【POJ】优先队列的应用一、优先队列基本语法二、POJ两题

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一、优先队列基本语法

1.定义

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#include<queue>
#include<functional>
#include<vector>
//大顶堆
priority_queue<int> maxheap;
//小顶堆
priority_queue<int, vector<int>, greater<int>> minheap;

2.函数

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maxheap.empty();
int t=maxheap.top();
maxheap.pop();
maxheap.push(5);
maxheap.size();

二、POJ两题

1、Huffman编码树

http://algorithm.openjudge.cn/2020hw1/2D/
题目：计算最小树外部路径长度总和。
思路：使用优先队列，每次弹出两个最小的数a b，ans+=a+b，再把(a+b)入队，直到队空。

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#include<iostream>
#include<cstring>
#include<queue>
#include<vector>
#include<functional>
using namespace std;

priority_queue<int> maxheap;
priority_queue<int, vector<int>, greater<int>> minheap;

int main(){
	int t, n; cin >> t;
	while (t--){
		int ans = 0;
		while (!minheap.empty())
			minheap.pop();
		cin >> n;
		for (int i = 0; i < n; i++){
			int temp; cin >> temp;
			minheap.push(temp);
		}
		while (!minheap.empty()){
			int a = minheap.top(); minheap.pop();
			if (minheap.empty()) break;
			int b = minheap.top(); minheap.pop();
			ans += (a + b);
			minheap.push(a + b);
		}
		cout << ans << endl;
	}
	return 0;
}

2、Dynamic Median（模拟堆）

http://algorithm.openjudge.cn/2020prefinaltest/C/

题目：找数列中的中位数。
思路：使用优先队列，模拟两个堆（e.g. 大顶堆：1,2,|小顶堆：3,4），保证左边的大顶堆元素个数永远比小顶堆多1或等于。则大顶堆的堆顶元素为中位数。
注：读入字符时%c前加一个空格防止读入空格，否则一直不能ac…scanf(" %c", &c);
插入数字前判断堆是否为空。

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#include<iostream>
#include<cstring>
#include<queue>
#include<vector>
#include<functional>
using namespace std;

priority_queue<int> maxheap;
priority_queue<int, vector<int>, greater<int>> minheap;

void query(){
	printf("%dn", maxheap.top());
}
void del(){
	maxheap.pop();
	if (maxheap.size() < minheap.size()){
		int temp = minheap.top();
		minheap.pop();
		maxheap.push(temp);
	}
}
void insert(){
	int temp; scanf("%d", &temp);
	if (maxheap.empty() || minheap.empty()){
		maxheap.push(temp);
	}
	else{
		if (temp > minheap.top())
			minheap.push(temp);
		else
			maxheap.push(temp);
	}
	if (maxheap.size() == minheap.size() + 2){
		temp = maxheap.top();
		maxheap.pop();
		minheap.push(temp);
	}
	if (maxheap.size() < minheap.size()){
		int temp = minheap.top();
		minheap.pop();
		maxheap.push(temp);
	}
}
int main(){
	int t, n;
	scanf("%d", &t);
	while (t--){
		while (!minheap.empty())
			minheap.pop();
		while (!maxheap.empty())
			maxheap.pop();
		scanf("%d", &n);
		while (n--){
			char c;
			scanf(" %c", &c);
			if (c == 'I') insert();
			else if (c == 'Q') query();
			else del();
		}
	}
	return 0;
}

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#include<iostream>
#include<cstring>
#include<queue>
#include<vector>
#include<functional>
using namespace std;

priority_queue<int> maxheap;
priority_queue<int, vector<int>, greater<int>> minheap;

void query(){
	printf("%dn", maxheap.top());
}
void del(){
	maxheap.pop();
	if (maxheap.size() < minheap.size()){
		int temp = minheap.top();
		minheap.pop();
		maxheap.push(temp);
	}
}
void insert(){
	int temp; scanf("%d", &temp);
	if (maxheap.empty() || minheap.empty()){
		maxheap.push(temp);
	}
	else{
		if (temp > minheap.top())
			minheap.push(temp);
		else
			maxheap.push(temp);
	}
	if (maxheap.size() == minheap.size() + 2){
		temp = maxheap.top();
		maxheap.pop();
		minheap.push(temp);
	}
	if (maxheap.size() < minheap.size()){
		int temp = minheap.top();
		minheap.pop();
		maxheap.push(temp);
	}
}
int main(){
	int t, n;
	scanf("%d", &t);
	while (t--){
		while (!minheap.empty())
			minheap.pop();
		while (!maxheap.empty())
			maxheap.pop();
		scanf("%d", &n);
		while (n--){
			char c;
			scanf(" %c", &c);
			if (c == 'I') insert();
			else if (c == 'Q') query();
			else del();
		}
	}
	return 0;
}