各种排序算法的C++实现与性能比较
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：
view sourceprint?001 //使用时注意将关键码加入
002 #ifndef MINHEAP_H
003 #define MINHEAP_H
004 #include <assert.h>
005 #include <iostream>
006 using std::cout;
007 using std::cin;
008 using std::endl;
009 using std::cerr;
010 #include <stdlib.h>
011 //const int maxPQSize = 50;
012 template <class Type> class MinHeap {
013 public:
014 MinHeap ( int maxSize );//根据最大长度建堆
015 MinHeap ( Type arr[], int n );//根据数组arr[]建堆
016 ~MinHeap ( ) { delete [] heap; }
017 const MinHeap<Type> & operator = ( const MinHeap &R );//重载赋值运算符
018 int Insert ( const Type &x );//插入元素
019 int RemoveMin ( Type &x );//移除关键码最小的元素，并赋给x
020 int IsEmpty ( ) const { return CurrentSize == 0; }//检查堆是否为空
021 int IsFull ( ) const { return CurrentSize == MaxHeapSize; }//检查对是否满
022 void MakeEmpty ( ) { CurrentSize = 0; }//使堆空
023 private:
024 enum { DefaultSize = 50 };//默认堆的大小
025 Type *heap;
026 int CurrentSize;
027 int MaxHeapSize;
028 void FilterDown ( int i, int m );//自上向下调整堆
029 void FilterUp ( int i );//自下向上调整堆
030 };
031
032 template <class Type> MinHeap <Type>::MinHeap ( int maxSize )
033 {
034 //根据给定大小maxSize,建立堆对象
035 MaxHeapSize = (DefaultSize < maxSize ) ? maxSize : DefaultSize; //确定堆大小
036 heap = new Type [MaxHeapSize]; //创建堆空间
037 CurrentSize = 0; //初始化
038 }
039
040 template <class Type> MinHeap <Type>::MinHeap ( Type arr[], int n )
041 {
042 //根据给定数组中的数据和大小,建立堆对象
043 MaxHeapSize = DefaultSize < n ? n : DefaultSize;
044 heap = new Type [MaxHeapSize];
045 if(heap==NULL){cerr <<"fail" <<endl;exit(1);}
046 for(int i =0; i< n; i++)
047 heap[i] = arr[i]; //数组传送
048 CurrentSize = n; //当前堆大小
049 int currentPos = (CurrentSize-2)/2; //最后非叶
050 while ( currentPos >= 0 ) {
051 //从下到上逐步扩大,形成堆
052 FilterDown ( currentPos, CurrentSize-1 );
053 currentPos-- ;
054 //从currentPos开始,到0为止, 调整currentPos--; }
055 }
056 }
057
058 template <class Type> void MinHeap<Type>::FilterDown ( const int start, const int EndOfHeap )
059 {
060 // 结点i的左、右子树均为堆，调整结点i
061 int i = start, j = 2*i+1; // j 是 i 的左子女
062 Type temp = heap[i];
063 while ( j <= EndOfHeap ) {
064 if ( j < EndOfHeap && heap[j] > heap[j+1] )
065 j++;//两子女中选小者
066 if ( temp<= heap[j] ) break;
067 else { heap[i] = heap[j]; i = j; j = 2*j+1; }
068 }
069 heap[i] = temp;
070 }
071
072 template <class Type> int MinHeap<Type>::Insert ( const Type &x )
073 {
074 //在堆中插入新元素 x
075 if ( CurrentSize == MaxHeapSize ) //堆满
076 {
077 cout << "堆已满" << endl; return 0;
078 }
079 heap[CurrentSize] = x; //插在表尾
080 FilterUp (CurrentSize); //向上调整为堆
081 CurrentSize++; //堆元素增一
082 return 1;
083 }
084
085 template <class Type> void MinHeap<Type>::FilterUp ( int start )
086 {
087 //从 start 开始,向上直到0,调整堆
088 int j = start, i = (j-1)/2; // i 是 j 的双亲
089 Type temp = heap[j];
090 while ( j > 0 ) {
091 if ( (heap[i].root->data.key )<= (temp.root->data.key) ) break;
092 else { heap[j] = heap[i]; j = i; i = (i -1)/2; }
093 }
094 heap[j] = temp;
095 }
096 template <class Type> int MinHeap <Type>::RemoveMin ( Type &x )
097 {
098 if ( !CurrentSize )
099 {
