简明现代魔法 -> 计算机算法 -> 各种排序算法的C++实现与性能比较

各种排序算法的C++实现与性能比较

2010-11-13

排序是计算机算法中非常重要的一项,而排序算法又有不少实现方法,那么哪些排序算法比较有效率,哪些算法在特定场合比较有效,下面将用C++实现各种算法,并且比较他们的效率,让我们对各种排序有个更深入的了解。

minheap.h 用于堆排序:

//使用时注意将关键码加入
#ifndef MINHEAP_H
#define MINHEAP_H
#include <assert.h>
#include <iostream>
using std::cout;
using std::cin;
using std::endl;
using std::cerr;
#include <stdlib.h>
//const int maxPQSize = 50;  
template <class Type> class MinHeap {
public: 
	MinHeap ( int maxSize );//根据最大长度建堆
	MinHeap ( Type arr[], int n );//根据数组arr[]建堆
	~MinHeap ( ) { delete [] heap; }
	const MinHeap<Type> & operator = ( const MinHeap &R );//重载赋值运算符
    int Insert ( const Type &x );//插入元素
	int RemoveMin ( Type &x );//移除关键码最小的元素,并赋给x
	int IsEmpty ( ) const { return CurrentSize == 0; }//检查堆是否为空     
	int IsFull ( ) const { return CurrentSize == MaxHeapSize; }//检查对是否满
    void MakeEmpty ( ) { CurrentSize = 0; }//使堆空
private: 
    enum { DefaultSize = 50 };//默认堆的大小
    Type *heap;                 
    int CurrentSize;
    int MaxHeapSize;
    void FilterDown ( int i, int m );//自上向下调整堆
    void FilterUp ( int i );//自下向上调整堆
};

template <class Type> MinHeap <Type>::MinHeap ( int maxSize )
{
	//根据给定大小maxSize,建立堆对象
    MaxHeapSize = (DefaultSize < maxSize ) ? maxSize : DefaultSize;	        //确定堆大小
    heap = new Type [MaxHeapSize];  //创建堆空间
    CurrentSize = 0;                               //初始化
}

template <class Type> MinHeap <Type>::MinHeap ( Type arr[], int n )
{
	//根据给定数组中的数据和大小,建立堆对象    
	MaxHeapSize = DefaultSize < n ? n : DefaultSize;
    heap = new Type [MaxHeapSize]; 
    if(heap==NULL){cerr <<"fail" <<endl;exit(1);}
	for(int i =0; i< n; i++)
		heap[i] = arr[i];               //数组传送
    CurrentSize = n;       //当前堆大小
    int currentPos = (CurrentSize-2)/2;   //最后非叶
    while ( currentPos >= 0 ) {       
		//从下到上逐步扩大,形成堆
        FilterDown ( currentPos, CurrentSize-1 );
		currentPos-- ;
        //从currentPos开始,到0为止, 调整currentPos--; }
	}
}

template <class Type> void MinHeap<Type>::FilterDown ( const int start, const int EndOfHeap )
{
	// 结点i的左、右子树均为堆,调整结点i
	int i = start,   j = 2*i+1;           // j 是 i 的左子女
	Type temp = heap[i];
	while ( j <= EndOfHeap ) {
		if ( j < EndOfHeap && heap[j] > heap[j+1] )
			j++;//两子女中选小者
		if ( temp<= heap[j] ) break;
		else { heap[i] = heap[j];  i = j;   j = 2*j+1; }
	}
	heap[i] = temp;
}

template <class Type> int MinHeap<Type>::Insert ( const Type &x ) 
{
	//在堆中插入新元素 x
	if ( CurrentSize == MaxHeapSize )       //堆满
	{ 
		cout << "堆已满" << endl;  return 0; 
	}
	heap[CurrentSize] = x;           //插在表尾  
	FilterUp (CurrentSize);          //向上调整为堆
	CurrentSize++;                       //堆元素增一
	return 1;
}

