poj_2352 Treap

题目大意

 
    给出N个点的坐标，求出覆盖点的个数分别为0, 1, ... N-1 的点各有多少个。

题目分析

 
    这就成了一个查找问题，查找问题可以考虑使用二查找树，于是可以使用treap这种平衡树。

实现(c++)

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<algorithm>
using namespace std;
#define MAX_NODE_NUM 15500
struct TreapNode{
	int key;
	int priority;
	int size;
	int count;
	TreapNode* child[2];
	TreapNode(int val){
		key = val;
		child[0] = child[1] = NULL;
		size = count = 1;
		priority = rand();
	}
	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();	//这时候node已经旋转到下方一层，因此size可能发生变化

		node = ch;
	}
	
	void Insert(TreapNode*& node, int key){
		if (!node){
			node = new TreapNode(key);
		}
		else if (node->key == key){
			node->count++;
		}
		else {
			int dir = node->key < key;
			Insert(node->child[dir], key);
			if (node->priority < node->child[dir]->priority){
				Rotate(node, dir);
			}
		}
		node->Update();
	}
	void debug(TreapNode* node){
		if (node){
			debug(node->child[0]);
			printf("node's key = %d, priority = %d, count = %d, size = %d\n", node->key, node->priority, node->count, node->size);
			debug(node->child[1]);
		}
	}
	
	int GetLessK(TreapNode* node, int k){
		int sum = 0;
		if (!node){
			return 0;
		}
		if (node->key > k){
			sum += GetLessK(node->child[0], k);
		}
		else{
			sum += node->count;
			if (node->child[0]){
				sum += node->child[0]->size;
			}
			sum += GetLessK(node->child[1], k);
		}
		return sum;
	}
};

struct Point{
	int x;
	int y;
};

Point gPoints[MAX_NODE_NUM];

Treap gTreap;
int gCoverNum[MAX_NODE_NUM];
int main(){

	int N;
	scanf("%d", &N);
	for (int i = 0; i < N; i++){
		scanf("%d %d", &gPoints[i].x, &gPoints[i].y);
		gCoverNum[i] = 0;
	}
	for (int i = 0; i < N; i++){
		int less_count = gTreap.GetLessK(gTreap.root, gPoints[i].x);
		gCoverNum[less_count] ++;

		gTreap.Insert(gTreap.root, gPoints[i].x);

	/*rintf("##################\n");
		gTreap.debug(gTreap.root);
		printf("##################\n");
		*/

	}
	for (int i = 0; i < N; i++){
		printf("%d\n", gCoverNum[i]);
	}
	return 0;
}