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：
1 //使用时注意将关键码加入 2 #ifndef MINHEAP_H 3 #define MINHEAP_H 4 #include <assert.h> 5 #include <iostream> 6 using std::cout; 7 using std::cin; 8 using std::endl; 9 using std::cerr; 10 #include <stdlib.h> 11 //const int maxPQSize = 50; 12 template <class Type> class MinHeap { 13 public: 14 MinHeap ( int maxSize );//根据最大长度建堆 15 MinHeap ( Type arr[], int n );//根据数组arr[]建堆 16 ~MinHeap ( ) { delete [] heap; } 17 const MinHeap<Type> & operator = ( const MinHeap &R );//重载赋值运算符 18 int Insert ( const Type &x );//插入元素 19 int RemoveMin ( Type &x );//移除关键码最小的元素，并赋给x 20 int IsEmpty ( ) const { return CurrentSize == 0; }//检查堆是否为空 21 int IsFull ( ) const { return CurrentSize == MaxHeapSize; }//检查对是否满 22 void MakeEmpty ( ) { CurrentSize = 0; }//使堆空 23 private: 24 enum { DefaultSize = 50 };//默认堆的大小 25 Type *heap; 26 int CurrentSize; 27 int MaxHeapSize; 28 void FilterDown ( int i, int m );//自上向下调整堆 29 void FilterUp ( int i );//自下向上调整堆 30 }; 31 template <class Type> MinHeap <Type>::MinHeap ( int maxSize ) 32 { 33 //根据给定大小maxSize,建立堆对象 34 MaxHeapSize = (DefaultSize < maxSize ) ? maxSize : DefaultSize; //确定堆大小 35 heap = new Type [MaxHeapSize]; //创建堆空间 36 CurrentSize = 0; //初始化 37 } 38 template <class Type> MinHeap <Type>::MinHeap ( Type arr[], int n ) 39 { 40 //根据给定数组中的数据和大小,建立堆对象 41 MaxHeapSize = DefaultSize < n ? n : DefaultSize; 42 heap = new Type [MaxHeapSize]; 43 if(heap==NULL){cerr <<"fail" <<endl;exit(1);} 44 for(int i =0; i< n; i++) 45 heap[i] = arr[i]; //数组传送 46 CurrentSize = n; //当前堆大小 47 int currentPos = (CurrentSize-2)/2; //最后非叶 48 while ( currentPos >= 0 ) { 49 //从下到上逐步扩大,形成堆 50 FilterDown ( currentPos, CurrentSize-1 ); 51 currentPos-- ; 52 //从currentPos开始,到0为止, 调整currentPos--; } 53 } 54 } 55 template <class Type> void MinHeap<Type>::FilterDown ( const int start, const int EndOfHeap ) 56 { 57 // 结点i的左、右子树均为堆，调整结点i 58 int i = start, j = 2*i+1; // j 是 i 的左子女 59 Type temp = heap[i]; 60 while ( j <= EndOfHeap ) { 61 if ( j < EndOfHeap && heap[j] > heap[j+1] ) 62 j++;//两子女中选小者 63 if ( temp<= heap[j] ) break; 64 else { heap[i] = heap[j]; i = j; j = 2*j+1; } 65 } 66 heap[i] = temp; 67 } 68 template <class Type> int MinHeap<Type>::Insert ( const Type &x ) 69 { 70 //在堆中插入新元素 x 71 if ( CurrentSize == MaxHeapSize ) //堆满 72 { 73 cout << "堆已满" << endl; return 0; 74 } 75 heap[CurrentSize] = x; //插在表尾 76 FilterUp (CurrentSize); //向上调整为堆 77 CurrentSize++; //堆元素增一 78 return 1; 79 } 80 template <class Type> void MinHeap<Type>::FilterUp ( int start ) 81 { 82 //从 start 开始,向上直到0,调整堆 83 int j = start, i = (j-1)/2; // i 是 j 的双亲 84 Type temp = heap[j]; 85 while ( j > 0 ) { 86 if ( (heap[i].root->data.key )<= (temp.root->data.key) ) break; 87 else { heap[j] = heap[i]; j = i; i = (i -1)/2; } 88 } 89 heap[j] = temp; 90 } 91 template <class Type> int MinHeap <Type>::RemoveMin ( Type &x ) 92 { 93 if ( !CurrentSize ) 94 { 95 cout << "堆已空 " << endl; 96 return 0; 97 } 98 x = heap[0]; //最小元素出队列 99 heap[0] = heap[CurrentSize-1]; 100 CurrentSize--; //用最小元素填补 101 FilterDown ( 0, CurrentSize-1 ); 102 //从0号位置开始自顶向下调整为堆 103 return 1; 104 } 105 #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：
