排序算法分析与程序设计以及使用OpenMP并行比较

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最近学了高性能计算这门课程，老师让用OpenMP、MPI或mapReduce写个大作业。我之前刚好在写排序，于是我就将常用的排序写了一遍并且用OpenMP进行并行，计算加速比等数据进行分析。在这篇文章中我主要介绍八大基本排序的实现原理及代码，以及对这些算法进行改进从而让它们可以并行，并且对他们的性能进行了比较。

</pre><pre name="code" class="cpp">首先是一些头文件和宏定义，如下：

</pre><pre name="code" class="cpp">#include "stdlib.h"
#include "iostream"
#include "omp.h"
#include "time.h"
#include "vector"
#include "stack"
using namespace std;

//#define random(x) (rand()%x)
#define BOUNDARY 1000000000	//定义随机数产生的区间
#define MAX_NUM 1000000	//随机数组的元素个数
const double MinProb = 1.0 / (RAND_MAX + 1);	//概率
typedef int KeyInt;
//定义一个记录待排序的区间[low,high]  
typedef struct Region
{
	int low;
	int high;
}Region;

下面是我写的一些函数：

KeyInt* randomCreate(int N);
bool happened(double probability);
int myrandom(int n);//产生0~n-1之间的等概率随机数
void DisPlay(int N, KeyInt *p);
KeyInt* BubbleAlgorithm(int N, KeyInt *p);//冒泡排序
KeyInt* BubbleAlgorithmParallel(int N, KeyInt *p);//奇偶排序
KeyInt* InsertSort(int N, KeyInt *p);//插入排序
KeyInt* InsertSort(int *p, int low, int high);//指定区间插入排序
vector<KeyInt> InsertSortPart(int N, KeyInt *p);//分区间插入排序
vector<KeyInt> InsertSortParallel(int N, KeyInt *p);//插入排序并行
vector<KeyInt> InsertVector(vector<KeyInt> &vec, int value);
vector<KeyInt> InsertVectorSort(vector<KeyInt> &vec); 
KeyInt* ShellSort(int N, KeyInt *p);//希尔排序
KeyInt* ShellSortParallel(int N, KeyInt *p);//希尔排序并行
KeyInt* InsertSort(int N, KeyInt *p, int start, int inc);//指定起始点和步长进行插入排序
void MergeSort(KeyInt *p, KeyInt *temp, int l, int r);//归并排序
void MergeSort(KeyInt *p, int N);//非递归归并排序
void MergeSortParallel(KeyInt *p, KeyInt *temp, int l, int r);//2核归并排序
void MergeSortParallel(KeyInt *p, KeyInt *temp, int N);//4核归并排序
void MergeSortParallel(KeyInt *p, int N);//并行非递归归并排序
void Merge(KeyInt *p, KeyInt *temp, int l, int r);//归并
void QuickSort(KeyInt *p, int low, int high);//快排
void QuickSortAverage(KeyInt *p, int low, int high);//快排+三数取中+插入
void QuickSortSame(KeyInt *p, int low, int high);//快排+三数取中+插入+聚集相等元素
int SelectPivotMedianOfThree(int *arr, int low, int high);//三数取中
int Partition(int * a, int low, int high);//分隔
void NonRecursiveQuickSort(int *a, int len);//用栈实现快排
void QuickSortParallel(KeyInt *p, int low, int high);//2核快排
void QuickSortParallel4Core(KeyInt *p, int low, int high);//4核快排

KeyInt* BubbleAlgorithm(int N, KeyInt *p)	//冒泡排序
{
	int i, j;
	KeyInt temp;
//#pragma omp parallel for
	for (i = 0; i<N-1; i++)
		for (j = 0; j<N-1-i; j++)
			if (p[j]>p[j+1])
			{
				temp = p[j];
				p[j] = p[j+1];
				p[j+1] = temp;
			}
	return (p);
}

