浅谈\(splay\)：https://www.cnblogs.com/AKMer/p/9979592.html

浅谈\(fhq\)_\(treap\)：https://www.cnblogs.com/AKMer/p/9981274.html

题目传送门：http://poj.org/problem?id=3580

对于\(REVOLVE\)操作，就相当于把\([r-t+1,r]\)剪切下来粘贴到\([l-1,l]\)中间，其余的操作都是平衡树较为模板的操作了。记得把零号点的最小值赋成\(inf\)，要不然空儿子更新父亲信息就会出错。下传标记记得不要传给空儿子，否则会加爆。

时间复杂度：\(O((n+m)logn)\)

空间复杂度：\(O(n)\)

\(splay\)代码如下：

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;const int maxn=2e5+5,inf=2e9;int n,m;
char s[10];
int a[maxn];int read() {int x=0,f=1;char ch=getchar();for(;ch<'0'||ch>'9';ch=getchar())if(ch=='-')f=-1;for(;ch>='0'&&ch<='9';ch=getchar())x=x*10+ch-'0';return x*f;
}struct Splay {int tot,root;bool rev[maxn];int add[maxn],val[maxn],mn[maxn];int siz[maxn],fa[maxn],son[maxn][2];int newnode(int v) {siz[++tot]=1;val[tot]=mn[tot]=v;return tot;}void update(int p) {siz[p]=siz[son[p][0]]+1+siz[son[p][1]];mn[p]=min(min(mn[son[p][0]],mn[son[p][1]]),val[p]);}void build(int l,int r,int lst) {if(r<l)return;if(l==r) {siz[l]=1,val[l]=mn[l]=a[l];fa[l]=lst,son[lst][l>lst]=l;return;}int mid=(l+r)>>1;val[mid]=a[mid];fa[mid]=lst,son[lst][mid>lst]=mid;build(l,mid-1,mid),build(mid+1,r,mid);update(mid);}void prepare() {mn[0]=inf,tot=n+2,build(1,n+2,0),root=(n+3)>>1;}void make_rev_tag(int p) {if(!p)return;rev[p]^=1,swap(son[p][0],son[p][1]);}void make_add_tag(int p,int v) {if(!p)return;val[p]+=v,add[p]+=v,mn[p]+=v;}void push_down(int p) {if(rev[p]) {make_rev_tag(son[p][0]);make_rev_tag(son[p][1]);rev[p]=0;}if(add[p]) {make_add_tag(son[p][0],add[p]);make_add_tag(son[p][1],add[p]);add[p]=0;}}int find(int u,int rk) {push_down(u);if(siz[son[u][0]]+1==rk)return u;if(siz[son[u][0]]>=rk)return find(son[u][0],rk);return find(son[u][1],rk-siz[son[u][0]]-1);}int t(int u) {return son[fa[u]][1]==u;}void rotate(int u) {int ret=t(u),f=fa[u],s=son[u][ret^1];son[f][ret]=s;if(s)fa[s]=f;son[u][ret^1]=f;fa[u]=fa[f];if(fa[f])son[fa[f]][t(f)]=u;fa[f]=u;update(f),update(u);}void splay(int goal,int u) {int tmp=fa[goal];while(fa[u]!=tmp) {if(fa[fa[u]]!=tmp) {if(t(fa[u])==t(u))rotate(fa[u]);else rotate(u);}rotate(u);}if(!tmp)root=u;}void ADD(int l,int r,int v) {int u1=find(root,l-1),u2=find(root,r+1);splay(root,u1),splay(son[u1][1],u2);make_add_tag(son[u2][0],v);update(u2),update(u1);}void REVERSE(int l,int r) {int u1=find(root,l-1),u2=find(root,r+1);splay(root,u1),splay(son[u1][1],u2);make_rev_tag(son[u2][0]);}int cut(int l,int r) {int u1=find(root,l-1),u2=find(root,r+1);splay(root,u1),splay(son[u1][1],u2);int tmp=son[u2][0];son[u2][0]=fa[tmp]=0;update(u2),update(u1);return tmp;}void paste(int pos,int node) {int u1=find(root,pos-1),u2=find(root,pos);splay(root,u1),splay(son[u1][1],u2);fa[node]=u2,son[u2][0]=node;update(u2),update(u1);}int query(int l,int r) {int u1=find(root,l-1),u2=find(root,r+1);splay(root,u1),splay(son[u1][1],u2);return mn[son[u2][0]];}
}T;int main() {n=read();for(int i=2;i<=n+1;i++)a[i]=read();a[1]=a[n+2]=inf;T.prepare();m=read();for(int i=1;i<=m;i++) {scanf("%s",s+1);if(s[1]=='A') {int l=read()+1,r=read()+1,v=read();T.ADD(l,r,v);}if(s[1]=='R') {int l=read()+1,r=read()+1;if(s[4]=='E')T.REVERSE(l,r);else {int t=read()%(r-l+1);int tmp=T.cut(r-t+1,r);T.paste(l,tmp);}}if(s[1]=='I') {int pos=read()+1,v=read();T.paste(pos+1,T.newnode(v));}if(s[1]=='D') {int pos=read()+1;T.cut(pos,pos);}if(s[1]=='M') {int l=read()+1,r=read()+1;printf("%d\n",T.query(l,r));}}return 0;
}

