#平衡树#洛谷 1110 [ZJOI2007]报表统计
分析
最小值只需要开两棵平衡树，一棵维护所有元素，一棵维护相邻最小值，
对于全局最小值，对于每次插入查找前驱后继更新最小值即可，
相邻最小值，对于每个原数列的数维护它的开头和结尾是什么数，
然后在往后插入一个数时直接先把原来的相邻删除再加进去，
求平衡树的最小值即可
代码
#include <cstdio>
#include <cctype>
#include <cstring>
#include <algorithm>
#define rr register
using namespace std;
const int N=500011,inf=1e9; char str[21];
const double alp=0.75; int ans,n,m,len,St[N],Ed[N],a[N];
inline signed iut(){
rr int ans=0,f=1; rr char c=getchar();
while (!isdigit(c)) f=(c=='-')?-f:f,c=getchar();
while (isdigit(c)) ans=(ans<<3)+(ans<<1)+(c^48),c=getchar();
return ans*f;
}
inline void print(int ans){
if (ans<0) putchar('-'),ans=-ans;
if (ans>9) print(ans/10);
putchar(ans%10+48);
}
inline signed min(int a,int b){return a<b?a:b;}
inline signed max(int a,int b){return a>b?a:b;}
struct ScapeGoat_Tree{
int siz[N<<1],son[N<<1][2],root,tot=0,fat[N<<1],w[N<<1],stac[N<<1],TOP;
inline void BUILD(){
tot=2,root=1;
w[1]=-inf,siz[1]=2,son[1][1]=2,
w[2]=inf,siz[2]=1,fat[2]=1;
}
inline bool balance(int x){return alp*siz[x]>=(max(siz[son[x][0]],siz[son[x][1]]));}
inline void recycle(int x){
if (son[x][0]) recycle(son[x][0]);
stac[++TOP]=x;
if (son[x][1]) recycle(son[x][1]);
}
inline signed build(int l,int r){
if (l>r) return 0;
rr int mid=(l+r)>>1,x=stac[mid];
fat[son[x][0]=build(l,mid-1)]=x;
fat[son[x][1]=build(mid+1,r)]=x;
siz[x]=siz[son[x][0]]+siz[son[x][1]]+1;
return x;
}
inline void rebuild(int x){
TOP=0; recycle(x);
rr int fa=fat[x],wh=son[fat[x]][1]==x;
rr int now=build(1,TOP);
fat[son[fa][wh]=now]=fa;
if (root==x) root=now;
}
inline void Insert(int x){
rr int now=root,renew=++tot;
siz[renew]=1,w[renew]=x;
while (1){
++siz[now];
rr bool wh=x>=w[now];
if (son[now][wh]) now=son[now][wh];
else {fat[son[now][wh]=renew]=now; break;}
}
rr int UP=0;
for (rr int i=renew;i;i=fat[i]) if (!balance(i)) UP=i;
if (UP) rebuild(UP);
}
inline void Delete(int x){
if (son[x][0]&&son[x][1]){
rr int now=son[x][0];
while (son[now][1]) now=son[now][1];
w[x]=w[now],x=now;
}
rr int cho=son[x][0]?son[x][0]:son[x][1],wh=son[fat[x]][1]==x;
fat[son[fat[x]][wh]=cho]=fat[x];
for (rr int i=fat[x];i;i=fat[i]) --siz[i];
if (x==root) root=cho;
}
inline signed arr(int x){
rr int now=root;
while (1){
if (w[now]==x) return now;
else now=son[now][w[now]<x];
}
}
inline signed rank(int x){
rr int now=root,ans=0;
while (now){
if (x>w[now]) ans+=siz[son[now][0]]+1,now=son[now][1];
else now=son[now][0];
}
return ans;
}
inline signed kth(int x){
rr int now=root;
while (1){
if (siz[son[now][0]]==x-1) return now;
else if (siz[son[now][0]]>=x) now=son[now][0];
else x-=siz[son[now][0]]+1,now=son[now][1];
}
}
inline signed pre(int x){
rr int now=root,ans=-inf;
while (now){
if (x>w[now]) ans=max(ans,w[now]),now=son[now][1];
else now=son[now][0];
}
return ans;
}
inline signed suf(int x){
rr int now=root,ans=inf;
while (now){
if (x<w[now]) ans=min(ans,w[now]),now=son[now][0];
else now=son[now][1];
}
return ans;
}
}Tre[2];
inline signed Abs(int x){return x<0?-x:x;}
signed main(){
n=iut(),m=iut(),Tre[0].BUILD(),Tre[1].BUILD();
for (rr int i=1;i<=n;++i) St[i]=Ed[i]=a[i]=iut();
for (rr int i=1;i<n;++i) Tre[0].Insert(Abs(St[i+1]-St[i]));
for (rr int i=1;i<=n;++i) Tre[1].Insert(St[i]);
sort(a+1,a+1+n),ans=Abs(a[2]-a[1]);
for (rr int i=3;i<=n;++i) ans=min(ans,Abs(a[i]-a[i-1]));
for (rr int i=1;i<=m;++i){
scanf("%s",str+1),len=strlen(str+1);
if (len==6){
rr int x=iut(),w=iut();
if (x<n) Tre[0].Delete(Tre[0].arr(Abs(St[x+1]-Ed[x])));
if (x<n) Tre[0].Insert(Abs(St[x+1]-w));
Tre[0].Insert(Abs(w-Ed[x])),Ed[x]=w;
rr int t1=Tre[1].suf(-inf),t2=Tre[1].pre(inf);
if (w<t1) ans=min(ans,t1-w);
else if (t2<w) ans=min(ans,w-t2);
else {
if (Tre[1].suf(w-1)==w) {ans=0; continue;}
ans=min(ans,min(w-Tre[1].pre(w),Tre[1].suf(w)-w));
}
Tre[1].Insert(w);
}else if (len==7) print(Tre[0].suf(-inf)),putchar(10);
else print(ans),putchar(10);
}
return 0;
}
