bzoj1901：Zju2112 Dynamic Rankings

思路：树套树，我写了两种，一种是线段树套splay，线段树维护区间信息，splay维护第k大，一种是树状数组套权值线段树（并不是什么可持久化线段树，只不过是动态开点罢了，为什么网上一大堆题解都是可持久化线段树。。。。。明明可以直接修改的，不过可持久化线段树应该也是可以写的），树状数组维护前缀和，权值线段树维护第k大，利用那道不带修改的裸题的思想即可。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
#define maxn 10005
 
int n,m;
int a[maxn];
char s[3];
 
inline 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_tree{
    int ch[200*maxn][2],fa[200*maxn],note[200*maxn],val[200*maxn],size[200*maxn],cover[200*maxn],tot;
    void clear(){
        memset(val,-1,sizeof(val));
    }
    void update(int x){
        if (!x) return;
        size[x]=size[ch[x][0]]+size[ch[x][1]]+cover[x];
    }
    void rotate(int x){
        int y=fa[x],z=fa[y],bo=note[x],bo1=note[y];
        ch[y][bo]=ch[x][bo^1],fa[ch[x][bo^1]]=y;
        ch[x][bo^1]=y,fa[y]=x;
        fa[x]=z;if (z) ch[z][bo1]=x;
        note[x]=bo1,note[y]=bo^1,note[ch[y][bo]]=bo;
        update(y);
    }
    void splay(int x){
        while (note[x]!=2){
            if (note[x]==note[fa[x]]) rotate(fa[x]);
            rotate(x);
        }
        update(x);
    }
    void insert(int &x,int v){
        int y;
        while (1){
            if (val[x]==v){cover[x]++,y=x;break;}
            y=ch[x][val[x]<v];
            if (!y){
                y=++tot;
                val[y]=v,size[y]=1,cover[y]=1;
                if (x) note[y]=(val[x]<v);else note[y]=2;
                fa[y]=x,ch[y][0]=ch[y][1]=0;
                if (x) ch[x][note[y]]=y;
                break;
            }
            x=y;
        }
        splay(y),x=y;
    }
    int find(int x,int v){
        splay(x);
        while (1){
            if (val[x]==v) return x;
            else if (val[x]<v) x=ch[x][1];
            else x=ch[x][0];
        }
    }
    int findk(int x,int v){
        splay(x);int ans=0;
        while (x){
            if (v<val[x]) x=ch[x][0];
            else if (v==val[x]) return ans+size[ch[x][0]]+cover[x];
            else ans+=size[ch[x][0]]+cover[x],x=ch[x][1];
        }
        return ans;
    }
    int suc(int x){
        splay(x);
        int tmp=ch[x][1];
        while (ch[tmp][0]) tmp=ch[tmp][0];
        return tmp;
    }
    void del(int &rt,int x){
        if (cover[x]>1){
            splay(x);rt=x;
            cover[x]--,size[x]--;
            return;
        }
        splay(x);int y=suc(x),z=ch[x][0];
        if (!y){
            if (!z){rt=0;return;}
            fa[z]=0,note[z]=2,rt=z;return;
        }
        fa[ch[x][1]]=0,note[ch[x][1]]=2,splay(y);
        ch[y][0]=z,fa[z]=y,update(y),rt=y;
    }
}S;

struct segment_tree{
    struct treenode{
        int root;
    }tree[6*maxn];
    void build(int p,int l,int r){
        for (int i=l;i<=r;i++) S.insert(tree[p].root,a[i]);
        if (l==r) return;
        int mid=(l+r)>>1;
        build(p<<1,l,mid),build(p<<1|1,mid+1,r);
    }
    void change(int p,int l,int r,int pos,int val){
        S.del(tree[p].root,S.find(tree[p].root,a[pos])),S.insert(tree[p].root,val);
        if (l==r) return;
        int mid=(l+r)>>1;
        if (pos<=mid) change(p<<1,l,mid,pos,val);
        else change(p<<1|1,mid+1,r,pos,val);
    }
    int query(int p,int l,int r,int x,int y,int v){
        if (x<=l && r<=y) return S.findk(tree[p].root,v);
        int mid=(l+r)>>1,ans=0;
        if (x<=mid) ans+=query(p<<1,l,mid,x,y,v);
        if (y>mid) ans+=query(p<<1|1,mid+1,r,x,y,v);
        return ans;
    }
}T;
 