100 cout << "堆已空 " << endl;
101 return 0;
102 }
103 x = heap[0]; //最小元素出队列
104 heap[0] = heap[CurrentSize-1];
105 CurrentSize--; //用最小元素填补
106 FilterDown ( 0, CurrentSize-1 );
107 //从0号位置开始自顶向下调整为堆
108 return 1;
109 }
110 #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：
view sourceprint?001 //n^2
002 //冒泡排序V[n]不参与排序
003 void BubbleSort (int V[], int n )
004 {
005 bool exchange; //设置交换标志置
006 for ( int i = 0; i < n; i++ ){
007 exchange=false;
008 for (int j=n-1; j>i; j--) { //反向检测，检查是否逆序
009 if (V[j-1] > V[j]) //发生逆序，交换相邻元素
010 {
011 int temp=V[j-1];
012 V[j-1]=V[j];
013 V[j]=temp;
014 exchange=true;//交换标志置位
015 }
016 }
017
018 if (exchange == false)
019 return; //本趟无逆序，停止处理
020 }
021 }
022
023
024
025 //插入排序,L[begin],L[end]都参与排序
026 void InsertionSort ( int L[], const int begin, const int end)
027 {
028 //按关键码 Key 非递减顺序对表进行排序
029 int temp;
030 int i, j;
031 for ( i = begin; i < end; i++ )
032 {
033 if (L[i]>L[i+1])
034 {
035 temp = L[i+1];
036 j=i;
037 do
038 {
039 L[j+1]=L[j];
040 if(j == 0)
041 {
042 j--;
043 break;
044 }
045 j--;
046
047 } while(temp<L[j]);
048 L[j+1]=temp;
049 }
050 }
051 }
052 //n*logn
053 //快速排序A[startingsub],A[endingsub]都参与排序
054 void QuickSort( int A[], int startingsub, int endingsub)
055 {
056 if ( startingsub >= endingsub )
057 ;
058 else{
059 int partition;
060 int q = startingsub;
061 int p = endingsub;
062 int hold;
063
064 do{
065 for(partition = q ; p > q ; p--){
066 if( A[q] > A[p]){
067 hold = A[q];
068 A[q] = A[p];
069 A[p] = hold;
070 break;
071 }
072 }
073 for(partition = p; p > q; q++){
074 if(A[p] < A[q]){
075 hold = A[q];
076 A[q] = A[p];
077 A[p] = hold;
078 break;
079 }
080 }
081
082 }while( q < p );
083 QuickSort( A, startingsub, partition - 1 );
084 QuickSort( A, partition + 1, endingsub );
085 }
086 }
087
088 //希尔排序,L[left],L[right]都参与排序
089 void Shellsort( int L[], const int left, const int right)
090 {
091 int i, j, gap=right-left+1; //增量的初始值
092 int temp;
093 do{
094 gap=gap/3+1; //求下一增量值
095 for(i=left+gap; i<=right; i++)
096 //各子序列交替处理
097 if( L[i]<L[i-gap]){ //逆序
098 temp=L[i]; j=i-gap;
099 do{
100 L[j+gap]=L[j]; //后移元素
101 j=j-gap; //再比较前一元素
102 }while(j>left&&temp<L[j]);
103 L[j+gap]=temp; //将vector[i]回送
104 }
105 }while(gap>1);
106 }
107
108 //n
109 //计数排序,L[n]不参与排序
110 void CountingSort( int L[], const int n )
111 {
112 int i,j;
113 const int k =1001;
114 int tmp[k];
115 int *R;
116 R = new int[n];
117 for(i=0;i<k;i++) tmp[i]= 0;
118 for(j=0;j<n;j++) tmp[L[j]]++;
119 //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
120 for(i=1;i<k;i++)
121 tmp[i]=tmp[i]+tmp[i-1]; //执行完上面的循环后，
122 //tmp[i]的值是L中小于等于i的元素的个数
123 for(j=n-1;j>=0;j--) //这里是逆向遍历，保证了排序的稳定性
124 {
125
126 R[tmp[L[j]]-1] = L[j];
127 //L[j]存放在输出数组R的第tmp[L[j]]个位置上
128 tmp[L[j]]--;
129 //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
130
131 }
132 for(j=0;j<n;j++) L[j] = R[j];
133 }
134
135 //基数排序
136 void printArray( const int Array[], const int arraySize );
137 int getDigit(int num, int dig);
138 const int radix=10; //基数
139 void RadixSort(int L[], int left, int right, int d){