template <class Type> void MinHeap<Type>::FilterUp ( int start ) 
{
	//从 start 开始,向上直到0,调整堆
	int j = start,  i = (j-1)/2;    // i 是 j 的双亲
	Type temp = heap[j];
	while ( j > 0 ) {      
		if ( (heap[i].root->data.key )<= (temp.root->data.key) ) break;
		else {  heap[j] = heap[i];  j = i;  i = (i -1)/2; }
	}
	heap[j] = temp;
}
template <class Type> int MinHeap <Type>::RemoveMin ( Type &x ) 
{
	if ( !CurrentSize )
	{ 
		cout << "堆已空 " << endl; 
		return 0; 
	}
	x = heap[0];             //最小元素出队列
	heap[0] = heap[CurrentSize-1];    
	CurrentSize--;        //用最小元素填补
	FilterDown ( 0, CurrentSize-1 );
	//从0号位置开始自顶向下调整为堆
	return 1;
}	
#endif

sort.cpp 主要的排序函数集包括冒泡排序、快速排序、插入排序、希尔排序、计数排序:

//n^2
//冒泡排序V[n]不参与排序
void BubbleSort (int V[], int n ) 
{
    bool exchange;	     //设置交换标志置
    for ( int i = 0;  i < n;  i++ ){
        exchange=false;
		for (int j=n-1; j>i; j--) { //反向检测,检查是否逆序
			if  (V[j-1] > V[j]) //发生逆序,交换相邻元素
			{ 
				int temp=V[j-1]; 
				V[j-1]=V[j];
				V[j]=temp; 
				exchange=true;//交换标志置位
			}
		}
		
		if  (exchange == false)
			return; //本趟无逆序,停止处理
	}
}



//插入排序,L[begin],L[end]都参与排序
void InsertionSort ( int L[], const int begin, const int end)
{
	//按关键码 Key 非递减顺序对表进行排序
	int temp;
	int i, j;
    for ( i = begin; i < end; i++ ) 
	{
		if  (L[i]>L[i+1]) 
		{
			temp = L[i+1]; 
			j=i;
			do 
			{
				L[j+1]=L[j];
				if(j == 0)
				{
					j--;
					break;
				}
				j--;
				
			} while(temp<L[j]);
			L[j+1]=temp;
		}
	}
}
//n*logn
//快速排序A[startingsub],A[endingsub]都参与排序
void QuickSort( int A[], int startingsub, int endingsub)
{
	if ( startingsub >= endingsub  )
		;
	else{
		int partition;
		int q = startingsub;
		int p = endingsub;
		int hold;
		
		do{
			for(partition = q ; p > q ; p--){
				if( A[q] > A[p]){
					hold = A[q];
					A[q] = A[p];
					A[p] = hold;
					break;
				}
			}
			for(partition = p; p > q; q++){
				if(A[p] < A[q]){
					hold = A[q];
					A[q] = A[p];
					A[p] = hold;
					break;
				}
			}
			
		}while( q < p );
		QuickSort( A, startingsub, partition - 1 );
		QuickSort( A, partition + 1, endingsub );
	}
}

//希尔排序,L[left],L[right]都参与排序
void Shellsort( int L[], const int left, const int right)
{
	int i, j, gap=right-left+1;   //增量的初始值
	int temp;
	do{
		gap=gap/3+1;               //求下一增量值
		for(i=left+gap; i<=right; i++)
			//各子序列交替处理
			if( L[i]<L[i-gap]){        //逆序
				temp=L[i]; j=i-gap;     
				do{
					L[j+gap]=L[j];    //后移元素
					j=j-gap;      //再比较前一元素
				}while(j>left&&temp<L[j]);
				L[j+gap]=temp;   //将vector[i]回送
			}
	}while(gap>1);
} 

//n
//计数排序,L[n]不参与排序
void CountingSort( int L[], const int n )
{
	int i,j;
	const int k =1001;
	int tmp[k];
	int *R;
	R = new int[n];
	for(i=0;i<k;i++) tmp[i]= 0; 
	for(j=0;j<n;j++) tmp[L[j]]++; 
    //执行完上面的循环后,tmp[i]的值是L中等于i的元素的个数
	for(i=1;i<k;i++)
		tmp[i]=tmp[i]+tmp[i-1]; //执行完上面的循环后,
	//tmp[i]的值是L中小于等于i的元素的个数
	for(j=n-1;j>=0;j--) //这里是逆向遍历,保证了排序的稳定性
	{
		
