主席树模板

静态版

#include<bits/stdc++.h>
using namespace std;

#define debug puts("YES");
#define rep(x,y,z) for(int (x)=(y);(x)<(z);(x)++)
#define ll long long

#define lrt int l,int r,int rt
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define root l,r,rt
#define mst(a,b) memset((a),(b),sizeof(a))
#define pii pair<int,int>
#define fi first
#define se second
#define mk(x,y) make_pair(x,y)
const int mod=1e9+7;
const int maxn=1e5+100;
const int ub=1e6;
ll powmod(ll x,ll y){ll t; for(t=1;y;y>>=1,x=x*x%mod) if(y&1) t=t*x%mod; return t;}
ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
int n,m;
int a[maxn],b[maxn],sz;///离散化数组
int rt[maxn*20],ls[maxn*20],rs[maxn*20],sum[maxn*20];
int tot=0;
void build(int& o,int l,int r){
    o=++tot;
    sum[o]=0;
    if(l==r) return ;
    int mid=l+r>>1;
    build(ls[o],l,mid);
    build(rs[o],mid+1,r);
}

void update(int& o,int l,int r,int last,int p){
    o=++tot;
    ls[o]=ls[last];
    rs[o]=rs[last];
    sum[o]=sum[last]+1;
    if(l==r) return ;
    int mid=l+r>>1;
    if(p<=mid) update(ls[o],l,mid,ls[last],p);
    else update(rs[o],mid+1,r,rs[last],p);
}
int query(int ss,int tt,int l,int r,int k){
    if(l==r) return l;
    int mid=l+r>>1;
    int cnt=sum[ls[tt]]-sum[ls[ss]];
    if(k<=cnt) return query(ls[ss],ls[tt],l,mid,k);
    else return query(rs[ss],rs[tt],mid+1,r,k-cnt);
}

int main(){
    int t;scanf("%d",&t);
    while(t--){
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n;i++) scanf("%d",&a[i]),b[i]=a[i];
        sort(b+1,b+n+1);
        int sz=unique(b+1,b+1+n)-(b+1);
        tot=0;build(rt[0],1,sz);///建一个空树
        for(int i=1;i<=n;i++) a[i]=lower_bound(b+1,b+1+sz,a[i])-b;///细节
        for(int i=1;i<=n;i++) update(rt[i],1,sz,rt[i-1],a[i]);
        while(m--){
            int x,y,k;
            scanf("%d%d%d",&x,&y,&k);
            int idx=query(rt[x-1],rt[y],1,sz,k);
            printf("%d\n",b[idx]);
        }
    }
    return 0;
}

动态版

#include<bits/stdc++.h>
using namespace std;

#define debug puts("YES");
#define rep(x,y,z) for(int (x)=(y);(x)<(z);(x)++)
#define ll long long

#define lrt int l,int r,int rt
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define root l,r,rt
#define mst(a,b) memset((a),(b),sizeof(a))
#define pii pair<int,int>
#define fi first
#define se second
#define mk(x,y) make_pair(x,y)
const int mod=1e9+7;
const int maxn=6e4+5;
const int Maxn=maxn<<5;
const int ub=1e6;
const double inf=1e-4;
ll powmod(ll x,ll y){ll t; for(t=1;y;y>>=1,x=x*x%mod) if(y&1) t=t*x%mod; return t;}
ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}

int n,m,a[maxn],b[maxn],cnt,x,y;
char tp[10];
struct Q{
    int x,y,z;
    bool flag;
}q[maxn];

int tot=0,rt[Maxn],L[Maxn],R[Maxn],sum[Maxn];
void build(int& o,int l,int r){
    o=++tot,sum[o]=0;
    if(l==r) return ;
    int mid=l+r>>1;
    build(L[o],l,mid);
    build(R[o],mid+1,r);
}
void update(int& o,int l,int r,int pre,int v,int pv){
    o=++tot;
    L[o]=L[pre],R[o]=R[pre];
    sum[o]=sum[pre]+pv;
    ///cout<<l<<" "<<r<<endl;
    if(l==r) return ;
    int mid=l+r>>1;
    if(v<=mid) update(L[o],l,mid,L[pre],v,pv);
    else update(R[o],mid+1,r,R[pre],v,pv);
}
int used[maxn],S[maxn];///对于树状数组的每个点都建树
int lowbit(int x){return x&-x;}
void add(int x,int v,int pv){
    for(;x<=n;update(S[x],1,n,S[x],v,pv),x+=lowbit(x));
}
int Sum(int x){
    int ret=0;for(;x>0;ret+=sum[L[used[x]]],x-=lowbit(x));
    return ret;
}
int query(int u,int v,int lu,int lv,int l,int r,int V){
    if(l>=r) return l;
    int ret=Sum(v)-Sum(u)+sum[L[lv]]-sum[L[lu]];
    int mid=l+r>>1;
    if(V<=ret){
        for(int i=v;i;i-=lowbit(i)) used[i]=L[used[i]];
        for(int i=u;i;i-=lowbit(i)) used[i]=L[used[i]];
        return query(u,v,L[lu],L[lv],l,mid,V);
    }
    else{
        for(int i=v;i;i-=lowbit(i)) used[i]=R[used[i]];
        for(int i=u;i;i-=lowbit(i)) used[i]=R[used[i]];
        return query(u,v,R[lu],R[lv],mid+1,r,V-ret);
    }
}

int main(){
    int t;scanf("%d",&t);
    while(t--){
        scanf("%d%d",&n,&m);cnt=0,mst(sum,0);
        rep(i,1,n+1) {scanf("%d",&a[i]);b[++cnt]=a[i];}
        rep(i,1,m+1){
            scanf("%s",tp);
            if(tp[0]=='Q'){
                scanf("%d%d%d",&q[i].x,&q[i].y,&q[i].z);
                q[i].flag=true;
            }
            else{
                scanf("%d%d",&q[i].x,&q[i].y);
                b[++cnt]=q[i].y;
                q[i].flag=false;
            }
        }
        sort(b+1,b+cnt+1);
        cnt=unique(b+1,b+1+cnt)-(b+1);
        tot=0;build(rt[0],1,cnt);///建立一颗空树
        rep(i,1,n+1){
            int val=lower_bound(b+1,b+1+cnt,a[i])-b;
            update(rt[i],1,cnt,rt[i-1],val,1);
            S[i]=rt[0];
        }///插值
        n=cnt;///
        rep(i,1,m+1){
            if(q[i].flag){
                for(int j=q[i].x-1;j;j-=lowbit(j)) used[j]=S[j];
                for(int j=q[i].y;j;j-=lowbit(j)) used[j]=S[j];///更新树状数组的值
                ///cout<<rt[q[i].y]<<" "<<L[rt[q[i].y]]<<" "<<sum[L[rt[q[i].y]]]<<endl;
                printf("%d\n",b[query(q[i].x-1,q[i].y,rt[q[i].x-1],rt[q[i].y],1,n,q[i].z)]);
            }
            else{
                int val1=lower_bound(b+1,b+1+n,a[q[i].x])-b;
                int val2=lower_bound(b+1,b+1+n,q[i].y)-b;
                add(q[i].x,val1,-1),add(q[i].x,val2,1);
                a[q[i].x]=q[i].y;
            }
        }
    }
    return 0;
}