【POJ2985】【Treap + 并查集】The k-th Largest Group

Description

Newman likes playing with cats. He possesses lots of cats in his home. Because the number of cats is really huge, Newman wants to group some of the cats. To do that, he first offers a number to each of the cat (1, 2, 3, …, n). Then he occasionally combines the group cat i is in and the group cat j is in, thus creating a new group. On top of that, Newman wants to know the size of the k-th biggest group at any time. So, being a friend of Newman, can you help him?

Input

1st line: Two numbers N and M (1 ≤ N, M ≤ 200,000), namely the number of cats and the number of operations.

2nd to (m + 1)-th line: In each line, there is number C specifying the kind of operation Newman wants to do. If C = 0, then there are two numbers i and j (1 ≤ i, j ≤ n) following indicating Newman wants to combine the group containing the two cats (in case these two cats are in the same group, just do nothing); If C = 1, then there is only one number k (1 ≤ k ≤ the current number of groups) following indicating Newman wants to know the size of the k-th largest group.

Output

For every operation “1” in the input, output one number per line, specifying the size of the kth largest group.

Sample Input

10 10
0 1 2
1 4
0 3 4
1 2
0 5 6
1 1
0 7 8
1 1
0 9 10
1 1

Sample Output

1
2
2
2
2

Hint

When there are three numbers 2 and 2 and 1, the 2nd largest number is 2 and the 3rd largest number is 1.

Source

POJ Monthly--2006.08.27, zcgzcgzcg

【分析】

这道题的正解是线段树，我只是拿来练个手而已。

写一遍直接交，狂T无压力....

Treap的常数实在是太大了，写了N遍，开始拿以为是内存池的问题.

尼玛开了内存池居然会比动态内存分配慢！！谁能告诉我为什么(╯‵□′)╯︵┻━┻。

好吧，关键不在这里...

treap写一般会t但是进行优化了以后还是可以过的。

只要不把大小为1的并查集加进去就可以了.........

 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 #include <vector>
 #include <utility>
 #include <iomanip>
 #include <string>
 #include <cmath>
 #include <queue>
 #include <assert.h>
 #include <map>
 #include <ctime>
 #include <cstdlib>

 const int N =  + ;
 const int SIZE = ;//块状链表的大小
 const int M =  + ;
 using namespace std;
 struct TREAP{
        struct Node{
               int fix, size;
               int val;
               Node *ch[];
        }mem[N], *root;
        struct mem_poor{//内存池
               queue<Node>Q;
               void push(Node *t){//消除指针t所占用的地址
                    Q.push((*t));
               }
               Node* get(){
                    Node* t = &Q.front();
                    Q.pop();
                    return t;
               }
        }poor;
        int tot, size;
        //大随机
        void init(){
            // for (int i = 0; i <= 200000 + 5; i++)
             //poor.Q.push(mem[i]);
             size = ;
             tot = ;
        }
        int BIG_RAND(){return rand();}
        Node *NEW(){
             Node *p = new Node;
             p->fix = rand();//BIG_RAND();
             p->size = ;
             p->ch[] = p->ch[] = NULL;
             return p;
        }
        //将t的d节点换到t
        void rotate(Node *&t, int d){
             Node *p = t->ch[d];
             t->ch[d] = p->ch[d ^ ];
             p->ch[d ^ ] = t;
             t->size = ;
             if (t->ch[] != NULL) t->size += t->ch[]->size;
             if (t->ch[] != NULL) t->size += t->ch[]->size;
             p->size = ;
             if (p->ch[] != NULL) p->size += p->ch[]->size;
             if (p->ch[] != NULL) p->size += p->ch[]->size;
             t = p;
             return;
        }
        void insert(Node *&t, int val){
             //插入
             if (t == NULL){
                t = NEW();
                t->val = val;
                //size++;
                return;
             }
             //大的在右边,小的在左边
             int dir = (val >= t->val);
             insert(t->ch[dir], val);
             //维护最大堆的性质
             if (t->ch[dir]->fix > t->fix) rotate(t, dir);
             t->size = ;
             if (t->ch[] != NULL) t->size += t->ch[]->size;
             if (t->ch[] != NULL) t->size += t->ch[]->size;
        }
        //在t的子树中找到第k小的值
        int kth(Node *t, int k){
            if (t == NULL ||  k<= || k > t -> size) return ;
            if (t->size ==  ) return t->val;
            int l = ;//t的左子树中有多少值
            if (t->ch[] != NULL) l += t->ch[]->size;
            if (k == (l + )) return t->val;
            if (k <= l) return kth(t->ch[], k);
            else return kth(t->ch[], k - (l + ));
        }
        /*int find(Node *t, int val){
            if (t == NULL) return 0;
            int l = 0;//累加值
            if (t->ch[0] != NULL) l += t->ch[0]->size;
            if (val == t->val) return l + 1;
            else if (val < t->val) return find(t->ch[0], val);
            else return l + 1 + find(t->ch[1], val);
        }*/
        //找到值为val的节点
        /*Node *&get(Node *&t, int val){
            //if (t == NULL) return NULL;
            if (val == t->val) return t;//根结点是，没办法 

