C++排序（小堆排序）

最新推荐文章于 2024-10-12 16:32:13 发布

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本文详细介绍了堆排序的概念，特别关注了使用小根堆进行排序的方法，并提供了C++实现代码，包括堆的初始化、插入、删除最小元素以及排序等关键操作。

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#include<iostream>
#include<string>
using namespace std;

template<class Type>
class MinHeap
{
public:
	MinHeap(int sz=DefaultSize)
	{
		capacity = sz>DefaultSize?sz:DefaultSize;
		heap = new Type[capacity];
		size = 0;
	}
	MinHeap(Type ar[], int n)
	{
		capacity = n>DefaultSize?n:DefaultSize;
		heap = new Type[capacity];
		for(int i=0; i<n; ++i)
		{
			heap[i] = ar[i];
		}
		size = n;

		int pos = n/2-1;
		while(pos >= 0)
		{
			SiftDown(pos,n-1);
			pos--;
		}
	}
	~MinHeap()
	{
		delete []heap;
		heap = NULL;
	}
	void Show()const
	{
		for(int i=0; i<size; ++i)
		{
			cout<<heap[i]<<" ";
		}
		cout<<endl;
	}
	bool IsEmpty()const
	{
		return size == 0;
	}
	bool IsFull()const
	{
		return size >= capacity;
	}
	void MakeHeap()
	{
		size = 0;
	}
	Type ReMoveMin()
	{
		Type tmp = heap[0];
		heap[0] = heap[size-1];
		size--;
		SiftDown(0,size-1);
		return tmp;
	}
	void Sort()
	{
		Type *data = new Type[size];
		int i = 0;
		while(!IsEmpty())
		{
			data[i++] = ReMoveMin();
		}

		size = i;
		for(i=0; i<size; ++i)
		{
			heap[i] = data[i];
		}
		delete []data;
		data = NULL;
	}
	void Insert(const Type &x)
	{
		heap[size] = x;
		SiftUp(size);
		size++;
	}

private:
	void SiftUp(int start)
	{
		int j = start;
		int i = (j-1)/2;

		Type tmp = heap[j];

		while(j>0)
		{
			if(tmp > heap[i])
				break;
			else
			{
				heap[j] = heap[i];
				j = i;
				i = (j-1)/2;
			}
		}
		heap[j] = tmp;
	}
	void SiftDown(int start, int end)
	{
		int i = start;
		int j = 2*i+1;

		Type temp = heap[i];

		while(j <= end)
		{
			if(j<end && heap[j] > heap[j+1])
				j = j+1;
			if(temp < heap[j])
				break;
			else
			{
				heap[i] = heap[j];
				i = j;
				j = 2*i+1;
			}
		}
		heap[i] = temp;
	}

private:
	enum{DefaultSize = 10};
	Type *heap;
	int capacity;
	int size;
};

堆可以被看作是一个完全二叉树，小堆排序利用小根堆堆顶记录的关键字最小这一个特征，使得从当前无序区中选取最小关键字并进一步记录操作变的简单。