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。

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#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\n",ans);         }     }     return 0; }

 

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#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\n",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; }