1 //n^2 2 //冒泡排序V[n]不参与排序 3 void BubbleSort (int V[], int n ) 4 { 5 bool exchange; //设置交换标志置 6 for ( int i = 0; i < n; i++ ){ 7 exchange=false; 8 for (int j=n-1; j>i; j--) { //反向检测，检查是否逆序 9 if (V[j-1] > V[j]) //发生逆序，交换相邻元素 10 { 11 int temp=V[j-1]; 12 V[j-1]=V[j]; 13 V[j]=temp; 14 exchange=true;//交换标志置位 15 } 16 } 17 18 if (exchange == false) 19 return; //本趟无逆序，停止处理 20 } 21 } 22 //插入排序,L[begin],L[end]都参与排序 23 void InsertionSort ( int L[], const int begin, const int end) 24 { 25 //按关键码 Key 非递减顺序对表进行排序 26 int temp; 27 int i, j; 28 for ( i = begin; i < end; i++ ) 29 { 30 if (L[i]>L[i+1]) 31 { 32 temp = L[i+1]; 33 j=i; 34 do 35 { 36 L[j+1]=L[j]; 37 if(j == 0) 38 { 39 j--; 40 break; 41 } 42 j--; 43 44 } while(temp<L[j]); 45 L[j+1]=temp; 46 } 47 } 48 } 49 //n*logn 50 //快速排序A[startingsub],A[endingsub]都参与排序 51 void QuickSort( int A[], int startingsub, int endingsub) 52 { 53 if ( startingsub >= endingsub ) 54 ; 55 else{ 56 int partition; 57 int q = startingsub; 58 int p = endingsub; 59 int hold; 60 61 do{ 62 for(partition = q ; p > q ; p--){ 63 if( A[q] > A[p]){ 64 hold = A[q]; 65 A[q] = A[p]; 66 A[p] = hold; 67 break; 68 } 69 } 70 for(partition = p; p > q; q++){ 71 if(A[p] < A[q]){ 72 hold = A[q]; 73 A[q] = A[p]; 74 A[p] = hold; 75 break; 76 } 77 } 78 79 }while( q < p ); 80 QuickSort( A, startingsub, partition - 1 ); 81 QuickSort( A, partition + 1, endingsub ); 82 } 83 } 84 //希尔排序,L[left],L[right]都参与排序 85 void Shellsort( int L[], const int left, const int right) 86 { 87 int i, j, gap=right-left+1; //增量的初始值 88 int temp; 89 do{ 90 gap=gap/3+1; //求下一增量值 91 for(i=left+gap; i<=right; i++) 92 //各子序列交替处理 93 if( L[i]<L[i-gap]){ //逆序 94 temp=L[i]; j=i-gap; 95 do{ 96 L[j+gap]=L[j]; //后移元素 97 j=j-gap; //再比较前一元素 98 }while(j>left&&temp<L[j]); 99 L[j+gap]=temp; //将vector[i]回送 100 } 101 }while(gap>1); 102 } 103 //n 104 //计数排序,L[n]不参与排序 105 void CountingSort( int L[], const int n ) 106 { 107 int i,j; 108 const int k =1001; 109 int tmp[k]; 110 int *R; 111 R = new int[n]; 112 for(i=0;i<k;i++) tmp[i]= 0; 113 for(j=0;j<n;j++) tmp[L[j]]++; 114 //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 115 for(i=1;i<k;i++) 116 tmp[i]=tmp[i]+tmp[i-1]; //执行完上面的循环后， 117 //tmp[i]的值是L中小于等于i的元素的个数 118 for(j=n-1;j>=0;j--) //这里是逆向遍历，保证了排序的稳定性 119 { 120 121 R[tmp[L[j]]-1] = L[j]; 122 //L[j]存放在输出数组R的第tmp[L[j]]个位置上 123 tmp[L[j]]--; 124 //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 125 126 } 127 for(j=0;j<n;j++) L[j] = R[j]; 128 } 129 //基数排序 130 void printArray( const int Array[], const int arraySize ); 131 int getDigit(int num, int dig); 132 const int radix=10; //基数 133 void RadixSort(int L[], int left, int right, int d){ 134 //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。 