KeyInt* BubbleAlgorithmParallel(int N, KeyInt *p)	//奇偶排序Odd-even Sort
{
	int i, j;
	for (i = 1; i < N; i++) {
		if ((i&0x1) == 1) {
#pragma omp parallel for
			for (j = 0; j < N - 1; j += 2) {
				if (p[j] > p[j + 1]) {
					int temp = p[j];
					p[j] = p[j + 1];
					p[j + 1] = temp;
				}
			}
		}
		else {
#pragma omp parallel for
			for (j = 2; j < N; j += 2) {
				if (p[j-1] > p[j]) {
					int temp = p[j-1];
					p[j-1] = p[j];
					p[j] = temp;
				}
			}
		}
	}
	return (p);
}

KeyInt* InsertSort(int N, KeyInt *p)//插入排序
{
	int temp;
	for (int i = 1; i < N; i++) {
		for (int j = i; (j > 0) && (p[j] < p[j - 1]); j--) {
			temp = p[j];
			p[j] = p[j - 1];
			p[j - 1] = temp;
		}
	}
	return p;
}

KeyInt* InsertSort(int *p, int low, int high)//指定区间插入排序
{
	int temp;
	for (int i = low+1; i <= high; i++) {
		for (int j = i; (j > low) && (p[j] < p[j - 1]); j--) {
			temp = p[j];
			p[j] = p[j - 1];
			p[j - 1] = temp;
		}
	}
	return p;
}

vector<KeyInt> InsertVector(vector<KeyInt> &vec, int value) {	//vector类型插入排序
	if (vec.size() == 0) {
		vec.push_back(value);
		return vec;
	}
	vec.push_back(value);
	//int temp;
	for (int j = vec.size()-1; j > 0; j--) {
		if (vec[j] < vec[j - 1]) {
			/*temp = vec[j];
			vec[j] = vec[j - 1];
			vec[j - 1] = temp;*/
			swap(vec[j-1], vec[j]);
		}
		else if (vec[j] >= vec[j - 1])
			break;
	}
	return vec;
}

vector<KeyInt> InsertVectorSort(vector<KeyInt> &vec)
{
	//int temp;
	for (int i = 1; i < vec.size(); i++) {
		for (int j = i; j > 0; j--) {
			if (vec[j] < vec[j - 1]) {
				/*temp = vec[j];
				vec[j] = vec[j - 1];
				vec[j - 1] = temp;*/
				swap(vec[j - 1], vec[j]);
			}
			else if (vec[j] >= vec[j - 1])
				break;
		}
	}
	return vec;
}

vector<KeyInt> InsertSortPart(int N, KeyInt *p)//分区间插入排序
{
	int i;
	int interval = BOUNDARY / 4;
	vector<int> vec[4];


	for (i = 0; i < N; i++) {
		if (p[i] < interval)
			vec[0].push_back(p[i]);
		else if (p[i] < 2 * interval)
			vec[1].push_back(p[i]);
		else if (p[i] < 3 * interval)
			vec[2].push_back(p[i]);
		else
			vec[3].push_back(p[i]);
	}
	int* arr0 = new int[vec[0].size()];
	int* arr1 = new int[vec[1].size()];
	int* arr2 = new int[vec[2].size()];
	int* arr3 = new int[vec[3].size()];
	for (i = 0; i < vec[0].size(); i++)
		arr0[i] = vec[0][i];
	for (i = 0; i < vec[1].size(); i++)
		arr1[i] = vec[1][i];
	for (i = 0; i < vec[2].size(); i++)
		arr2[i] = vec[2][i];
	for (i = 0; i < vec[3].size(); i++)
		arr3[i] = vec[3][i];

	arr0 = InsertSort(vec[0].size(), arr0);
	arr1 = InsertSort(vec[1].size(), arr1);
	arr2 = InsertSort(vec[2].size(), arr2);
	arr3 = InsertSort(vec[3].size(), arr3);