		R[tmp[L[j]]-1] = L[j];  
		//L[j]存放在输出数组R的第tmp[L[j]]个位置上
		tmp[L[j]]--; 
		//tmp[L[j]]表示L中剩余的元素中小于等于L[j]的元素的个数 
		
	}
	for(j=0;j<n;j++) L[j] = R[j];
}

//基数排序
void printArray( const int Array[], const int arraySize );
int getDigit(int num, int dig);
const int radix=10;   //基数
void RadixSort(int L[], int left, int right, int d){
//MSD排序算法的实现。从高位到低位对序列划分,实现排序。d是第几位数,d=1是最低位。left和right是待排序元素子序列的始端与尾端。
   int i, j, count[radix], p1, p2;
   int *auxArray;
   int M = 5;
   auxArray = new int[right-left+1];
   if (d<=0) return; //位数处理完递归结束
   if (right-left+1<M){//对于小序列可调用直接插入排序
       InsertionSort(L,left,right); return;
   }
for (j=0; j<radix; j++) count[j]=0;
   for (i=left; i<=right; i++) //统计各桶元素的存放位置
       count[getDigit(L[i],d)]++;
   for (j=1; j<radix; j++) //安排各桶元素的存放位置
       count[j]=count[j]+count[j-1];
   for (i=right; i>=left; i--){ //将待排序序列中的元素按位置分配到各个桶中,存于助数组auxArray中
       j=getDigit(L[i],d);  //取元素L[i]第d位的值
       auxArray[count[j]-1]=L[i]; //按预先计算位置存放
       count[j]--;  //计数器减1
   }
   for (i=left, j=0; i<=right; i++, j++)	
       L[i]=auxArray[j];  //从辅助数组顺序写入原数组
   delete []auxArray;
	for (j=0; j<radix; j++){ //按桶递归对d-1位处理
       p1=count[j]+left;  //取桶始端,相对位置,需要加上初值$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
       (j+1 <radix )?(p2=count[j+1]-1+left):(p2=right) ; //取桶尾端
	//	delete []count;
	   if(p1<p2){
       RadixSort(L, p1, p2, d-1);  //对桶内元素进行基数排序 
	 //  printArray(L,10);
	   }
   }
 
} 

int getDigit(int num, int dig)
{
	int myradix = 1;
/*	for(int i = 1;i<dig;i++)
	{
	myradix *= radix;
	}*/
	switch(dig)
	{
	case 1:
		myradix = 1;
		break;
case 2:
		myradix = 10;
		break;
case 3:
		myradix = 1000;
		break;
case 4:
		myradix = 10000;
		break;
default:
		myradix = 1;
		break;
	}
	return (num/myradix)%radix;
}

maintest.cpp 测试例子:

#include<iostream>
using std::cout;
using std::cin;
using std::endl;
#include <cstdlib>
#include <ctime>
#include<iostream>
using std::cout;
using std::cin;
using std::ios;
using std::cerr;
using std::endl;
#include<iomanip>
using std::setw;
using std::fixed;
#include<fstream>
using std::ifstream;
using std::ofstream;
using std::flush;
#include<string>
using std::string;
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include"minheap.h"
void BubbleSort(int arr[], int size);//冒泡排序
void QuickSort( int A[], int startingsub, int endingsub);//快速排序
void InsertionSort ( int L[], const int begin,const int n);//插入排序
void Shellsort( int L[], const int left, const int right);//希尔排序
void CountingSort( int L[], const int n );//计数排序
int getDigit(int num, int dig);//基数排序中获取第dig位的数字
void RadixSort(int L[], int left, int right, int d);//基数排序
void printArray( const int Array[], const int arraySize );//输出数组

int main()
{
	clock_t start, finish;
	double  duration;
	/* 测量一个事件持续的时间*/
	ofstream *ofs;
	string fileName = "sortResult.txt";
	ofs = new ofstream(fileName.c_str(),ios::out|ios::app);
	const int size = 100000;
	int a[size];
	int b[size];
	srand(time(0));
	ofs->close();
	for(int i = 0; i < 20;i++)
	{
		ofs->open(fileName.c_str(),ios::out|ios::app);
		if( ofs->fail()){
                cout<<"!!";
				ofs->close();
		}

		for(int k =0; k <size;k++)
		{
			a[k] = rand()%1000;
			b[k] = a[k];
			
