int y){ //连边 makeroot(x); if(findroot(y)!=x) fa(x)=y; } void cut(int x,int y){ //断边 makeroot(x); if(findroot(y)==x&&fa(y)==x&&!lc(y)) fa(y)=0, pushup(x); } void change(int x,int y){ //修改 splay(x); tr[x].v=y; pushup(x); } int main(){ scanf("%d%d",&n,&m); int t,x,y; for(int i=1; i<=n; i++)scanf("%d",&tr[i].v); while(m--){ scanf("%d%d%d",&t,&x,&y); if(t==0) output(x,y); else if(t==1) link(x,y); else if(t==2) cut(x,y); else change(x,y); } }
#include <iostream> #include <cstring> #include <algorithm> using namespace std; #define N 100010 #define lc(x) ch[x][0] #define rc(x) ch[x][1] #define notroot(x) lc(fa[x])==x||rc(fa[x])==x int n,m; int ch[N][2],fa[N],v[N],sum[N],tag[N]; //splay:ch儿,fa父,v点权,sum异或和,tag翻转懒标记 void pushup(int x){ //上传 sum[x]=sum[lc(x)]^v[x]^sum[rc(x)]; } void pushdown(int x){ //下传 if(tag[x]){ swap(lc(x),rc(x)); tag[lc(x)]^=1; tag[rc(x)]^=1; tag[x]=0; } } void pushall(int x){ //递归下传 if(notroot(x)) pushall(fa[x]); pushdown(x); } void rotate(int x){ //旋转x int y=fa[x],z=fa[y],k=rc(y)==x; //y的右儿是x吗 if(notroot(y)) ch[z][rc(z)==y]=x; fa[x]=z; //z的儿是x,x的父是z ch[y][k]=ch[x][k^1]; fa[ch[x][k^1]]=y; //y的儿是x的异儿,x的异儿的父是y ch[x][k^1]=y; fa[y]=x; //x的异儿是y,y的父是x pushup(y); pushup(x); //自底向上pushup } void splay(int x){ //x伸展到根 pushall(x); //递归下传 while(notroot(x)){ //折线转xx,直线转yx int y=fa[x],z=fa[y]; if(notroot(y)) (rc(y)==x)^(rc(z)==y)?rotate(x):rotate(y); rotate(x); } } void access(int x){ //打通x到树根的路 for(int y=0; x;){ splay(x); //x转到当前splay的根 rc(x)=y; //x的右儿指向下面splay的根 pushup(x); //更新x的sum x=fa[y=x]; //把x给y,x爬到上面的splay } } void makeroot(int x){ //换根 access(x); //通路 splay(x); //伸展 tag[x]^=1; //翻转懒标记 } void split(int x,int y){ //分离x到y的路径 makeroot(x); //x换根 access(y); //y通路 splay(y); //y伸展 } void output(int x,int y){ //输出 split(x,y); //分离 printf("%d\n",sum[y]); } int findroot(int x){ //找根 access(x); //通路 splay(x); //伸展 while(lc(x)) pushdown(x),x=lc(x); splay(x); //防止卡链 return x; } void link(int x,int y){ //连边 makeroot(x); //x换根 if(findroot(y)!=x) fa[x]=y; } void cut(int x,int y){ //断边 makeroot(x); //x换根 if(findroot(y)==x&&fa[y]==x&&!lc(y)) fa[y]=0, pushup(x); } void change(int x,int y){ //修改 splay(x); //伸展 v[x]=y; pushup(x); } int main(){ scanf("%d%d",&n,&m); int t,x,y; for(int i=1; i<=n; i++)scanf("%d",&v[i]); while(m--){ scanf("%d%d%d",&t,&x,&y); if(t==0) output(x,y); else if(t==1) link(x,y); else if(t==2) cut(x,y); else change(x,y); } }
