poj_1442 Treap

Treap是一种动态平衡二叉树结构，具有期望的O(log2n)的复杂度。适用于动态区间数据的查询、更改、维护等操作。

题目大意

一组数从前向后插入队列中，插入的过程中会有查询，查询当前队列中的第k小的数。

题目分析

对于数据的查询，可以考虑使用treap这种平衡二叉树来实现。而且treap这种动态平衡树结构，可以很方便的实现第k大的查询。
需要注意的是，每个节点保存与该节点相同元素的个数count对查询第k个数据时候的影响，见代码。

实现(c++)

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<algorithm>
#define MAX_NUM 30010
struct TreapNode{
int key;
int priority;
int size;
int count;
TreapNode* child[2];
TreapNode(int val){
key = val;
priority = rand();
child[0] = child[1] = NULL;
count = size = 1;
}
void Update(){
size = count;
if (child[0]){
size += child[0]->size;
}
if (child[1]){
size += child[1]->size;
}
}
};

struct Treap{
TreapNode* root;
Treap() :root(NULL){};
void Rotate(TreapNode*& node, int dir){
TreapNode* ch = node->child[dir];
node->child[dir] = ch->child[!dir];
ch->child[!dir] = node;

node->Update();
node = ch; //reference
}
void Insert(TreapNode*& node, int k){
if (!node){
node = new TreapNode(k);
}
else if (node->key == k){
node->count++;
}
else{
int dir = node->key < k;
Insert(node->child[dir], k);
if (node->priority < node->child[dir]->priority){
Rotate(node, dir);
}
}
node->Update();
}
int GetKth(TreapNode* root, int k){
TreapNode* node = root;
while (node){
if (!node->child[0]){
if (k <= node->count){
return node->key;
}
else{
k -= (node->count);
node = node->child[1];
}
}
else{
if (node->child[0]->size < k && node->child[0]->size + node->count >= k){
return node->key;
}
else if (node->child[0]->size >= k){
node = node->child[0];
}
else{
k -= (node->child[0]->size + node->count);
node = node->child[1];

}
}
}
return 0;
}
};
int gNumber[MAX_NUM];
Treap gTreap;
int main(){
int number_count, query_count;
scanf("%d%d", &number_count, &query_count);
for (int i = 0; i < number_count; i++){
scanf("%d", &gNumber[i]);
}

int query_old = 0;
int query_new;
for (int i = 1; i <= query_count; i++){
scanf("%d", &query_new);
for (int k = query_old; k < query_new; k++){
gTreap.Insert(gTreap.root, gNumber[k]);
}
query_old = query_new;
int result = gTreap.GetKth(gTreap.root, i);
printf("%d\n", result);
}
return 0;
}