	vector<int> vec1[4];
	for (i = 0; i < vec[0].size(); i++)
		vec1[0].push_back(arr0[i]);
	for (i = 0; i < vec[1].size(); i++)
		vec1[1].push_back(arr1[i]);
	for (i = 0; i < vec[2].size(); i++)
		vec1[2].push_back(arr2[i]);
	for (i = 0; i < vec[3].size(); i++)
		vec1[3].push_back(arr3[i]);
	vec1[0].insert(vec1[0].end(), vec1[1].begin(), vec1[1].end());
	vec1[0].insert(vec1[0].end(), vec1[2].begin(), vec1[2].end());
	vec1[0].insert(vec1[0].end(), vec1[3].begin(), vec1[3].end());

	return vec1[0];
}

vector<KeyInt> InsertSortParallel(int N, KeyInt *p)//插入排序并行
{
	int i;
	int interval = BOUNDARY / 4;
	vector<int> vec[4];
	//vec[0].reserve(MAX_NUM);
	//vec[1].reserve(MAX_NUM/2);
	//vec[2].reserve(MAX_NUM/2);
	//vec[3].reserve(MAX_NUM/2);
	
	//long start = clock();
	for (i = 0; i < N; i++) {
		if (p[i] < interval)
			vec[0].push_back(p[i]);
		else if (p[i] < 2 * interval)
			vec[1].push_back(p[i]);
		else if (p[i] < 3 * interval)
			vec[2].push_back(p[i]);
		else
			vec[3].push_back(p[i]);
	}
	//long end = clock();
	//printf("The time1 is:%lf\n", (double)(end - start));
	//printf("%d %d %d %d\n", vec[0].size(), vec[1].size(), vec[2].size(), vec[3].size);
	//cout << vec[0].size() << '\n';
	//cout << vec[1].size() << '\n';
	//cout << vec[2].size() << '\n';
	//cout << vec[3].size() << '\n';
	//long start1 = clock();
	int* arr0 = new int[vec[0].size()];
	int* arr1 = new int[vec[1].size()];
	int* arr2 = new int[vec[2].size()];
	int* arr3 = new int[vec[3].size()];
	for (i = 0; i < vec[0].size(); i++)
		arr0[i] = vec[0][i];
	for (i = 0; i < vec[1].size(); i++)
		arr1[i] = vec[1][i];
	for (i = 0; i < vec[2].size(); i++)
		arr2[i] = vec[2][i];
	for (i = 0; i < vec[3].size(); i++)
		arr3[i] = vec[3][i];
	omp_set_num_threads(4);

#pragma omp parallel
	{
#pragma omp sections
	{
#pragma omp section
	{
		//InsertVectorSort(vec[0]);
		arr0 = InsertSort(vec[0].size(), arr0);
		//printf("%d\n", omp_get_thread_num());
	}
#pragma omp section
	{
		//InsertVectorSort(vec[1]);
		arr1 = InsertSort(vec[1].size(), arr1);
		//printf("%d\n", omp_get_thread_num());
	}
#pragma omp section
	{
		//InsertVectorSort(vec[2]);
		arr2 = InsertSort(vec[2].size(), arr2);
		//printf("%d\n", omp_get_thread_num());
	}
#pragma omp section
	{
		//InsertVectorSort(vec[3]);
		arr3 = InsertSort(vec[3].size(), arr3);
		//printf("%d\n", omp_get_thread_num());
	}
	}
	}
	
