HDU 4006 The kth great number [2011 大连网络赛] [AVL树解法]

题意:

找第K大的数惊讶


分析:

可以用STL里的priority_queue解决,这里尝试使用AVL树~生气


//AC CODE:


#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
int delta;
const int INF = 10000000;
template<typename T>
class AVL
{
public:
    AVL()
    {
        pp = pool;
        TMP = node(0,0,NULL,NULL);
        MYNULL = &TMP;
        roof = MYNULL;
    }
    void insert(T k)
    {
        insert(roof,k);
    }

    void erase(T k)
    {
        erase(roof,k);
    }

    bool empty()
    {
        return roof == MYNULL;
    }
    int findK(int k)
    {
        if(k <= 0)
            return -INF;
        return findK(roof,k);
    }
    struct node
    {
        node *lchild,*rchild;
        T value;
        int h,size;//h表示高度,size表示以当前节点为跟的子树有多少个节点
        node() {}
        node (int h,int size,node * lchild,node *rchild)
        {
            this->size = size;
            this->h = h;
            this->lchild = lchild;
            this->rchild = rchild;
        }
    };
    node* roof;
private:
#define max(a,b) ((a) < (b) ? (b) : (a))

    static const int N = 1000000;
    node* MYNULL,TMP;
    //为了快速方便的求高度而设立的虚空节点
    node pool[N],*pp;
    int findK(node* &R,int k)
    {
        if(k == R->lchild->size + 1)
            return R->value;
        else if(k <= R->lchild->size)
            return findK(R->lchild,k);
        else if(k > R->size - R->rchild->size)
            return findK(R->rchild,k + R->rchild->size - R->size);
    }
    //旋转前维护该节点的子树的height和size,然后才能根据更新的数据,判断该树是否平衡,然后旋转
    //该函数维护了平衡树的数据域
    void fix(node* &R)
    {
        R->h = max(R->rchild->h,R->lchild->h) + 1;
        R->size = R->rchild->size + R->lchild->size + 1;
    }

    void rightsinglerotate(node* &R)//LL型旋转,单旋一次
    {
        node * lc = R->lchild;
        R->lchild = lc->rchild;
        fix(R);
        lc->rchild = R;
        R = lc;
        fix(R);
    }

    void leftsinglerotate(node* &R)//RR型旋转,单选一次
    {
        node * rc = R->rchild;
        R->rchild = rc->lchild;
        fix(R);
        rc->lchild = R;
        R = rc;
        fix(R);
    }

    void leftdoublerotate(node* &R)//RL型旋转,双旋
    {
        rightsinglerotate(R->rchild);
        leftsinglerotate(R);
    }

    void rightdoublerotate(node* &R)//LR型旋转,双旋
    {
        leftsinglerotate(R->lchild);
        rightsinglerotate(R);
    }

    void maintain(node* &R)//维护平衡
    {
        if(R->lchild != MYNULL)
        {
            if(R->lchild->lchild->h == R->rchild->h + 1)
                rightsinglerotate(R);
            else if(R->lchild->rchild->h == R->rchild->h + 1)
                rightdoublerotate(R);
        }
        if(R->rchild != MYNULL)
        {
            if(R->rchild->rchild->h == R->lchild->h + 1)
                leftsinglerotate(R);
            else if(R->rchild->lchild->h == R->lchild->h + 1)
                leftdoublerotate(R);
        }
    }

    void insert(node* &R,T value)
    {
        if(R == MYNULL)
        {
            R = mynew(value);
            return;
        }
        else if(value <= R->value)
            insert(R->lchild,value);
        else if(value > R->value)
            insert(R->rchild,value);
        fix(R);
        maintain(R);
    }
    //找到该节点后,
    //如果该节点R没有右儿子,直接删除,把他的左子树R->child接到他的父节点即可。
    //如果有右儿子,那就找到他右子树中最小的元素的节点tmp,
    //把他放到当前节点R->value = tmp->value。再以他的右子树为根递归的删除tmp->value;递归完右子树维护数据域。
    //最后在调整树使其不失衡。
    void erase(node* &R,T value)
    {
        if(R == MYNULL)
            return;
        if(R->value == value)
        {
            if(R->rchild == MYNULL)
            {
                node * tmp = R;
                R = tmp->lchild;
            }
            else
            {
                node *tmp = R->rchild;
                while(tmp->lchild != MYNULL)
                    tmp = tmp->lchild;
                R->value = tmp->value;
                erase(R->rchild,tmp->value);
                fix(R);
            }
            return;
        }
        else if(value < R->value)
            erase(R->lchild,value);
        else if(value < R->value)
            erase(R->rchild,value);
        fix(R);
        maintain(R);
    }

    node* mynew(T value)
    {
        pp->lchild = pp->rchild = MYNULL;
        pp->size = pp->h = 1;
        pp->value = value;
        return pp++;
    }
#undef max
};
AVL<int> avltree;
int main()
{
    int n,k,tmp;
    char cmd;
    while(scanf("%d %d",&n,&k)!=EOF)
    {
        getchar();
        while(!avltree.empty())
        {
            avltree.erase(avltree.roof->value);
        }
        for(int i=0;i<n;i++)
        {
            scanf("%c",&cmd);
            if(cmd=='I')
            {
                scanf("%d",&tmp);
                avltree.insert(tmp);
            }
            else
            {
                int tmp = avltree.findK(avltree.roof->size - k + 1);
                if(tmp == -INF)
                    printf("-1\n");
                else
                    printf("%d\n",tmp);
            }
            getchar();
        }
    }
    return 0;
}


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