135 int i, j, count[radix], p1, p2; 136 int *auxArray; 137 int M = 5; 138 auxArray = new int[right-left+1]; 139 if (d<=0) return; //位数处理完递归结束 140 if (right-left+1<M){//对于小序列可调用直接插入排序 141 InsertionSort(L,left,right); return; 142 } 143 for (j=0; j<radix; j++) count[j]=0; 144 for (i=left; i<=right; i++) //统计各桶元素的存放位置 145 count[getDigit(L[i],d)]++; 146 for (j=1; j<radix; j++) //安排各桶元素的存放位置 147 count[j]=count[j]+count[j-1]; 148 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 149 j=getDigit(L[i],d); //取元素L[i]第d位的值 150 auxArray[count[j]-1]=L[i]; //按预先计算位置存放 151 count[j]--; //计数器减1 152 } 153 for (i=left, j=0; i<=right; i++, j++) 154 L[i]=auxArray[j]; //从辅助数组顺序写入原数组 155 delete []auxArray; 156 for (j=0; j<radix; j++){ //按桶递归对d-1位处理 157 p1=count[j]+left; //取桶始端,相对位置，需要加上初值$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 158 (j+1 <radix )?(p2=count[j+1]-1+left):(p2=right) ; //取桶尾端 159 // delete []count; 160 if(p1<p2){ 161 RadixSort(L, p1, p2, d-1); //对桶内元素进行基数排序 162 // printArray(L,10); 163 } 164 } 165 166 } 167 int getDigit(int num, int dig) 168 { 169 int myradix = 1; 170 /* for(int i = 1;i<dig;i++) 171 { 172 myradix *= radix; 173 }*/ 174 switch(dig) 175 { 176 case 1: 177 myradix = 1; 178 break; 179 case 2: 180 myradix = 10; 181 break; 182 case 3: 183 myradix = 1000; 184 break; 185 case 4: 186 myradix = 10000; 187 break; 188 default: 189 myradix = 1; 190 break; 191 } 192 return (num/myradix)%radix; 193 }
maintest.cpp 测试例子：
1 #include<iostream> 2 using std::cout; 3 using std::cin; 4 using std::endl; 5 #include <cstdlib> 6 #include <ctime> 7 #include<iostream> 8 using std::cout; 9 using std::cin; 10 using std::ios; 11 using std::cerr; 12 using std::endl; 13 #include<iomanip> 14 using std::setw; 15 using std::fixed; 16 #include<fstream> 17 using std::ifstream; 18 using std::ofstream; 19 using std::flush; 20 #include<string> 21 using std::string; 22 #include <stdio.h> 23 #include <stdlib.h> 24 #include <time.h> 25 #include"minheap.h" 26 void BubbleSort(int arr[], int size);//冒泡排序 27 void QuickSort( int A[], int startingsub, int endingsub);//快速排序 28 void InsertionSort ( int L[], const int begin,const int n);//插入排序 29 void Shellsort( int L[], const int left, const int right);//希尔排序 30 void CountingSort( int L[], const int n );//计数排序 31 int getDigit(int num, int dig);//基数排序中获取第dig位的数字 32 void RadixSort(int L[], int left, int right, int d);//基数排序 33 void printArray( const int Array[], const int arraySize );//输出数组 34 int main() 35 { 36 clock_t start, finish; 37 double duration; 38 /* 测量一个事件持续的时间*/ 39 ofstream *ofs; 40 string fileName = "sortResult.txt"; 41 ofs = new ofstream(fileName.c_str(),ios::out|ios::app); 42 const int size = 100000; 43 int a[size]; 44 int b[size]; 45 srand(time(0)); 46 ofs->close(); 47 for(int i = 0; i < 20;i++) 48 { 49 ofs->open(fileName.c_str(),ios::out|ios::app); 50 if( ofs->fail()){ 51 cout<<"!!"; 52 ofs->close(); 53 } 54 for(int k =0; k <size;k++) 55 { 56 a[k] = rand()%1000; 57 b[k] = a[k]; 58 