	/*InsertVectorSort(vec[0]);
	InsertVectorSort(vec[1]);
	InsertVectorSort(vec[2]);
	InsertVectorSort(vec[3]);*/
	/*arr0 = InsertSort(vec[0].size(), arr0);
	arr1 = InsertSort(vec[1].size(), arr1);
	arr2 = InsertSort(vec[2].size(), arr2);
	arr3 = InsertSort(vec[3].size(), arr3);*/
	//long end1 = clock();
	//printf("The time2 is:%lf\n", (double)(end1 - start1));
	/*vec[0].clear();
	vec[1].clear();
	vec[2].clear();
	vec[3].clear();*/
	//long start2 = clock();
	vector<int> vec1[4];
	for (i = 0; i < vec[0].size(); i++)
		vec1[0].push_back(arr0[i]);
	for (i = 0; i < vec[1].size(); i++)
		vec1[1].push_back(arr1[i]);
	for (i = 0; i < vec[2].size(); i++)
		vec1[2].push_back(arr2[i]);
	for (i = 0; i < vec[3].size(); i++)
		vec1[3].push_back(arr3[i]);
	vec1[0].insert(vec1[0].end(), vec1[1].begin(), vec1[1].end());
	vec1[0].insert(vec1[0].end(), vec1[2].begin(), vec1[2].end());
	vec1[0].insert(vec1[0].end(), vec1[3].begin(), vec1[3].end());
	//long end2 = clock();
	//printf("The time3 is:%lf\n", (double)(end2 - start2));
	return vec1[0];
	/*vec[0].insert(vec[0].end(), vec[1].begin(), vec[1].end());
	vec[0].insert(vec[0].end(), vec[2].begin(), vec[2].end());
	vec[0].insert(vec[0].end(), vec[3].begin(), vec[3].end());
	return vec[0];*/
}

KeyInt* ShellSort(int N, KeyInt *p)	//希尔排序
{
	for (int i = N / 2; i > 2; i /= 2) {
		for (int j = 0; j < i; j++) {
			InsertSort(N, p, j, i);
		}
	}
	InsertSort(N, p, 0, 1);
	return p;
}

KeyInt* ShellSortParallel(int N, KeyInt *p)//希尔排序并行
{
	for (int i = N / 2; i > 2; i /= 2) {
#pragma omp parallel for
		for (int j = 0; j < i; j++) {
			InsertSort(N, p, j, i);
		}
	}
	InsertSort(N, p, 0, 1);
	return p;
}

KeyInt* InsertSort(int N, KeyInt *p, int start, int inc)//指定起始点和步长进行插入排序
{
	int temp;
	for (int i = start + inc; i < N; i += inc) {
		for (int j = i; (j >= inc) && (p[j] < p[j - inc]); j -= inc) {
			int temp = p[j];
			p[j] = p[j-inc];
			p[j-inc] = temp;
		}
	}
	return p;
}

void Merge(KeyInt *p, KeyInt *temp, int l, int r)//归并
{
	int mid = (l + r) / 2;
	int i1 = l;
	int i2 = mid + 1;
	for (int cur = l; cur <= r; cur++) {
		if (i1 == mid + 1)
			p[cur] = temp[i2++];
		else if (i2 > r)
			p[cur] = temp[i1++];
		else if (temp[i1] < temp[i2])
			p[cur] = temp[i1++];
		else
			p[cur] = temp[i2++];
	}
}

void MergeSort(KeyInt *p, KeyInt *temp, int l, int r)	//归并排序
{
	int mid = (l + r) / 2;
	if (l == r)
		return;
	
	MergeSort(p, temp, l, mid);
	MergeSort(p, temp, mid + 1, r);

	for (int i = l; i <= r; i++) {
		temp[i] = p[i];
	}
	/*int i1 = l;
	int i2 = mid + 1;
	for (int cur = l; cur <= r; cur++) {
		if (i1 == mid + 1)
			p[cur] = temp[i2++];
		else if (i2 > r)
			p[cur] = temp[i1++];
		else if (temp[i1] < temp[i2])
			p[cur] = temp[i1++];
		else
			p[cur] = temp[i2++];
	}*/
	Merge(p, temp, l, r);
}

void MergeSort(KeyInt *p, int N)//非递归归并排序
{
	int i, left_min, left_max, right_min, right_max, next;
	int *tmp = (int*)malloc(sizeof(int) * N);
	
