BZOJ3685 普通 van Emde Boas 树 题解（vEB 树模板题）

（题目描述略）

vEB 树的模板题，似乎用 zkw 线段树也可以过。

因为 vEB 树的建树过程花费大量时间，所以若用 STL 中的 vector 开不定长数组，其常数之大难免有超时的危险。解决方法是用统一的外部数组保存，记下每个节点在外部数组中的开始位置，并保证每个节点在外部数组中占用的地址连续。

最后，还是请 KikiDMW 大神帮助了面对超时问题无解的笔者，写了一段读入优化的代码，才勉强保证了时间在可接受的范围之内。

这里有个细节：vEB 树维护的是从 0 到 n - 1 的区间，所以建树时大小为 n + 1。

代码如下：

#include"math.h"#include"stdio.h"#define MAX_N (1500000)#define NIL (-1)#define Exchange_Integer(x,y) \{ \    int __tmp_x=x; \    x=y,y=__tmp_x; \}struct VANEMDEBOAS_TREE;inline void in(int &x);int cluster_top=0;VANEMDEBOAS_TREE *cluster[MAX_N];struct VANEMDEBOAS_TREE{    int c,max,min,sqr,u;    VANEMDEBOAS_TREE *summary;    int High(int x)    {        return (int)(x/sqr);    }    int Low(int x)    {        return x%sqr;    }    int Index(int x,int y)    {        return x*sqr+y;    }    inline int Maximum()    {        return max;    }    inline int Minimum()    {        return min;    }    bool Member(int x)    {        if(min==x||max==x)            return true;        if(u<=2)            return false;        return cluster[c+High(x)]->Member(Low(x));    }    int Successor(int x)    {        if(u<=2)            if(max==1&&x==0)                return 1;            else                return NIL;        if(min!=NIL&&min>x)            return min;        int max_low=cluster[c+High(x)]->Maximum();        if(max_low!=NIL&&max_low>Low(x))            return Index(High(x),cluster[c+High(x)]->Successor(Low(x)));        int succ_cluster=summary->Successor(High(x));        if(succ_cluster==NIL)            return NIL;        return Index(succ_cluster,cluster[c+succ_cluster]->Minimum());    }    int Predecessor(int x)    {        if(u<=2)            if(min==0&&x==1)                return 0;            else                return NIL;        if(max!=NIL&&max<x)            return max;        int min_low=cluster[c+High(x)]->Minimum();        if(min_low!=NIL&&min_low<Low(x))            return Index(High(x),cluster[c+High(x)]->Predecessor(Low(x)));        int pred_cluster=summary->Predecessor(High(x));        if(pred_cluster==NIL)            if(min!=NIL&&min<x)                return min;            else                return NIL;        return Index(pred_cluster,cluster[c+pred_cluster]->Maximum());    }    void Insert(int x)    {        if(min!=NIL&&min!=x)        {            if(min>x)                Exchange_Integer(min,x);            if(u>2)            {                if(cluster[c+High(x)]->Minimum()==NIL)                    summary->Insert(High(x));                cluster[c+High(x)]->Insert(Low(x));            }            if(max<x)                max=x;        }        else if(min!=x)            max=min=x;    }    void Delete(int x)    {        if(max!=min&&u>2)        {            if(min==x)                min=x=Index(summary->Minimum(),cluster[c+summary->Minimum()]->Minimum());            cluster[c+High(x)]->Delete(Low(x));            if(cluster[c+High(x)]->Minimum()==NIL)            {                summary->Delete(High(x));                if(max==x)                    if(summary->Maximum()!=NIL)                        max=Index(summary->Maximum(),cluster[c+summary->Maximum()]->Maximum());                    else                        max=min;            }            else if(max==x)                max=Index(High(x),cluster[c+High(x)]->Maximum());        }        else if(max!=min&&u==2)            max=min=1-x;        else if(min==x)            max=min=NIL;    }};void VEBT_Create(VANEMDEBOAS_TREE *V,int u){    V->max=V->min=NIL;    V->u=u;    if(u>2)    {        V->c=cluster_top;        V->sqr=(int)sqrt(u);        V->sqr=V->sqr*V->sqr<u?V->sqr+1:V->sqr;        int x=u/V->sqr;        for(int i=0;i<x;i++)            cluster[cluster_top++]=new VANEMDEBOAS_TREE;        if(u%V->sqr>0)            cluster[cluster_top++]=new VANEMDEBOAS_TREE;        for(int i=0;i<x;i++)            VEBT_Create(cluster[V->c+i],V->sqr);        if(u%V->sqr>0)            VEBT_Create(cluster[V->c+x++],u%V->sqr);        V->summary=new VANEMDEBOAS_TREE;        VEBT_Create(V->summary,x);    }    else        V->summary=NULL;}int main(){    int m,n;    VANEMDEBOAS_TREE *vEBTree=new VANEMDEBOAS_TREE;    in(n);in(m);    VEBT_Create(vEBTree,n+1);    while(m--)    {        in(n);        switch(n)        {            case 1:in(n);vEBTree->Insert(n);break;            case 2:in(n);vEBTree->Delete(n);break;            case 3:printf("%d\n",vEBTree->Minimum());break;            case 4:printf("%d\n",vEBTree->Maximum());break;            case 5:in(n);printf("%d\n",vEBTree->Predecessor(n));break;            case 6:in(n);printf("%d\n",vEBTree->Successor(n));break;            case 7:in(n);printf("%d\n",vEBTree->Member(n)?1:-1);break;        }    }    return 0;}inline void in(int &x){    x = 0; char c; c = getchar();    while(c < '0' || c > '9') c = getchar();    while(c >= '0' && c <= '9'){        x = x * 10 + c - '0';        c = getchar();    }}