140 //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。
141 int i, j, count[radix], p1, p2;
142 int *auxArray;
143 int M = 5;
144 auxArray = new int[right-left+1];
145 if (d<=0) return; //位数处理完递归结束
146 if (right-left+1<M){//对于小序列可调用直接插入排序
147 InsertionSort(L,left,right); return;
148 }
149 for (j=0; j<radix; j++) count[j]=0;
150 for (i=left; i<=right; i++) //统计各桶元素的存放位置
151 count[getDigit(L[i],d)]++;
152 for (j=1; j<radix; j++) //安排各桶元素的存放位置
153 count[j]=count[j]+count[j-1];
154 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
155 j=getDigit(L[i],d); //取元素L[i]第d位的值
156 auxArray[count[j]-1]=L[i]; //按预先计算位置存放
157 count[j]--; //计数器减1
158 }
159 for (i=left, j=0; i<=right; i++, j++)
160 L[i]=auxArray[j]; //从辅助数组顺序写入原数组
161 delete []auxArray;
162 for (j=0; j<radix; j++){ //按桶递归对d-1位处理
163 p1=count[j]+left; //取桶始端,相对位置，需要加上初值$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
164 (j+1 <radix )?(p2=count[j+1]-1+left):(p2=right) ; //取桶尾端
165 // delete []count;
166 if(p1<p2){
167 RadixSort(L, p1, p2, d-1); //对桶内元素进行基数排序
168 // printArray(L,10);
169 }
170 }
171
172 }
173
174 int getDigit(int num, int dig)
175 {
176 int myradix = 1;
177 /* for(int i = 1;i<dig;i++)
178 {
179 myradix *= radix;
180 }*/
181 switch(dig)
182 {
183 case 1:
184 myradix = 1;
185 break;
186 case 2:
187 myradix = 10;
188 break;
189 case 3:
190 myradix = 1000;
191 break;
192 case 4:
193 myradix = 10000;
194 break;
195 default:
196 myradix = 1;
197 break;
198 }
199 return (num/myradix)%radix;
200 }
maintest.cpp 测试例子：
view sourceprint?001 #include<iostream>
002 using std::cout;
003 using std::cin;
004 using std::endl;
005 #include <cstdlib>
006 #include <ctime>
007 #include<iostream>
008 using std::cout;
009 using std::cin;
010 using std::ios;
011 using std::cerr;
012 using std::endl;
013 #include<iomanip>
014 using std::setw;
015 using std::fixed;
016 #include<fstream>
017 using std::ifstream;
018 using std::ofstream;
019 using std::flush;
020 #include<string>
021 using std::string;
022 #include <stdio.h>
023 #include <stdlib.h>
024 #include <time.h>
025 #include"minheap.h"
026 void BubbleSort(int arr[], int size);//冒泡排序
027 void QuickSort( int A[], int startingsub, int endingsub);//快速排序
028 void InsertionSort ( int L[], const int begin,const int n);//插入排序
029 void Shellsort( int L[], const int left, const int right);//希尔排序
030 void CountingSort( int L[], const int n );//计数排序
031 int getDigit(int num, int dig);//基数排序中获取第dig位的数字
032 void RadixSort(int L[], int left, int right, int d);//基数排序
033 void printArray( const int Array[], const int arraySize );//输出数组
034
035 int main()
036 {
037 clock_t start, finish;
038 double duration;
039 /* 测量一个事件持续的时间*/
040 ofstream *ofs;
041 string fileName = "sortResult.txt";
042 ofs = new ofstream(fileName.c_str(),ios::out|ios::app);
043 const int size = 100000;
044 int a[size];
045 int b[size];
046 srand(time(0));
047 ofs->close();
048 for(int i = 0; i < 20;i++)
049 {
050 ofs->open(fileName.c_str(),ios::out|ios::app);
051 if( ofs->fail()){
052 cout<<"!!";
053 ofs->close();
054 }
055
056 for(int k =0; k <size;k++)