	for (i = 1; i < N; i *= 2) // i为步长，1,2,4,8……
	{
	    for (left_min = 0; left_min < N - i; left_min = right_max)
		 {
			right_min = left_max = left_min + i;
			right_max = left_max + i;

			if (right_max > N)
				right_max = N;

			next = 0;
			while (left_min < left_max && right_min < right_max)
					tmp[next++] = p[left_min] > p[right_min] ? p[right_min++] : p[left_min++];

			while (left_min < left_max)
				p[--right_min] = p[--left_max];

			while (next > 0)
				p[--right_min] = tmp[--next];
		 }
	}
	
	free(tmp);
}

void MergeSortParallel(KeyInt *p, int N)//并行非递归归并排序
{
	//int left_max, right_min, right_max, next;
	int *tmp = (int*)malloc(sizeof(int) * N);
	for (int i = 1; i < N; i *= 2) // i为步长，1,2,4,8……
	{
#pragma omp parallel for
		for (int left_min = 0; left_min < N - i; left_min += 2*i)
		{
			//int *tmp = (int*)malloc(sizeof(int) * 2*i);
			int temp = left_min;
			int right_min = temp + i;
			int left_max = temp + i;
			int right_max = left_max + i;


			if (right_max > N)
				right_max = N;

			//int next = 0;
			int next = left_min;
			while (temp < left_max && right_min < right_max)
				tmp[next++] = p[temp] > p[right_min] ? p[right_min++] : p[temp++];

			while (temp < left_max)
				p[--right_min] = p[--left_max];

			while (next > left_min)
				p[--right_min] = tmp[--next];
		}
	}

	free(tmp);
}

void MergeSortParallel(KeyInt *p, KeyInt *temp, int l, int r)//2核归并排序
{
	int mid = (l + r) / 2;
	if (l == r)
		return;
#pragma omp parallel
	{
#pragma omp sections
	{
#pragma omp section
	{
		//printf("%d,", omp_get_num_threads());
		//printf("%d,", omp_get_thread_num());
		MergeSort(p, temp, l, mid);
	}
#pragma omp section
	{
		//printf("%d,", omp_get_num_threads());
		//printf("%d,", omp_get_thread_num());
		MergeSort(p, temp, mid + 1, r);
	}
	}
	}
	//MergeSort(p, temp, l, mid);
	//MergeSort(p, temp, mid + 1, r);
	//printf("%d,", omp_get_num_threads());

	/*for (int i = l; i <= r; i++) {
		temp[i] = p[i];
	}
	int i1 = l;
	int i2 = mid + 1;
	for (int cur = l; cur <= r; cur++) {
		if (i1 == mid + 1)
			p[cur] = temp[i2++];
		else if (i2 > r)
			p[cur] = temp[i1++];
		else if (temp[i1] < temp[i2])
			p[cur] = temp[i1++];
		else
			p[cur] = temp[i2++];
	}*/
	Merge(p, temp, l, r);
}

void MergeSortParallel(KeyInt *p, KeyInt *temp, int N)//4核归并排序
{
	int i;
	int *p1 = new int[N / 4];
	int *p11 = new int[N / 4];
	for (i = 0; i < N / 4; i++)
		p1[i] = p[i];
	int *p2 = new int[N / 4];
	int *p22 = new int[N / 4];
	for (i = 0; i < N / 4; i++)
		p2[i] = p[i+N/4];
	int *p3 = new int[N / 4];
	int *p33 = new int[N / 4];
	for (i = 0; i < N / 4; i++)
		p3[i] = p[i+N/4+N/4];
	int *p4 = new int[N - N / 4 * 3];
	int *p44 = new int[N - N / 4 * 3];
	for (i = 0; i < (N - N / 4 * 3); i++)
		p4[i] = p[i+N/4+N/4+N/4];
#pragma omp parallel
	{
#pragma omp sections
	{
#pragma omp section
	{
		MergeSort(p1, p11, 0, N / 4-1);
	}
#pragma omp section
	{
		MergeSort(p2, p22, 0, N / 4-1);
	}
#pragma omp section
	{
		MergeSort(p3, p33, 0, N / 4 - 1);
	}
#pragma omp section
	{
		MergeSort(p4, p44, 0, N - N / 4 * 3-1);
	}
	}
	}

