$all$ 维护 $a$ 序列中的所有元素，由于没有删除元素的操作，去重后对最小值没影响，所以我用的是 $set$ 类型。$diff$ 维护的 $a$ 序列中所有相邻元素的差。

#include<bits/stdc++.h>
using namespace std;
const int N=5e5+10;
struct nd{int st,ed;}a[N];
multiset<int>diff;
int n,m,mn;set<int>all;
void INSERT(int x)
{
    if(mn==0)return;
    if(all.count(x)){mn=0;return;}
    auto it=all.lower_bound(x);
    if(it!=all.end())mn=min(mn,abs(*it-x));
    if(it!=all.begin())mn=min(mn,abs(*(--it)-x));
    all.insert(x);
}
signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);cout.tie(0);
	mn=5e8;cin>>n>>m;
    for(int i=1,x;i<=n;i++)
    {
        cin>>x;a[i].st=a[i].ed=x;INSERT(x);
        if(i>1)diff.insert(abs(a[i-1].ed-x));
    }
    while(m--)
    {
        string op;cin>>op;
        if(op[0]=='I')
        {
            int pos,k;cin>>pos>>k;
            if(pos<n)
            {
                diff.erase(diff.find(abs(a[pos].ed-a[pos+1].st)));
                diff.insert(abs(k-a[pos+1].st));
            }
			diff.insert(abs(a[pos].ed-k));
            a[pos].ed=k;INSERT(k);
        }
        else
        {
            if(op[4]=='G')cout<<*diff.begin()<<'\n';
            else cout<<mn<<'\n';
        }
    }
	return 0;
}

https://blog.csdn.net/tenkuo/article/details/154030819

#include<cstdio>
#include<set>
#include<cstdlib>
#include<cctype>
using namespace std;
const int maxn=5e5+1e2;
const int inf=0x3f3f3f3f;

multiset<int> delta,full;
int st[maxn],ed[maxn];
int srt=inf;
int n,m;

inline void update_srt(int x)
{
    multiset<int>::iterator it = full.lower_bound(x);
    int nw = *it - x;
    --it;
    nw = min( nw , x - *it );
    srt = min( srt , nw );
    full.insert(x);
}

inline void replac(int pos,int x)
{
    delta.insert( abs( x - ed[pos] ) );
    if( pos != n )
        delta.erase( delta.find( abs( st[pos+1] - ed[pos] ) ) ),
        delta.insert( abs( st[pos+1] - x ) );
    ed[pos] = x;
}

inline int getint()
{
    int ret = 0 , fix = 1;
    char ch = getchar();
    while( !isdigit(ch) )
    {
        if( ch == '-' )
            fix = -1;
        ch = getchar();
    }
    while( isdigit(ch) )
        ret = ret * 10 + ( ch - '0' ),
        ch = getchar();
    return ret * fix;
}

int main()
{
    static char str[1<<5];
    n = getint() , m = getint();
    for(int i=1;i<=n;i++)
        st[i] = ed[i] = getint();
    
    full.insert(inf),
    full.insert(-inf);
    for(int i=1;i<n;i++)
        delta.insert( abs( st[i+1] - ed[i] ) );
    for(int i=1;i<=n;i++)
        update_srt(st[i]);
    for(int i=1,pos,x;i<=m;i++)
    {
        scanf("%s",str);
        if( *str == 'I' )
        {
            pos = getint() , x = getint();
            update_srt(x);
            replac(pos,x);
        }
        else if( str[4] == 'S' )
            printf("%d\n",srt);
        else
            printf("%d\n",*delta.begin());
    }
    return 0;
}