057 {
058 a[k] = rand()%1000;
059 b[k] = a[k];
060
061 }
062 /* for( k =0; k <size;k++)
063 {
064 a[k] = k;
065 b[k] = a[k];
066
067 } */
068 //printArray(a,size);
069 //计数排序
070 for( k =0; k <size;k++)
071 {
072 a[k] = b[k];
073 }
074 start = clock();
075 CountingSort(a,size);
076
077 finish = clock();
078 // printArray(a,size);
079
080 duration = (double)(finish - start) / CLOCKS_PER_SEC;
081 printf( "%s%f seconds\n", "计数排序:",duration );
082 *ofs<<"第"<<i<<"次:\n " <<"排序内容：0~999共" << size << " 个整数\n" ;
083 *ofs<<"第"<<i<<"次计数排序:\n " <<" Time: " <<fixed<< duration << " seconds\n";
084 //基数排序
085 for( k =0; k <size;k++)
086 {
087 a[k] = b[k];
088 }
089 start = clock();
090 RadixSort(a, 0,size-1, 3);
091 finish = clock();
092 // printArray(a,size);
093
094 duration = (double)(finish - start) / CLOCKS_PER_SEC;
095 printf( "%s%f seconds\n", "基数排序:",duration );
096 *ofs<<"第"<<i<<"次基数排序:\n " <<" Time: " << duration << " seconds\n";
097 //堆排序
098 MinHeap<int> mhp(a,size);
099 start = clock();
100 for( k =0; k <size;k++)
101 {
102 mhp.RemoveMin(a[k]);
103 }
104 finish = clock();
105 // printArray(a,size);
106 duration = (double)(finish - start) / CLOCKS_PER_SEC;
107 printf( "%s%f seconds\n", "堆排序:",duration );
108 *ofs<<"第"<<i<<"次堆排序:\n " <<" Time: " << duration << " seconds\n";
109 //快速排序
110 for( k =0; k <size;k++)
111 {
112 a[k] = b[k];
113
114 }
115 //printArray(a,size);
116 start = clock();
117 QuickSort(a,0,size-1);
118 finish = clock();
119 // printArray(a,size);
120 duration = (double)(finish - start) / CLOCKS_PER_SEC;
121 printf( "%s%f seconds\n", "快速排序:",duration );
122 *ofs<<"第"<<i<<"次快速排序:\n " <<" Time: " << duration << " seconds\n";
123
124 //希尔排序
125 for( k =0; k <size;k++)
126 {
127 a[k] = b[k];
128 }
129 start = clock();
130 Shellsort(a,0,size-1);
131
132 finish = clock();
133 // printArray(a,size);
134
135 duration = (double)(finish - start) / CLOCKS_PER_SEC;
136 printf( "%s%f seconds\n", "希尔排序:",duration );
137 *ofs<<"第"<<i<<"次希尔排序:\n " <<" Time: " << duration << " seconds\n";
138
139 //插入排序
140 for( k =0; k <size;k++)
141 {
142 a[k] = b[k];
143 }
144 start = clock();
145 InsertionSort (a,0,size-1);
146 finish = clock();
147 // printArray(a,size);
148
149 duration = (double)(finish - start) / CLOCKS_PER_SEC;
150 printf( "%s%f seconds\n", "插入排序:",duration );
151 *ofs<<"第"<<i<<"次插入排序:\n " <<" Time: " << duration << " seconds\n";
152 //冒泡排序
153 for( k =0; k <size;k++)
154 {
155 a[k] = b[k];
156 }
157 start = clock();
158 BubbleSort(a,size);
159 finish = clock();
160 // printArray(a,size);
161
162 duration = (double)(finish - start) / CLOCKS_PER_SEC;
163 printf( "%s%f seconds\n", "冒泡排序:",duration );
164 *ofs<<"第"<<i<<"次冒泡排序:\n " <<" Time: " << duration << " seconds\n";
165
166 ofs->close();
167 }
168 return 0;
169 }
170
171 void printArray( const int Array[], const int arraySize )
172 {
173 for( int i = 0; i < arraySize; i++ ) {
174 cout << Array[ i ] << " ";
175 if ( i % 20 == 19 )
176 cout << endl;
177 }
178 cout << endl;
179 }
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