	delete[] p11;
	delete[] p22;
	delete[] p33;
	delete[] p44;

	int* temp1 = new int[N / 4 + N / 4];
	int* temp11 = new int[N / 4 + N / 4];
	for (i = 0; i < N / 4; i++)
	{
		temp1[i] = p1[i];
		temp11[i] = p1[i];
	}
	delete[] p1;
	for (i = 0; i < N / 4; i++)
	{
		temp1[i + N / 4] = p2[i];
		temp11[i + N / 4] = p2[i];
	}
	delete[] p2;
	int* temp2 = new int[N-(N / 4 + N / 4)];
	int* temp22 = new int[N - (N / 4 + N / 4)];
	for (i = 0; i < N / 4; i++)
	{
		temp2[i] = p3[i];
		temp22[i] = p3[i];
	}
	delete[] p3;
	for (i = 0; i < (N - N / 4 * 3); i++)
	{
		temp2[i + N / 4] = p4[i];
		temp22[i + N / 4] = p4[i];
	}
	delete[] p4;
	Merge(temp1, temp11, 0, N / 4 + N / 4 - 1);
	Merge(temp2, temp22, 0, N - (N / 4 + N / 4) - 1);

	delete[] temp11;
	delete[] temp22;
	
	int* temp3 = new int[N];
	int* temp33 = new int[N];
	for (i = 0; i < N / 4 + N / 4; i++)
	{
		temp3[i] = temp1[i];
		temp33[i] = temp1[i];
	}
	delete[] temp1;
	for (i = 0; i < N - (N / 4 + N / 4); i++)
	{
		temp3[i + N / 4 + N / 4] = temp2[i];
		temp33[i + N / 4 + N / 4] = temp2[i];
	}
	delete[] temp2;
	Merge(temp3, temp33, 0, N-1);
	for (i = 0; i < N; i++)
		p[i] = temp3[i];
	delete[] temp3;
	delete[] temp33;
}

void QuickSort(KeyInt *p, int low, int high)//快排
{
	if (low >= high)
	{
		return;
	}
	int first = low;
	int last = high;
	int key = p[first];/*用字表的第一个记录作为枢轴*/

	while (first < last)
	{
		while (first < last && p[last] >= key)
		{
			--last;
		}

		p[first] = p[last];/*将比第一个小的移到低端*/

		while (first < last && p[first] <= key)
		{
			++first;
		}

		p[last] = p[first];
		/*将比第一个大的移到高端*/
	}
	p[first] = key;/*枢轴记录到位*/
	QuickSort(p, low, first - 1);
	QuickSort(p, first + 1, high);
}

void QuickSortAverage(KeyInt *p, int low, int high)//快排+三数取中+插入
{
	if (high - low + 1 < 20)
	{
		InsertSort(p, low, high);
		return;
	}//else时，正常执行快排
	int first = low;
	int last = high;
	//int key = p[first];/*用字表的第一个记录作为枢轴*/
	int key = SelectPivotMedianOfThree(p, low, high);

	while (first < last)
	{
		while (first < last && p[last] >= key)
		{
			--last;
		}

		p[first] = p[last];/*将比第一个小的移到低端*/

		while (first < last && p[first] <= key)
		{
			++first;
		}

		p[last] = p[first];
		/*将比第一个大的移到高端*/
	}
	p[first] = key;/*枢轴记录到位*/
	QuickSortAverage(p, low, first - 1);
	QuickSortAverage(p, first + 1, high);
}

void QuickSortSame(KeyInt *p, int low, int high)//快排+三数取中+插入+聚集相等元素
{
	if (high - low + 1 < 20)
	{
		InsertSort(p, low, high);
		return;
	}
	int temp;
	int first = low;
	int last = high;

	int left = low;
	int right = high;

	int leftLen = 0;
	int rightLen = 0;