		} 		
		/*	for( k =0; k <size;k++)
		{
		a[k] = k;
		b[k] = a[k];
		
	} */
		//printArray(a,size);	
		//计数排序
		for( k =0; k <size;k++)
		{
			a[k] = 	b[k];
		}
		start = clock();
		CountingSort(a,size);
		
		finish = clock();
		//	printArray(a,size);
		
		duration = (double)(finish - start) / CLOCKS_PER_SEC;
		printf( "%s%f seconds\n", "计数排序:",duration );
		*ofs<<"第"<<i<<"次:\n " <<"排序内容:0~999共" << size <<  " 个整数\n" ;
		*ofs<<"第"<<i<<"次计数排序:\n " <<"		Time:	" <<fixed<< duration <<  " seconds\n";
		//基数排序
		for( k =0; k <size;k++)
		{
			a[k] = 	b[k];
		}
		start = clock();
		RadixSort(a, 0,size-1, 3);
		finish = clock();
		//	printArray(a,size);
		
		duration = (double)(finish - start) / CLOCKS_PER_SEC;
		printf( "%s%f seconds\n", "基数排序:",duration );
		*ofs<<"第"<<i<<"次基数排序:\n " <<"		Time:	" << duration <<  " seconds\n";
		//堆排序
		MinHeap<int> mhp(a,size); 
		start = clock();
		for( k =0; k <size;k++)
		{
			mhp.RemoveMin(a[k]);
		}
		finish = clock();
		//	printArray(a,size);
		duration = (double)(finish - start) / CLOCKS_PER_SEC;
		printf( "%s%f seconds\n", "堆排序:",duration );
		*ofs<<"第"<<i<<"次堆排序:\n " <<"		Time:	" << duration <<  " seconds\n";
		//快速排序
		for( k =0; k <size;k++)
		{
			a[k] = 	b[k];
			
		}
		//printArray(a,size);
		start = clock();
		QuickSort(a,0,size-1);
		finish = clock();
		//	printArray(a,size);
		duration = (double)(finish - start) / CLOCKS_PER_SEC;
		printf( "%s%f seconds\n", "快速排序:",duration );
		*ofs<<"第"<<i<<"次快速排序:\n " <<"		Time:	" << duration <<  " seconds\n";

		//希尔排序
		for( k =0; k <size;k++)
		{
			a[k] = 	b[k];
		}
		start = clock();
		Shellsort(a,0,size-1);
		
		finish = clock();
		//	printArray(a,size);
		
		duration = (double)(finish - start) / CLOCKS_PER_SEC;
		printf( "%s%f seconds\n", "希尔排序:",duration );
		*ofs<<"第"<<i<<"次希尔排序:\n " <<"		Time:	" << duration <<  " seconds\n";
		
		//插入排序
		for( k =0; k <size;k++)
		{
			a[k] = 	b[k];
		}
		start = clock();
		InsertionSort (a,0,size-1);
		finish = clock();
		//	printArray(a,size);
		
		duration = (double)(finish - start) / CLOCKS_PER_SEC;
		printf( "%s%f seconds\n", "插入排序:",duration );
		*ofs<<"第"<<i<<"次插入排序:\n " <<"		Time:	" << duration <<  " seconds\n";
		//冒泡排序
		for( k =0; k <size;k++)
		{
			a[k] = 	b[k];
		}
		start = clock();
		BubbleSort(a,size);
		finish = clock();
		//	printArray(a,size);
		
		duration = (double)(finish - start) / CLOCKS_PER_SEC;
		printf( "%s%f seconds\n", "冒泡排序:",duration );
		*ofs<<"第"<<i<<"次冒泡排序:\n " <<"		Time:	" << duration <<  " seconds\n";

		ofs->close();
		}
		return 0;
}

void printArray( const int Array[], const int arraySize )
{
	for( int i = 0; i < arraySize; i++ ) {
		cout << Array[ i ] << "   ";
		if ( i % 20 == 19 )
			cout << endl;
	}
	cout << endl;
}

排序算法性能仿真:

