那些排序算法

第二次上课的作业之一是实现所有会的排序算法（之二是实现查找欧拉回路的算法），用了总计大概两天的时间写好了这九个排序算法。没有一个算法是一次通过的，都经过了调试，甚至冒泡，而且后来才发现我第一次写的冒泡程序竟然是错误的，囧。这还是第一次把这些算法全部亲手实现，收获还是很大的，真的加深了理解。期待通过这门课有效地提高自己的编程能力。废话不说，上代码。以下算法，没给出参数的默认排序范围为data[]的第0位到第N位。有些采用分治思想的算法需要范围参数，如快排和归并。为了优化，在递归过程中如果待排序长度较短则使用插入排序代替递归，因此插入排序函数有一个带参数版本为此所用。桶排序需要一个算法实现桶内排序，这里选择了快排，因此快排有一个带三个参数的重载版本。另外堆排序的实现用了一个类加一个外部函数。genData函数用于生成随机数据；check函数用于检查数据是否有序；exchange函数用于交换两个数据；show函数用于打印；digit函数返回数据的某一位（用于基数排序）；

0.其它函数

#include #include #include using namespace std;#define N 10000000#define MAX 100000int data[N];void genData()//~generate data{srand((unsigned)time(NULL));for(int i = 0;i < N;i++){data[i] = rand()%MAX;  }}void show()//~show the data sequentially{  for(int i = 0;i < N;i++)     cout<<<"/t"; cout<<= j;k++)    cout<<<"/t";cout<< N-1;i++){if(data[i] > data[i+1]){cout<<"unsorted!"<<<"sorted!"<

1.冒泡排序

void BubbleSort(){int t;for(int i = N-1;i > 0;i--){for(int j = 0;j < i;j++){if(data[j] > data[i]){t = data[i];data[i] = data[j];data[j] = t; }    }  }}

2.插入排序

void InsertionSort(int l,int r){int t;int pos = l+1;//pos as the beginning of the unsorted area for(int i = pos;i <= r;i++){t = data[i];int j;for(j = i - 1;j >= l && data[j] > t;j--){data[j+1] = data[j];}data[j+1] = t;   }}void InsertionSort(){int t;int pos = 1;//pos as the beginning of the unsorted area for(int i = pos;i < N;i++){t = data[i];int j;for(j = i - 1;j >= 0 && data[j] > t;j--){data[j+1] = data[j];}data[j+1] = t;   }}

3.选择排序

void SelectionSort(){int t; int pos = 0,min = MAX + 1;for(int i = 0;i < N;i++){min = MAX + 1;for(int j = i;j < N;j++){if(data[j] < min){pos = j;min = data[j];    } }exchange(pos,i);}  }

4.快速排序

void QuickSort(int l,int r,int* data)//this version of QuickSort is for BucketSort's use{int length = r-l+1;// when length <= 20,use InsertionSort instead./*if(length <= 20){InsertionSort(l,r);return;    }*/if(length <= 1)return;int pos = rand()%(r - l + 1) + l;exchange(l,pos,data);int i = l+1,j = r;while(i <= j){while(data[i] <= data[l] && i <= r)i++;while(data[j] >= data[l] && j >= l+1)j--;if(i < j)exchange(i,j,data); }exchange(l,j,data);QuickSort(l,j-1,data);QuickSort(j+1,r,data);}void QuickSort(int l,int r){int length = r-l+1;// when length <= 20,use InsertionSort instead.if(length <= 20){InsertionSort(l,r);return;    }int pos = rand()%(r - l + 1) + l;exchange(l,pos);int i = l+1,j = r;while(i <= j){while(data[i] <= data[l] && i <= r)i++;while(data[j] >= data[l] && j >= l+1)j--;if(i < j)exchange(i,j); }exchange(l,j);QuickSort(l,j-1);QuickSort(j+1,r);}

5.堆排序

class Heap{//1 for root//for each node i,2*i is its left child,2*i+1 is its right childpublic:Heap(int n):m_MaxSize(n),m_NumOfData(0){m_pData = new int[m_MaxSize + 1];};~Heap(){delete m_pData;   }void exchange(int i,int j){int t = m_pData[i];m_pData[i] = m_pData[j];m_pData[j] = t;  }void insert(int NewData){if(m_NumOfData >= m_MaxSize){cout<<"full! can not insert!"< 0 && m_pData[cur] < m_pData[(int)(cur/2)]){exchange(cur,(int)(cur/2));cur = (int)(cur/2);    }}int deleteNode(){int cur = 1;int result = m_pData[cur];m_pData[cur] = m_pData[m_MaxSize--];while(cur <= m_MaxSize){if(cur*2 > m_MaxSize)break;else if(cur*2+1 > m_MaxSize){if(m_pData[cur] > m_pData[2*cur])exchange(cur,2*cur);break;}else if(m_pData[cur] < m_pData[cur*2] && m_pData[cur] < m_pData[cur*2+1])break;else if(m_pData[2*cur] > m_pData[2*cur+1]){exchange(cur,2*cur+1);cur = 2*cur+1;}else{exchange(cur,2*cur);  cur = 2*cur;}}return result;}void Print(){cout<<"Print:"<<= m_MaxSize;i++)cout<<<"/t"; cout<< N;i++){h.insert(data[i]);}for(int i = 0;i < N;i++){data[i] = h.deleteNode();}}