\(fhq\)_\(treap\)版代码如下：

#include <ctime>
#include <cstdio>
#include <algorithm>
using namespace std;
typedef pair<int,int> pii;const int maxn=2e5+5,inf=2e9;int n,m;
char s[10];
int a[maxn];int read() {int x=0,f=1;char ch=getchar();for(;ch<'0'||ch>'9';ch=getchar())if(ch=='-')f=-1;for(;ch>='0'&&ch<='9';ch=getchar())x=x*10+ch-'0';return x*f;
}struct fhq_treap {int tot,root;bool rev[maxn];int val[maxn],mn[maxn],add[maxn];int siz[maxn],fix[maxn],son[maxn][2];int newnode(int v) {siz[++tot]=1;fix[tot]=rand();val[tot]=mn[tot]=v;return tot;}void update(int p) {siz[p]=siz[son[p][0]]+1+siz[son[p][1]];mn[p]=min(min(mn[son[p][0]],mn[son[p][1]]),val[p]);}void build(int l,int r,int lst) {if(r<l)return;if(l==r) {siz[l]=1,fix[l]=rand();son[lst][l>lst]=l;val[l]=mn[l]=a[l];return;}int mid=(l+r)>>1;val[mid]=a[mid],fix[mid]=rand();son[lst][mid>lst]=mid;build(l,mid-1,mid),build(mid+1,r,mid);update(mid);}void prepare() {mn[0]=inf,tot=n,build(1,n,0),root=(n+1)>>1;}void make_add_tag(int u,int v) {if(!u)return;val[u]+=v,add[u]+=v,mn[u]+=v;}void make_rev_tag(int u) {if(!u)return;rev[u]^=1,swap(son[u][0],son[u][1]);}void push_down(int u) {if(add[u]) {make_add_tag(son[u][0],add[u]);make_add_tag(son[u][1],add[u]);add[u]=0;}if(rev[u]) {make_rev_tag(son[u][0]);make_rev_tag(son[u][1]);rev[u]=0;}}pii split(int u,int rk) {if(!rk)return make_pair(0,u);if(rk==siz[u])return make_pair(u,0);push_down(u);if(siz[son[u][0]]>=rk) {pii tmp=split(son[u][0],rk);son[u][0]=tmp.second,update(u);return make_pair(tmp.first,u);}else {pii tmp=split(son[u][1],rk-siz[son[u][0]]-1);son[u][1]=tmp.first,update(u);return make_pair(u,tmp.second);}}int merge(int a,int b) {if(!a||!b)return a+b;push_down(a),push_down(b);if(fix[a]>fix[b])return son[a][1]=merge(son[a][1],b),update(a),a;else return son[b][0]=merge(a,son[b][0]),update(b),b;}void ADD(int l,int r,int v) {pii tmp1=split(root,r);pii tmp2=split(tmp1.first,l-1);make_add_tag(tmp2.second,v);root=merge(merge(tmp2.first,tmp2.second),tmp1.second);}void REVERSE(int l,int r) {pii tmp1=split(root,r);pii tmp2=split(tmp1.first,l-1);make_rev_tag(tmp2.second);root=merge(merge(tmp2.first,tmp2.second),tmp1.second);}int cut(int l,int r) {pii tmp1=split(root,r);pii tmp2=split(tmp1.first,l-1);root=merge(tmp2.first,tmp1.second);return tmp2.second;}void paste(int pos,int node) {pii tmp=split(root,pos-1);root=merge(merge(tmp.first,node),tmp.second);}int query(int l,int r) {pii tmp1=split(root,r);pii tmp2=split(tmp1.first,l-1);int res=mn[tmp2.second];root=merge(merge(tmp2.first,tmp2.second),tmp1.second);return res;}
}T;int main() {srand(time(0)),n=read();for(int i=1;i<=n;i++)a[i]=read();T.prepare();m=read();for(int i=1;i<=m;i++) {scanf("%s",s+1);if(s[1]=='A') {int l=read(),r=read(),v=read();T.ADD(l,r,v);}if(s[1]=='R') {int l=read(),r=read();if(s[4]=='E')T.REVERSE(l,r);else {int t=read()%(r-l+1);int tmp=T.cut(r-t+1,r);T.paste(l,tmp);}}if(s[1]=='I') {int pos=read(),v=read();T.paste(pos+1,T.newnode(v));}if(s[1]=='D') {int pos=read();T.cut(pos,pos);}if(s[1]=='M') {int l=read(),r=read();printf("%d\n",T.query(l,r));}}return 0;
}