	//一次分割  
	int key = SelectPivotMedianOfThree(p, low, high);//使用三数取中法选择枢轴  

	while (low < high)
	{
		while (high > low && p[high] >= key)
		{
			if (p[high] == key)//处理相等元素  
			{
				//swap(p[right], p[high]);
				temp = p[right];
				p[right] = p[high];
				p[high] = temp;
				right--;
				rightLen++;
			}
			high--;
		}
		p[low] = p[high];
		while (high > low && p[low] <= key)
		{
			if (p[low] == key)
			{
				//swap(p[left], p[low]);
				temp = p[left];
				p[left] = p[low];
				p[low] = temp;
				left++;
				leftLen++;
			}
			low++;
		}
		p[high] = p[low];
	}
	p[low] = key;

	//一次快排结束  
	//把与枢轴key相同的元素移到枢轴最终位置周围  
	int i = low - 1;
	int j = first;
	while (j < left && p[i] != key)
	{
		//swap(p[i], p[j]);
		temp = p[i];
		p[i] = p[j];
		p[j] = temp;
		i--;
		j++;
	}
	i = low + 1;
	j = last;
	while (j > right && p[i] != key)
	{
		//swap(p[i], p[j]);
		temp = p[i];
		p[i] = p[j];
		p[j] = temp;
		i++;
		j--;
	}
	QuickSortSame(p, first, low - 1 - leftLen);
	QuickSortSame(p, low + 1 + rightLen, last);
}

void QuickSortParallel(KeyInt *p, int low, int high)//2核快排
{
	p[0] = BOUNDARY / 2;
	/*for (int i = low; i <= high; i++)
	{
		if (abs(p[i] - BOUNDARY / 2) < 10)
		{
			int temp = p[i];
			p[i] = p[0];
			p[0] = temp;
			break;
		}
	}*/
	int mid = Partition(p, low, high);
#pragma omp parallel
{
#pragma omp sections
{
#pragma omp section
{
	QuickSortAverage(p, low, mid-1);
}
#pragma omp section
{
	QuickSortAverage(p, mid+1, high);
}
}
}
}

void QuickSortParallel4Core(KeyInt *p, int low, int high)//4核快排
{
	p[0] = BOUNDARY / 2;
	/*for (int i = low; i <= high; i++)
	{
		if (abs(p[i] - BOUNDARY / 2) < 10)
		{
			int temp = p[i];
			p[i] = p[0];
			p[0] = temp;
			break;
		}
	}*/
	int mid = Partition(p, low, high);
	p[low] = BOUNDARY / 4;
	int quarter1 = Partition(p, low, mid - 1);
	p[mid + 1] = BOUNDARY / 4 * 3;
	int quarter2 = Partition(p, mid + 1, high);
#pragma omp parallel
	{
#pragma omp sections
	{
#pragma omp section
	{
		//double start1 = omp_get_wtime();
		QuickSortAverage(p, low, quarter1-1);
		//double end1 = omp_get_wtime();
		//printf("%lf\n", end1 - start1);
	}
#pragma omp section
	{
		//double start2 = omp_get_wtime();
		QuickSortAverage(p, quarter1 + 1, mid-1);
		//double end2 = omp_get_wtime();
		//printf("%lf\n", end2 - start2);
	}
#pragma omp section
	{
		//double start3 = omp_get_wtime();
		QuickSortAverage(p, mid+1, quarter2-1);
		//double end3 = omp_get_wtime();
		//printf("%lf\n", end3 - start3);
	}
#pragma omp section
	{
		//double start4 = omp_get_wtime();
		QuickSortAverage(p, quarter2+1, high);
		//double end4 = omp_get_wtime();
		//printf("%lf\n", end4 - start4);
	}
	}
	}
}

