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LibreOJ #107. 维护全序集
二次联通门 : LibreOJ #107. 维护全序集
/* LibreOJ #107. 维护全序集 Splay 支持 1.把 x 加入 S 2.删除 S 中的一个 x,保证删除的 x 一定存在 3.求 S 中第 k 小 4.求 S 中有多少个元素小于 x 5.求 S 中小于 x 的最大数 6.求 S 中大于 x 的最小数 我之前用Splay找数x的排名时采用的是挨个找的 现在发现根本没必要 只需要把splay(x)后减去右子树的大小与根节点的数出现几次即可 */ #include <cstdio> void read (int &now) { register char word = getchar (); bool temp = false; for (now = 0; word < ‘0‘ || word > ‘9‘; word = getchar ()) if (word == ‘-‘) temp = true; for (; word >= ‘0‘ && word <= ‘9‘; now = now * 10 + word - ‘0‘, word = getchar ()); if (temp) now = -now; } struct S_D { S_D *child[2], *father; int value; int weigth, size; S_D () { child[0] = child[1] = NULL; father = NULL; value = 0; size = 1; weigth = 1; } inline int Get_Pos () { return this->father->child[1] == this; } inline void Updata () { this->size = this->weigth; if (this->child[0]) this->size += this->child[0]->size; if (this->child[1]) this->size += this->child[1]->size; } inline void Clear () { child[0] = child[1] = NULL; father = NULL; value = size = weigth = 0; } }; class Splay_Tree_Type { private : S_D *Root; inline void Rotate (S_D *now) { S_D *Father = now->father; register int pos = now->Get_Pos () ^ 1; Father->child[pos ^ 1] = now->child[pos]; if (now->child[pos]) now->child[pos]->father = Father; if ((now->father = Father->father) != NULL) now->father->child[now->father->child[1] == Father] = now; Father->father = now; now->child[pos] = Father; Father->Updata (); now->Updata (); if (now->father == NULL) Root = now; } inline void Splay (S_D *now) { for (S_D *Father; Father = now->father; Rotate (now)) if (Father->father) Rotate (now->Get_Pos () == Father->Get_Pos () ? Father : now); } public : void Insert (int key) { if (Root == NULL) { Root = new S_D; Root->value =http://www.mamicode.com/ key; return ; } S_D *now = Root, *Father; for (; ;Father = now, now = now->child[key > now->value]) { if (now == NULL) { now = new S_D; now->father = Father; now->value =http://www.mamicode.com/ key; Father->child[key > Father->value] = now; Splay (now); return ; } if (now->value =http://www.mamicode.com/= key) { now->weigth ++; Splay (now); return ; } } } S_D *Find (int key) { S_D *now = Root; for (S_D *Father; (now != NULL && now->value != key); Father = now, now = now->child[key > now->value]); if (now == NULL) return now; Splay (now); return now; } int Find_Prifix (int key) { S_D *now = Find (key); bool flag = false; if (now == NULL) { this->Insert (key); now = Root; flag = true; } if (now->child[0] == NULL) { if (flag) this->Delete (key); return -1; } for (now = now->child[0]; now->child[1]; now = now->child[1]); if (flag) this->Delete (key); return now->value; } S_D* Find_Prifix_pos (int key) { S_D *now = Find (key); bool flag = false; if (now == NULL) { this->Insert (key); now = Root; flag = true; } if (now->child[0] == NULL) { if (flag) this->Delete (key); return NULL; } for (now = now->child[0]; now->child[1]; now = now->child[1]); if (flag) this->Delete (key); return now; } int Find_Suffix (int key) { S_D *now = Find (key); bool flag = false; if (now == NULL) { this->Insert (key); now = Root; flag = true; } if (now->child[1] == NULL) { if (flag) this->Delete (key); return -1; } for (now = now->child[1]; now->child[0]; now = now->child[0]); if (flag) this->Delete (key); return now->value; } int Get_rank (int key) { S_D *now = Find (key); bool flag = false; if (now == NULL) { this->Insert (key); flag = true; } int Answer = Root->size; if (Root->child[1]) Answer -= Root->child[1]->size; Answer -= Root->weigth; if (flag) this->Delete (key); return Answer; } void Delete (int key) { S_D *now = Find (key); if (now->weigth > 1) { now->weigth --; now->size --; return ; } if (now->child[0] == NULL && now->child[1] == NULL) { now->Clear (); now = NULL; // ????could change to delete Root = NULL; return ; } if (now->child[0] == NULL) { S_D *res = now; Root = now->child[1]; now->child[1]->father = NULL; now->Clear (); now = NULL; return ; } if (now->child[1] == NULL) { S_D *res = now; Root = now->child[0]; now->child[0]->father = NULL; now->Clear (); now = NULL; return ; } S_D *res_pre = Find_Prifix_pos (now->value); S_D *res = Root; Splay (res_pre); Root->child[1] = res->child[1]; res->child[1]->father = Root; res->Clear (); Root->Updata (); } int Get_kth_number (int key) { int Answer = 0; register int res; for (S_D *now = Root; ;) { if (now->child[0] && key <= now->child[0]->size) { now = now->child[0]; continue; } res = (now->child[0] ? now->child[0]->size : 0) + now->weigth; if (key <= res) return now->value; key -= res; now = now->child[1]; } } }; Splay_Tree_Type Splay; int main (int argc, char *argv[]) { int N; read (N); int type, x; for (register int i = 1; i <= N; i ++) { read (type); read (x); switch (type) { case 0: { Splay.Insert (x); break; } case 1: { Splay.Delete (x); break; } case 2: { printf ("%d\n", Splay.Get_kth_number (x)); break; } case 3: { printf ("%d\n", Splay.Get_rank (x)); break; } case 4: { printf ("%d\n", Splay.Find_Prifix (x)); break; } case 5: { printf ("%d\n", Splay.Find_Suffix (x)); break; } } } return 0; }
LibreOJ #107. 维护全序集
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