SPOJ 3273 Order statistic set

Treap 模板題

題意： 要求實現一種資料結構，支援：

Insert： 插入原來不存在的元素。

Remove： 刪除原來存在的元素。

Kth： 詢問第K大的元素，詢問不合法(即k大於元素數量)，輸出“invalid”。

Count：詢問小於x的元素的數量。

解法： Treap的基本操作全齊了，紅果果的裸題。

訓練指南版

#include <stdio.h>#include <string.h>#include <algorithm>#include <stdlib.h>#include <time.h>using namespace std;// Treap, 大根堆寫法,指標寫法struct Node {Node *ch[2];int r;int v;int size;int cmp(int x) const {if(x == v) return -1;return x < v ? 0 : 1;}void maintain() {size = ch[0]->size + ch[1]->size + 1;}};Node* nill;void rotate(Node* &o, int d) {Node* k = o->ch[d^1];o->ch[d^1] = k->ch[d];k->ch[d] = o;o = k;o->ch[d]->maintain();o->maintain();}void insert(Node* &o, int x) {if(o == nill) {o = new Node();o->ch[0] = o->ch[1] = nill;o->v = x;o->r = rand();}else {int d = o->cmp(x);insert(o->ch[d],x);if(o->ch[d]->r > o->r) rotate(o,d^1);}o->maintain();}void remove(Node* &o, int x) {int d = o->cmp(x);if(d == -1) {if(o->ch[0] == nill || o->ch[1] == nill) {Node* u = o;if(o->ch[0] == nill) o = o->ch[1];else  o = o->ch[0];delete u;}else {int d2 = (o->ch[0]->r > o->ch[1]->r ? 1 : 0);rotate(o,d2);remove(o->ch[d2],x);}}else remove(o->ch[d],x);if(o != nill) o->maintain();}int find(Node* o, int x) {while(o != nill) {int d = o->cmp(x);if(d == -1) return 1;else o = o->ch[d];}return 0;}int count(Node* o, int x) {int ret = 0;while(o != nill) {if(x > o->v) {ret += o->ch[0]->size + 1;o = o->ch[1];}else o = o->ch[0];}return ret;}int Kth(Node* o, int x) {while(o != nill) {if(o->ch[0]->size == x-1) return o->v;if(o->ch[0]->size >= x) o = o->ch[0];else {x -= o->ch[0]->size + 1;o = o->ch[1];}}return -1;}void init() {nill = new Node();nill->ch[0] = nill->ch[1] = nill;nill->size = 0;srand(time(NULL));}int main() {init();Node* root = nill;int q,x;char s[2];scanf("%d", &q);while(q--) {scanf("%s%d", s, &x);if(s[0] == 'I' && find(root,x) == 0) insert(root,x);else if(s[0] == 'D' && find(root,x) == 1) remove(root,x);else if(s[0] == 'C') printf("%d\n",count(root,x));else if(s[0] == 'K') {if(root->size < x) printf("invalid\n");else printf("%d\n", Kth(root,x));}}return 0;}