【HDU 4441】 Queue Sequence(Splay)

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这道题也是一道splay的基础操作的集合题，主要包含有三种操作：

insert p ：在p位置插入当前未出现的最小的数，如当前出现了1 2 3 6，那再插入4

且正数和负数同时插入，而负数插入的位置要求：该负数左边负数的个数和该数的相反数的左边的正数的个数一样多且最为靠右

则若2左边有4个正数，那么-2就应该插入在满足左边有4个负数的最靠右的位置

而如何找到最小的数呢？用一个优先队列维护一下应该不难想到

remove p:删除p以及-p。这个操作只需要在插入的时候记录一下p和-p的地址就好了

query p：计算从p到 -p的和为多少。只需要将p旋为根，将-p旋为右子树，那么关键树就是区间的和，维护一下子树和应该OK的

下面是代码：

#include<cstdio>#include<queue>#include<cstring>#include<algorithm>#define keytree (ch[ ch[root][1] ][0])typedef long long LL;using namespace std;const int SIZEN = 200005;struct SplayTree{    int ch[SIZEN][2];    int pre[SIZEN];    int sz[SIZEN];    int top,top2,root,rest;    priority_queue<int,vector<int>,greater<int> > q;    inline void pushup(int x){        sz[x] = sz[ ch[x][0] ] + sz[ ch[x][1] ] + 1;        cnt[x] = cnt[ ch[x][0] ] + cnt[ ch[x][1] ] + (val[x] < 0);        sum[x] = sum[ ch[x][0] ] + sum[ ch[x][1] ] + val[x];    }    inline void Rotate(int x,int f){        int y = pre[x];        ch[y][!f] = ch[x][f];        pre[ ch[x][f] ] = y;        pre[x] = pre[y];        if(pre[y]) ch[ pre[y] ][ ch[ pre[y] ][1] == y ] = x;        ch[x][f] = y;        pre[y] = x;        pushup(y);    }    inline void Splay(int x,int goal){        while(pre[x] != goal){            if(pre[ pre[x] ] == goal)                Rotate(x,ch[ pre[x] ][0] == x);            else{                int y = pre[x],z = pre[y];                int f = ch[z][0] == y;                if(ch[y][f] == x){                    Rotate(x,!f),Rotate(x,f);                }                else{                    Rotate(y,f),Rotate(x,f);                }            }        }        pushup(x);        if(goal == 0) root = x;    }    inline void Rotateto(int k,int goal){        int x = root;        while(sz[ ch[x][0] ] != k){            if(sz[ ch[x][0] ] > k){                x = ch[x][0];            }            else{                k -= sz[ ch[x][0] ] + 1;                x = ch[x][1];            }        }        Splay(x,goal);    }    inline void init(){        ch[0][0] = ch[0][1] = pre[0] = 0;        sz[0] = val[0] = sum[0] = 0;        cnt[0] = 0;        while(!q.empty()) q.pop();        top = top2 = root = rest = 0;        root = Newnode(0);        ch[root][1] = Newnode(0);        sz[root] = 2;        pre[ ch[root][1] ] = root;        pre[root] = 0;    }    int Newnode(int c){        int x = ++top;        ch[x][0] = ch[x][1] = pre[0] = 0;        val[x] = sum[x] = c;        sz[x] = 1;        cnt[x] = (c < 0);        if(c > 0) loc[c] = x;            else n_loc[-c] = x;        return x;    }    int Find(int k,int x){        if(cnt[ ch[x][0] ] + 1 == k && val[x] < 0) return x;        if(cnt[ ch[x][0] ] >= k) return Find(k,ch[x][0]);            else return Find(k - cnt[ ch[x][0] ] - (val[x] < 0),ch[x][1]);    }    inline int findmax(int x){        while(ch[x][1]) x = ch[x][1];        return x;    }    inline int findmin(int x){        while(ch[x][0]) x = ch[x][0];        return x;    }    inline void debug(){        printf("root:%d\n",root);        Travel(root);    }    void Travel(int x){        if(ch[x][0]) Travel(ch[x][0]);        printf("node:%d lson:%d rson:%d pre:%d sz:%d cnt:%d val:%d\n",x,ch[x][0],ch[x][1],pre[x],sz[x],cnt[x],val[x]);        if(ch[x][1]) Travel(ch[x][1]);    }    void Insert(){        int c,p;        scanf(" %d",&p);        if(!q.empty()) {c = q.top(),q.pop();}            else c = ++top2;        Rotateto(p,0);        Rotateto(p + 1,root);        keytree = Newnode(c);        rest++;        pre[keytree] = ch[root][1];        pushup(ch[root][1]);        pushup(root);        Splay(keytree,0);        int n_cnt = sz[ ch[root][0] ] - cnt[ ch[root][0] ];        if(cnt[root]  < n_cnt){            Rotateto(rest,0);            Rotateto(rest + 1,root);            keytree = Newnode(-c);            pre[keytree] = ch[root][1];            pushup(ch[root][1]);            pushup(root);        }        else{            int lloc = Find(n_cnt,root);            Splay(lloc,0);            int x = findmax(ch[root][0]);            Splay(x,0);            Splay(lloc,root);            keytree = Newnode(-c);            pre[keytree] = ch[root][1];            pushup(ch[root][1]);            pushup(root);        }        rest++;    }    inline void del(int x){        Splay(x,0);        if(!ch[root][0]){            root = ch[root][1];            pre[root] = 0;            return;        }        int tmp = findmax(ch[root][0]);        Splay(tmp,root);        ch[ ch[root][0] ][1] = ch[root][1];        pre[ ch[root][1] ] = ch[root][0];        root = ch[root][0];        pre[root] = 0;        pushup(root);    }    inline void Del(){        int c;        scanf("%d",&c);        del(loc[c]);        del(n_loc[c]);        q.push(c);        rest -= 2;    }    inline void Query(){        int c;        scanf("%d",&c);        Splay(loc[c],0);        Splay(n_loc[c],root);        printf("%I64d\n",sum[keytree]);    }    LL sum[SIZEN];    int val[SIZEN],cnt[SIZEN];    int n_loc[SIZEN],loc[SIZEN];};SplayTree spt;void solve(int n){    char op[10];    spt.init();    for(int i = 0 ; i < n ; i ++){        scanf(" %s",op);        if(op[0] == 'i') spt.Insert();        else if(op[0] == 'r') spt.Del();        else if(op[0] == 'q') spt.Query();    }}int main(){    int n,txt = 1;    while(scanf("%d",&n) != EOF){        printf("Case #%d:\n",txt++);        solve(n);    }}

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