排序内容:从0~999中随机产生,共100000 个整数,该表中单位为秒。

次数 计数排序 基数排序 堆排序 快速排序 希尔排序 直接插入排序 冒泡排序
1 0.0000 0.0310 0.0470 0.0470 0.0310 14.7970 58.0930
2 0.0000 0.0470 0.0310 0.0470 0.0470 16.2500 53.3280
3 0.0000 0.0310 0.0310 0.0310 0.0310 14.4850 62.4380
4 0.0000 0.0320 0.0320 0.0470 0.0310 17.1090 61.8440
5 0.0000 0.0310 0.0470 0.0470 0.0310 16.9380 62.3280
6 0.0000 0.0310 0.0310 0.0470 0.0310 16.9380 57.7030
7 0.0000 0.0310 0.0470 0.0310 0.0310 16.8750 61.9380
8 0.0150 0.0470 0.0310 0.0470 0.0320 17.3910 62.8600
9 0.0000 0.0320 0.0470 0.0460 0.0310 16.9530 62.2660
10 0.0000 0.0470 0.0310 0.0470 0.0310 17.0160 60.1410
11 0.0000 0.0930 0.0780 0.0320 0.0310 14.6090 54.6570
12 0.0000 0.0310 0.0320 0.0310 0.0310 15.0940 62.3430
13 0.0000 0.0310 0.0310 0.0470 0.0310 17.2340 61.9530
14 0.0000 0.0320 0.0470 0.0470 0.0310 16.9060 61.0620
15 0.0000 0.0320 0.0320 0.0460 0.0320 16.7810 62.5310
16 0.0000 0.0470 0.0470 0.0620 0.0310 17.2350 57.1720
17 0.0150 0.0160 0.0320 0.0470 0.0310 14.1400 52.0320
18 0.0150 0.0160 0.0310 0.0310 0.0310 14.1100 52.3590
19 0.0000 0.0310 0.0320 0.0460 0.0320 14.1090 51.8750
20 0.0000 0.0310 0.0320 0.0460 0.0320 14.0780 52.4840
21 0.0150 0.0780 0.0470 0.0470 0.0310 16.3750 59.5150
22 0.0000 0.0310 0.0310 0.0470 0.0320 16.8900 60.3440
23 0.0000 0.0310 0.0310 0.0310 0.0310 16.3440 60.0930
24 0.0000 0.0310 0.0310 0.0470 0.0310 16.3440 60.5780
25 0.0000 0.0320 0.0470 0.0470 0.0470 16.3590 59.7810
26 0.0160 0.0470 0.0310 0.0470 0.0310 16.1250 61.0620
27 0.0000 0.0310 0.0470 0.0470 0.0310 16.7810 59.6100
28 0.0150 0.0320 0.0320 0.0470 0.0310 16.9220 56.8130
29 0.0000 0.0310 0.0310 0.0310 0.0310 15.0790 57.8120
30 0.0000 0.0310 0.0320 0.0460 0.0320 14.7810 58.8280
31 0.0000 0.0310 0.0310 0.0470 0.0310 15.8590 59.1400
32 0.0000 0.0470 0.0320 0.0310 0.0310 16.0940 59.1560
33 0.0000 0.0470 0.0310 0.0310 0.0310 15.9850 59.1400
34 0.0000 0.0310 0.0310 0.0470 0.0320 16.0150 59.2500
35 0.0000 0.0310 0.0470 0.0470 0.0310 16.7660 57.9840
36 0.0000 0.0310 0.0320 0.0470 0.0310 15.3750 59.0470
37 0.0000 0.0320 0.0460 0.0470 0.0320 16.0310 58.9060
38 0.0000 0.0310 0.0310 0.0470 0.0310 15.9530 57.2650
39 0.0160 0.0310 0.0470 0.0470 0.0310 15.9530 57.5160
40 0.0150 0.0310 0.0320 0.0470 0.0310 14.7030 56.6710
平均值 0.0031 0.0360 0.0372 0.0437 0.0320 15.9946 58.7480
最小值 0.0000 0.0160 0.0310 0.0310 0.0310 14.0780 51.8750
最大值 0.0160 0.0930 0.0780 0.0620 0.0470 17.3910 62.8600
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