【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.........
1 #include <iostream> 2 #include <cstdio> 3 #include <algorithm> 4 #include <cstring> 5 #include <vector> 6 #include <utility> 7 #include <iomanip> 8 #include <string> 9 #include <cmath> 10 #include <queue> 11 #include <assert.h> 12 #include <map> 13 #include <ctime> 14 #include <cstdlib> 15 16 const int N = 200000 + 10; 17 const int SIZE = 250;//块状链表的大小 18 const int M = 50000 + 5; 19 using namespace std; 20 struct TREAP{ 21 struct Node{ 22 int fix, size; 23 int val; 24 Node *ch[2]; 25 }mem[N], *root; 26 struct mem_poor{//内存池 27 queue<Node>Q; 28 void push(Node *t){//消除指针t所占用的地址 29 Q.push((*t)); 30 } 31 Node* get(){ 32 Node* t = &Q.front(); 33 Q.pop(); 34 return t; 35 } 36 }poor; 37 int tot, size; 38 //大随机 39 void init(){ 40 // for (int i = 0; i <= 200000 + 5; i++) 41 //poor.Q.push(mem[i]); 42 size = 0; 43 tot = 0; 44 } 45 int BIG_RAND(){return rand();} 46 Node *NEW(){ 47 Node *p = new Node; 48 p->fix = rand();//BIG_RAND(); 49 p->size = 1; 50 p->ch[0] = p->ch[1] = NULL; 51 return p; 52 } 53 //将t的d节点换到t 54 void rotate(Node *&t, int d){ 55 Node *p = t->ch[d]; 56 t->ch[d] = p->ch[d ^ 1]; 57 p->ch[d ^ 1] = t; 58 t->size = 1; 59 if (t->ch[0] != NULL) t->size += t->ch[0]->size; 60 if (t->ch[1] != NULL) t->size += t->ch[1]->size; 61 p->size = 1; 62 if (p->ch[0] != NULL) p->size += p->ch[0]->size; 63 if (p->ch[1] != NULL) p->size += p->ch[1]->size; 64 t = p; 65 return; 66 } 67 void insert(Node *&t, int val){ 68 //插入 69 if (t == NULL){ 70 t = NEW(); 71 t->val = val; 72 //size++; 73 return; 74 } 75 //大的在右边,小的在左边 76 int dir = (val >= t->val); 77 insert(t->ch[dir], val); 78 //维护最大堆的性质 79 if (t->ch[dir]->fix > t->fix) rotate(t, dir); 80 t->size = 1; 81 if (t->ch[0] != NULL) t->size += t->ch[0]->size; 82 if (t->ch[1] != NULL) t->size += t->ch[1]->size; 83 } 84 //在t的子树中找到第k小的值 85 int kth(Node *t, int k){ 86 if (t == NULL || k<=0 || k > t -> size) return 1; 87 if (t->size == 1 ) return t->val; 88 int l = 0;//t的左子树中有多少值 89 if (t->ch[0] != NULL) l += t->ch[0]->size; 90 if (k == (l + 1)) return t->val; 91 if (k <= l) return kth(t->ch[0], k); 92 else return kth(t->ch[1], k - (l + 1)); 93 } 94 /*int find(Node *t, int val){ 95 if (t == NULL) return 0; 96 int l = 0;//累加值 97 if (t->ch[0] != NULL) l += t->ch[0]->size; 98 if (val == t->val) return l + 1; 99 else if (val < t->val) return find(t->ch[0], val); 100 else return l + 1 + find(t->ch[1], val); 101 }*/ 102 //找到值为val的节点 103 /*Node *&get(Node *&t, int val){ 104 //if (t == NULL) return NULL; 105 if (val == t->val) return t;//根结点是，没办法 106 107 if (t->ch[0] != NULL && t->ch[0]->val == val) return t; 108 if (t->ch[1] != NULL && t->ch[1]->val == val) return t; 109 110 if (val < t->val) return get(t->ch[0], val); 111 else return get(t->ch[1], val); 112 }*/ 113 /*void update(Node *&t){ 114 if (t == NULL) return; 115 update(t->ch[0]); 116 update(t->ch[1]); 117 t->size = 1; 118 if (t->ch[0] != NULL) t->size += t->ch[0]->size; 119 if (t->ch[1] != NULL) t->size += t->ch[1]->size; 120 }*/ 121 void Delete(Node* &t,int x){ 122 int d; 123 if (x == t->val) d = -1; 124 else d = (x > t->val); 125 if (d == -1){ 126 Node *tmp = t; 127 if(t->ch[0] == NULL){ 128 t = t->ch[1]; 129 //poor.push(tmp); 130 delete tmp; 131 tmp = NULL; 132 }else if(t->ch[1] == NULL){ 133 t = t->ch[0]; 134 //poor.push(tmp); 135 delete tmp; 136 tmp = NULL; 137 }else{ 138 int k = t->ch[0]->fix > t->ch[1]->fix ? 0 : 1; 139 //int k = 1; 140 rotate(t,k); 141 Delete(t->ch[k ^ 1],x); 142 } 143 }else Delete(t->ch[d],x); 144 if (t!=NULL){ 145 t->size = 1; 146 if (t->ch[0] != NULL) t->size += t->ch[0]->size; 147 if (t->ch[1] != NULL) t->size += t->ch[1]->size; 148 } 149 } 150 /*void print(Node *t){ 151 if (t == NULL) return; 152 print(t->ch[0]); 153 printf("%d ", t->val); 154 print(t->ch[1]); 155 }*/ 156 }treap; 157 /*int Scan() { 158 int res = 0, ch, flag = 0; 159 if((ch = getchar()) == '-') //判断正负 160 flag = 1; 161 else if(ch >= '0' && ch <= '9') //得到完整的数 162 res = ch - '0'; 163 while((ch = getchar()) >= '0' && ch <= '9' ) 164 res = res * 10 + ch - '0'; 165 return flag ? -res : res; 166 } */ 167 int parent[N], n ,m; 168 int find(int x){return parent[x] < 0? x : parent[x] = find(parent[x]);} 169 170 void init(){ 171 treap.init(); 172 treap.root = NULL; 173 //memset(parent, -1, sizeof(parent)); 174 scanf("%d%d", &n, &m); 175 for (int i = 1; i <= n; i++) parent[i] = -1; 176 //n = Scan(); 177 //m = Scan(); 178 //for (int i = 1; i <= n; i++) treap.insert(treap.root, 1); 179 } 180 void work(){ 181 for (int i = 1; i <= m; i++){ 182 int t; 183 //t = Scan(); 184 scanf("%d", &t); 185 if (t == 0){ 186 int x, y; 187 scanf("%d%d", &x, &y); 188 //x = Scan();y = Scan(); 189 x = find(x); 190 y = find(y); 191 if (x == y) continue; 192 if (parent[x] < -1) treap.Delete(treap.root, -parent[x]); 193 if (parent[y] < -1) treap.Delete(treap.root, -parent[y]); 194 treap.insert(treap.root, -(parent[x] + parent[y])); 195 parent[y] += parent[x]; 196 parent[x] = y; 197 }else{ 198 int k; 199 scanf("%d", &k); 200 //k = Scan();i 201 if (treap.root == NULL || k > treap.root->size) {printf("1\n");continue;} 202 k = treap.root->size - k + 1; 203 printf("%d\n", treap.kth(treap.root, k)); 204 } 205 } 206 } 207 208 int main(){ 209 int T; 210 srand(time(0)); 211 #ifdef LOCAL 212 freopen("data.txt", "r", stdin); 213 freopen("out.txt", "w", stdout); 214 #endif 215 init(); 216 work(); 217 //debug(); 218 return 0; 219 }