6.归并排序

void MergeSort(int l,int r){int length = r - l + 1;// when length <= 20,use InsertionSort instead.if(length <= 20){InsertionSort(l,r);return;    } /*if(length <= 1)return;*/else{MergeSort(l,l+length/2-1);MergeSort(l+length/2,r);}int* tempBuf = new int[r-l+1];int pos_1 = l,pos_2 = l+length/2;int i;for(i = 0;i < length && pos_1 <= l+length/2-1 && pos_2 <= r;i++){if(data[pos_1] < data[pos_2]){tempBuf[i] = data[pos_1++];} else{tempBuf[i] = data[pos_2++];}}  while(pos_1 <= l+length/2-1){tempBuf[i++] = data[pos_1++]; }while(pos_2 <= r){tempBuf[i++] = data[pos_2++]; }for(int i = l;i <= r;i++){data[i] = tempBuf[i-l];  }delete tempBuf;}

7.计数排序

void CountingSort(){int* b = new int[N];int* c = new int[MAX+1];for(int i = 0;i <= MAX;i++)c[i] = 0;for(int i = 0;i < N;i++)c[data[i]]++; for(int i = 1;i <= MAX;i++)c[i] += c[i-1];for(int i = N-1;i >= 0;i--){b[c[data[i]]-1] = data[i];c[data[i]]--; }for(int i = 0;i < N;i++)data[i] = b[i];delete b;delete c;}

8.桶排序

void CountingSort(){int* b = new int[N];int* c = new int[MAX+1];for(int i = 0;i <= MAX;i++)c[i] = 0;for(int i = 0;i < N;i++)c[data[i]]++; for(int i = 1;i <= MAX;i++)c[i] += c[i-1];for(int i = N-1;i >= 0;i--){b[c[data[i]]-1] = data[i];c[data[i]]--; }for(int i = 0;i < N;i++)data[i] = b[i];delete b;delete c;}

9.基数排序

int digit(int data,int i)//return the ith digit of data,from right to left is 0,1,2...{while(i>0){data /= 10;   i--;}return data % 10;}void RadixSort(){int digits = 0;int max = MAX;while(max != 1){max /= 10;  digits++;   } int** pData = new int*[10];int len[10];for(int i = 0;i < 10;i++){pData[i] = new int[N];//len[i] = 0;}    for(int i = 0;i < digits;i++){for(int j = 0;j < 10;j++)len[j] = 0;for(int j = 0;j < N;j++){pData[digit(data[j],i)][len[digit(data[j],i)]++] = data[j];} //system("PAUSE");int pos = 0;for(int j = 0;j < 10;j++){for(int k = 0;k < len[j];k++){data[pos++] = pData[j][k];} }}}

测试代码

int main(int argc, char *argv[]){LARGE_INTEGER BegainTime; LARGE_INTEGER EndTime; LARGE_INTEGER Frequency;int TotalTime = 0;//sort M groups of data and calculate the average run timefor(int i = 1;i <= M;i++){genData(i);//check();QueryPerformanceFrequency(&Frequency);QueryPerformanceCounter(&BegainTime);//BubbleSort();//InsertionSort();//SelectionSort();//QuickSort(0,N-1);//HeapSort();//MergeSort(0,N-1);//CountingSort();//BucketSort();RadixSort();QueryPerformanceCounter(&EndTime);//cout<<"run time : "<<(EndTime.QuadPart - BegainTime.QuadPart)*1000/Frequency.QuadPart<<" MS."<<<"Average run time : "<<<" MS."<<<"run time : "<<( EndTime.QuadPart - BegainTime.QuadPart )*1000 / Frequency.QuadPart<<"MS."<

测试数据如下，短时间的测50次，超过十秒的都测10次，没耐心。。

函数名|10^5|10^6|10^7|||||   BubbleSort|17751|||InsertionSort |11037|||SelectionSort|14616|||    QuickSort|   19|297|      7808|     HeapSort|   54|981|     15307|    MergeSort|   30|397|      4211|   BucketSort|   28|427|       645| CountingSort|    3| 69|out of mem|    RadixSort|   28|313|out of mem|