59 } 60 /* for( k =0; k <size;k++) 61 { 62 a[k] = k; 63 b[k] = a[k]; 64 65 } */ 66 //printArray(a,size); 67 //计数排序 68 for( k =0; k <size;k++) 69 { 70 a[k] = b[k]; 71 } 72 start = clock(); 73 CountingSort(a,size); 74 75 finish = clock(); 76 // printArray(a,size); 77 78 duration = (double)(finish - start) / CLOCKS_PER_SEC; 79 printf( "%s%f seconds\n", "计数排序:",duration ); 80 *ofs<<"第"<<i<<"次:\n " <<"排序内容：0~999共" << size << " 个整数\n" ; 81 *ofs<<"第"<<i<<"次计数排序:\n " <<" Time: " <<fixed<< duration << " seconds\n"; 82 //基数排序 83 for( k =0; k <size;k++) 84 { 85 a[k] = b[k]; 86 } 87 start = clock(); 88 RadixSort(a, 0,size-1, 3); 89 finish = clock(); 90 // printArray(a,size); 91 92 duration = (double)(finish - start) / CLOCKS_PER_SEC; 93 printf( "%s%f seconds\n", "基数排序:",duration ); 94 *ofs<<"第"<<i<<"次基数排序:\n " <<" Time: " << duration << " seconds\n"; 95 //堆排序 96 MinHeap<int> mhp(a,size); 97 start = clock(); 98 for( k =0; k <size;k++) 99 { 100 mhp.RemoveMin(a[k]); 101 } 102 finish = clock(); 103 // printArray(a,size); 104 duration = (double)(finish - start) / CLOCKS_PER_SEC; 105 printf( "%s%f seconds\n", "堆排序:",duration ); 106 *ofs<<"第"<<i<<"次堆排序:\n " <<" Time: " << duration << " seconds\n"; 107 //快速排序 108 for( k =0; k <size;k++) 109 { 110 a[k] = b[k]; 111 112 } 113 //printArray(a,size); 114 start = clock(); 115 QuickSort(a,0,size-1); 116 finish = clock(); 117 // printArray(a,size); 118 duration = (double)(finish - start) / CLOCKS_PER_SEC; 119 printf( "%s%f seconds\n", "快速排序:",duration ); 120 *ofs<<"第"<<i<<"次快速排序:\n " <<" Time: " << duration << " seconds\n"; 121 //希尔排序 122 for( k =0; k <size;k++) 123 { 124 a[k] = b[k]; 125 } 126 start = clock(); 127 Shellsort(a,0,size-1); 128 129 finish = clock(); 130 // printArray(a,size); 131 132 duration = (double)(finish - start) / CLOCKS_PER_SEC; 133 printf( "%s%f seconds\n", "希尔排序:",duration ); 134 *ofs<<"第"<<i<<"次希尔排序:\n " <<" Time: " << duration << " seconds\n"; 135 136 //插入排序 137 for( k =0; k <size;k++) 138 { 139 a[k] = b[k]; 140 } 141 start = clock(); 142 InsertionSort (a,0,size-1); 143 finish = clock(); 144 // printArray(a,size); 145 146 duration = (double)(finish - start) / CLOCKS_PER_SEC; 147 printf( "%s%f seconds\n", "插入排序:",duration ); 148 *ofs<<"第"<<i<<"次插入排序:\n " <<" Time: " << duration << " seconds\n"; 149 //冒泡排序 150 for( k =0; k <size;k++) 151 { 152 a[k] = b[k]; 153 } 154 start = clock(); 155 BubbleSort(a,size); 156 finish = clock(); 157 // printArray(a,size); 158 159 duration = (double)(finish - start) / CLOCKS_PER_SEC; 160 printf( "%s%f seconds\n", "冒泡排序:",duration ); 161 *ofs<<"第"<<i<<"次冒泡排序:\n " <<" Time: " << duration << " seconds\n"; 162 ofs->close(); 163 } 164 return 0; 165 } 166 void printArray( const int Array[], const int arraySize ) 167 { 168 for( int i = 0; i < arraySize; i++ ) { 169 cout << Array[ i ] << " "; 170 if ( i % 20 == 19 ) 171 cout << endl; 172 } 173 cout << endl; 174 }
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 |