            if (t->ch[0] != NULL && t->ch[0]->val == val) return t;
            if (t->ch[1] != NULL && t->ch[1]->val == val) return t;

            if (val < t->val) return get(t->ch[0], val);
            else return get(t->ch[1], val);
        }*/
        /*void update(Node *&t){
             if (t == NULL) return;
             update(t->ch[0]);
             update(t->ch[1]);
             t->size = 1;
             if (t->ch[0] != NULL) t->size += t->ch[0]->size;
             if (t->ch[1] != NULL) t->size += t->ch[1]->size;
        }*/
        void Delete(Node* &t,int x){
             int d;
             if (x == t->val) d = -;
             else d = (x > t->val);
             if (d == -){
                Node *tmp = t;
                if(t->ch[] == NULL){
                   t = t->ch[];
                   //poor.push(tmp);
                   delete tmp;
                   tmp = NULL;
                }else if(t->ch[] == NULL){
                   t = t->ch[];
                   //poor.push(tmp);
                   delete tmp;
                   tmp = NULL;
                }else{
                   int k = t->ch[]->fix > t->ch[]->fix ?  : ;
                   //int  k = 1;
                   rotate(t,k);
                   Delete(t->ch[k ^ ],x);
                }
             }else Delete(t->ch[d],x);
             if (t!=NULL){
                 t->size = ;
                 if (t->ch[] != NULL) t->size += t->ch[]->size;
                 if (t->ch[] != NULL) t->size += t->ch[]->size;
             }
        }
        /*void print(Node *t){
             if (t == NULL) return;
             print(t->ch[0]);
             printf("%d ", t->val);
             print(t->ch[1]);
        }*/
 }treap;
 /*int Scan()  {
     int res = 0, ch, flag = 0;
     if((ch = getchar()) == '-')             //判断正负
         flag = 1;
     else if(ch >= '0' && ch <= '9')           //得到完整的数
         res = ch - '0';
     while((ch = getchar()) >= '0' && ch <= '9' )
         res = res * 10 + ch - '0';
     return flag ? -res : res;
 }  */
 int parent[N], n ,m;
 int find(int x){return parent[x] < ? x : parent[x] = find(parent[x]);}

 void init(){
      treap.init();
      treap.root = NULL;
      //memset(parent, -1, sizeof(parent));
      scanf("%d%d", &n, &m);
      for (int i = ; i <= n; i++) parent[i] = -;
      //n = Scan();
      //m = Scan();
      //for (int i = 1; i <= n; i++) treap.insert(treap.root, 1);
 }
 void work(){
      for (int i = ; i <= m; i++){
          int t;
          //t = Scan();
          scanf("%d", &t);
          if (t == ){
             int x, y;
             scanf("%d%d", &x, &y);
             //x = Scan();y = Scan();
             x = find(x);
             y = find(y);
             if (x == y) continue;
             if (parent[x] < -) treap.Delete(treap.root, -parent[x]);
             if (parent[y] < -) treap.Delete(treap.root, -parent[y]);
             treap.insert(treap.root, -(parent[x] + parent[y]));
             parent[y] += parent[x];
             parent[x] = y;
          }else{
             int k;
             scanf("%d", &k);
             //k = Scan();i
             if (treap.root == NULL || k > treap.root->size) {printf("1\n");continue;}
             k = treap.root->size - k + ;
             printf("%d\n", treap.kth(treap.root, k));
          }
      }
 }

 int main(){
     int T;
     srand(time());
     #ifdef LOCAL
     freopen("data.txt", "r", stdin);
     freopen("out.txt", "w", stdout);
     #endif
     init();
     work();
     //debug();
     return ;
 }