/*函数作用：取待排序序列中low、mid、high三个位置上数据，选取他们中间的那个数据作为枢轴*/
int SelectPivotMedianOfThree(int *arr, int low, int high)//三数取中
{
	int temp;
	int mid = low + ((high - low) >> 1);//计算数组中间的元素的下标  

										//使用三数取中法选择枢轴  
	if (arr[mid] > arr[high])//目标: arr[mid] <= arr[high]  
	{
		//swap(arr[mid], arr[high]);
		temp = arr[mid];
		arr[mid] = arr[high];
		arr[high] = temp;
	}
	if (arr[low] > arr[high])//目标: arr[low] <= arr[high]  
	{
		//swap(arr[low], arr[high]);
		temp = arr[low];
		arr[low] = arr[high];
		arr[high] = temp;
	}
	if (arr[mid] > arr[low]) //目标: arr[low] >= arr[mid]  
	{
		//swap(arr[mid], arr[low]);
		temp = arr[mid];
		arr[mid] = arr[low];
		arr[low] = temp;
	}
	//此时，arr[mid] <= arr[low] <= arr[high]  
	return arr[low];
	//low的位置上保存这三个位置中间的值  
	//分割时可以直接使用low位置的元素作为枢轴，而不用改变分割函数了  
}

int Partition(int * a, int low, int high)//分隔
{
	int pivotkey = a[low];
	while (low<high)
	{
		while (low<high && a[high] >= pivotkey)
			--high;
		a[low] = a[high];
		while (low<high && a[low] <= pivotkey)
			++low;
		a[high] = a[low];
	}
	//此时low==high 
	a[low] = pivotkey;
	return low;
}

void NonRecursiveQuickSort(int *a, int len)//用栈实现快排
{
	stack<Region> regions;//定义一个栈变量  
	Region region;
	region.low = 0;
	region.high = len - 1;
	regions.push(region);
	while (!regions.empty())
	{
		region = regions.top();
		regions.pop();
		int p = Partition(a, region.low, region.high);
		if (p - 1>region.low)
		{
			Region regionlow;
			regionlow.low = region.low;
			regionlow.high = p - 1;
			regions.push(regionlow);
		}
		if (p + 1<region.high)
		{
			Region regionhigh;
			regionhigh.low = p + 1;
			regionhigh.high = region.high;
			regions.push(regionhigh);
		}
	}
}

KeyInt* randomCreate(int N) {
	int i = 0;
	KeyInt *p;
	p =(KeyInt*) malloc(N * sizeof(KeyInt));

	for (i = 0; i < N; i++)
		p[i] = myrandom(BOUNDARY);
		//p[i] = random(BOUNDARY);
	return (p);
}

bool happened(double probability)//probability 0~1
{
	if (probability <= 0)
	{
		return false;
	}
	if (probability<MinProb)
	{
		return rand() == 0 && happened(probability*(RAND_MAX + 1));
	}
	if (rand() <= probability*(RAND_MAX + 1))
	{
		return true;
	}
	return false;
}

int myrandom(int n)//产生0~n-1之间的等概率随机数
{
	int t = 0;
	if (n <= RAND_MAX)
	{
		int R = RAND_MAX - (RAND_MAX + 1) % n;//尾数
		t = rand();
		while (t > R)
		{
			t = rand();
		}
		return t % n;
	}
	else
	{
		int r = n % (RAND_MAX + 1);//余数
		if (happened((double)r / n))//取到余数的概率
		{
			return n - r + myrandom(r);
		}
		else
		{
			return rand() + myrandom(n / (RAND_MAX + 1))*(RAND_MAX + 1);
		}
	}
}

void DisPlay(int N, KeyInt *p)
{
	for (int i = 0; i < 100; i++)
		printf("%d\n", p[i]);
}

排序算法分析与程序设计以及使用OpenMP并行比较

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原文地址：http://blog.csdn.net/secyb/article/details/51319391