【数据结构】最大堆和最小堆

最新推荐文章于 2022-03-07 17:12:11 发布

原创最新推荐文章于 2022-03-07 17:12:11 发布 · 393 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#c++

本文深入探讨了堆数据结构，包括最大堆和最小堆的概念、性质及实现代码。详细介绍了堆作为完全二叉树的特性，以及如何通过模板类在C++中实现堆的插入、删除和查找操作。

定义

最大堆：一个完全二叉树结构体。同时满足所有父节点大于等于子节点。
最大堆：一个完全二叉树结构体。同时满足所有父节点小于等于子节点。

性质

对于最大堆，根节点是最大值
对于N个节点的堆，其深度为 $O (l g N)$ .

Code: MinHeap

代码应该没问题，在洛谷里全AC。

#include <cstring>

template <typename ValueType>
class MinHeap{
public:
	MinHeap();
	~MinHeap();
	void push(ValueType const &n);
	void pop();
	ValueType top();
	int size();
	bool empty();
private:
	ValueType* heap;
	int len;
};

template <typename ValueType>
MinHeap<ValueType>::MinHeap(){
	heap = new ValueType[10001];
	len = 0;
	memset(heap, 0, sizeof(heap));
}

template <typename ValueType>
MinHeap<ValueType>::~MinHeap(){
	delete []heap;
}

template <typename ValueType>
void MinHeap<ValueType>::push(ValueType const & n){
	heap[++len] = n;
	int son = len, father = son / 2;
	ValueType tmp;
	while(heap[son] < heap[father] && father >= 1){
		swap(heap[son],heap[father]);
		son = father, father = son / 2;
	}
}

template <typename ValueType>
void MinHeap<ValueType>::pop(){
	swap(heap[1],heap[len]);
	heap[len--] = 0;
	int father = 1, son = 2;
	while(son <= len){
		if(son < len && heap[son] > heap[son+1]) son++;
		if(heap[father] > heap[son]){
			swap(heap[father], heap[son]);
			father = son, son = father * 2;
		}
		else break;
	}
}

template <typename ValueType>
ValueType MinHeap<ValueType>::top(){
	return heap[1];
}

template <typename ValueType>
int MinHeap<ValueType>::size(){
	return len;
}

template <typename ValueType>
bool MinHeap<ValueType>::empty(){
	return len;
}

Code: MaxHeap

#include <cstring>

template <typename ValueType>
class MaxHeap{
public:
	MaxHeap();
	~MaxHeap();
	void push(ValueType const &n);
	void pop();
	ValueType top();
	int size();
	bool empty();
private:
	ValueType* heap;
	int len;
};

template <typename ValueType>
MaxHeap<ValueType>::MaxHeap(){
	heap = new ValueType[10001];
	len = 0;
	memset(heap, 0, sizeof(heap));
}

template <typename ValueType>
MaxHeap<ValueType>::~MaxHeap(){
	delete []heap;
}

template <typename ValueType>
void MaxHeap<ValueType>::push(ValueType const & n){
	heap[++len] = n;
	int son = len, father = son / 2;
	ValueType tmp;
	while(heap[son] > heap[father] && father >= 1){
		swap(heap[son],heap[father]);
		son = father, father = son / 2;
	}
}

template <typename ValueType>
void MaxHeap<ValueType>::pop(){
	swap(heap[1],heap[len]);
	heap[len--] = 0;
	int father = 1, son = 2;
	while(son <= len){
		if(son < len && heap[son] < heap[son+1]) son++;
		if(heap[father] < heap[son]){
			swap(heap[father], heap[son]);
			father = son, son = father * 2;
		}
		else break;
	}
}

template <typename ValueType>
ValueType MaxHeap<ValueType>::top(){
	return heap[1];
}

template <typename ValueType>
int MaxHeap<ValueType>::size(){
	return len;
}

template <typename ValueType>
bool MaxHeap<ValueType>::empty(){
	return len;
}