splay維護區間最大值、最小值、相鄰兩數差的絕對值的最小值即可。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
#define ll long long
#define N 100010
#define inf 2100000000
#define lson tree[k].ch[0]
#define rson tree[k].ch[1]
char
 
 getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<'0'||c>'9')) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while
 
 (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int n,m,a[N],cnt,root;
struct data{int ch[2],fa,x,d,s,max,min,mind;
}tree[N<<1];
void up(int k)
{
    tree[k].max=max(max(tree[lson].max,tree[rson].max),tree[k].x);
    tree[k].min=min(min(tree[lson].min,tree[rson].min),tree[k].x);
    tree[k].mind
 
=min(min(tree[lson].mind,tree[rson].mind),tree[k].d);
    tree[k].s=tree[lson].s+tree[rson].s+1;
}
int build(int l,int r,int from)
{
    if (l>r) return 0;
    int mid=l+r>>1,k=++cnt;tree[k].fa=from;tree[k].s=1;
    tree[k].x=tree[k].max=tree[k].min=a[mid];
    tree[k].d=tree[k].mind=abs(a[mid]-a[mid+1]);
    lson=build(l,mid-1,k),rson=build(mid+1,r,k);
    up(k);
    return k;
}
int whichson(int k){return tree[tree[k].fa].ch[1]==k;}
void move(int k)
{
    int fa=tree[k].fa,gf=tree[fa].fa,p=whichson(k);
    tree[gf].ch[whichson(fa)]=k,tree[k].fa=gf;
    tree[tree[k].ch[!p]].fa=fa,tree[fa].ch[p]=tree[k].ch[!p];
    tree[k].ch[!p]=fa,tree[fa].fa=k;
    up(fa),up(k);
}
void splay(int k,int rt)
{
    while (tree[k].fa!=rt)
    {
        int fa=tree[k].fa;
        if (tree[fa].fa!=rt)
            if (whichson(k)^whichson(fa)) move(k);
            else move(fa);
        move(k);
    }
    if (!rt) root=k;
}
int find(int k,int x)
{
    if (tree[lson].s==x) return k;
    else if (tree[lson].s>x) return find(lson,x);
    else return find(rson,x-tree[lson].s-1);
}
void ins(int k,int x)
{
    int p=find(root,k-1),q=find(root,k);
    splay(p,0),splay(q,p);
    k=++cnt;tree[k].fa=q;tree[k].s=1;
    tree[k].x=tree[k].max=tree[k].min=x;
    tree[k].d=tree[k].mind=abs(x-tree[q].x);
    tree[q].ch[0]=k,up(q);
    tree[p].d=abs(tree[p].x-x),up(p);
}
void del(int k)
{
    int p=find(root,k-1),q=find(root,k+1);
    splay(p,0),splay(q,p);
    tree[q].ch[0]=0,up(q);
    tree[p].d=abs(tree[p].x-tree[q].x),up(p);
}
int query(int l,int r,int op)
{
    int p=find(root,l-1),q=find(root,r+1);
    splay(p,0),splay(q,p);
    int k=tree[q].ch[0];
    if (op==0) return tree[k].max;
    else if (op==1) return tree[k].min;
    else return tree[k].mind;
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj4864.in","r",stdin);
    freopen("bzoj4864.out","w",stdout);
    const char LL[]="%I64d\n";
#else
    const char LL[]="%lld\n";
#endif
    n=read(),m=read();
    for (int i=1;i<=n;i++) a[i]=read();
    tree[0].max=tree[0].d=-inf,tree[0].min=tree[0].mind=tree[0].d=inf;
    root=build(0,n+1,0);
    while (m--)
    {
        char c=getc();
        if (c=='m')
        {
            c=getc();
            if (c=='e')
            {
                int x=read(),y=read();
                del(x);del(x);ins(x,y);
            }
            else
            {
                int l=read(),r=read();
                if (c=='a') printf("%d\n",query(l,r,0)-query(l,r,1));
                else printf("%d\n",query(l,r-1,2));
            }
        }
        else
        {
            int x=read(),y=read();
            ins(x+1,y);
        }
    }
    return 0;
}