int main(){
    n=read(),m=read();S.clear();
    for (int i=1;i<=n;i++) a[i]=read();
    T.build(1,1,n);
    while (m--){
        scanf("%s",s+1);int aa=read(),b=read();
        if (s[1]=='C') T.change(1,1,n,aa,b),a[aa]=b;
        else{
            int k=read();int l=-1e9-7,r=1e9+7,ans=0;
            while (l<=r){
                int mid=(l+r)>>1;
                if (T.query(1,1,n,aa,b,mid)<k) l=mid+1;
                else r=mid-1,ans=mid;
            }
            printf("%d
",ans);
        }
    }
    return 0;
}

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
#define maxn 100005
 
int n,Q,tot,top1,top2,maxv;
int a[maxn],t1[maxn],t2[maxn];
char s[2];
 
struct node{
    int val,pos;
    bool operator <(const node &a)const{return val<a.val;}
}b[maxn],c[maxn];
 
struct query{
    int type,a,b,c;
}q[maxn];
 
bool cmp(node a,node b){return a.pos<b.pos;}
 
struct segment_tree{
    int root[maxn],treedeg;
    struct node{
        int sum,ls,rs;
    }tree[10*maxn];
    void change(int &p,int l,int r,int pos,int val){
        if (!p) p=++treedeg;int mid=(l+r)>>1;
        tree[p].sum+=val;
        if (l==r) return;
        if (pos<=mid) change(tree[p].ls,l,mid,pos,val);
        else change(tree[p].rs,mid+1,r,pos,val);
    }
}T;
 
void change(int i,int pos,int val){
    for (;i<=n;i+=i&(-i)) T.change(T.root[i],1,maxv,pos,val);
}
 
void query(int x,int y,int rank){
    top1=top2=0;
    for (int i=x;i;i-=i&(-i)) t1[++top1]=T.root[i];
    for (int i=y;i;i-=i&(-i)) t2[++top2]=T.root[i];
    int l=1,r=maxv;
    while (l<r){
        int sum=0,mid=(l+r)>>1;
        for (int i=1;i<=top1;i++) sum+=T.tree[T.tree[t1[i]].ls].sum;
        for (int i=1;i<=top2;i++) sum-=T.tree[T.tree[t2[i]].ls].sum;
        if (sum>=rank){
            for (int i=1;i<=top1;i++) t1[i]=T.tree[t1[i]].ls;
            for (int i=1;i<=top2;i++) t2[i]=T.tree[t2[i]].ls;
            r=mid;
        }
        else{
            for (int i=1;i<=top1;i++) t1[i]=T.tree[t1[i]].rs;
            for (int i=1;i<=top2;i++) t2[i]=T.tree[t2[i]].rs;
            l=mid+1,rank-=sum;
        }
    }
    printf("%d
",b[l].val);
}
 
int main(){
    scanf("%d%d",&n,&Q);
    for (int i=1;i<=n;i++) scanf("%d",&a[i]),b[i].val=a[i],b[i].pos=i;int tmp=n;
    for (int i=1;i<=Q;i++){
        scanf("%s%d%d",s+1,&q[i].a,&q[i].b),q[i].type=(s[1]=='C'?0:1);
        if (q[i].type) scanf("%d",&q[i].c);else b[++tmp].val=q[i].b,b[tmp].pos=n+i;
    }
    sort(b+1,b+tmp+1),sort(a+1,a+n+1);
    for (int i=1;i<=tmp;i++)
        if (b[i].pos>n) q[b[i].pos-n].b=i;
        else c[++tot].val=i,c[tot].pos=b[i].pos;
    sort(c+1,c+tot+1,cmp);maxv=tmp;
    for (int i=1;i<=n;i++) change(i,c[i].val,1);
    for (int i=1;i<=Q;i++){
        if (q[i].type==0){
            int pos=q[i].a,val=q[i].b;
            change(pos,c[pos].val,-1),change(pos,val,1),c[pos].val=val;
        }
        else query(q[i].b,q[i].a-1,q[i].c);
    }
    return 0;
}