一文彻底搞清楚数据结构之排序算法大揭秘

//直接插入排序
void InsertSort(int* arr, int n)
{
for (int i = 0; i < n - 1; i++)// 循环控制“未排序元素”的选取
{
    int end = i;                 // end：“已排序部分”的最后一个元素下标
    int tmp = arr[end + 1];      // tmp：当前要插入的“未排序元素”（已排序区的下一个元素）
    // 在“已排序部分”中找tmp的插入位置
    while (end >= 0)
    {
        if (arr[end] > tmp)      // 如果已排序元素比tmp大
        {
            arr[end + 1] = arr[end];  // 把该元素往后移一位（给tmp腾位置）
            end--;                    // 继续往前找更小的元素
        }
        else  // 如果已排序元素 <= tmp，说明找到了插入位置
        {
            break;  // 退出循环，准备插入tmp
        }
    }
    arr[end + 1] = tmp;  // 把tmp放到最终的插入位置
}
}

//希尔排序
void ShellSort(int* arr, int n)
{
	int gap = n;// gap初始化为数组长度（第一步的分组步长）
	while (gap > 1)
	{
		gap = gap / 3 + 1;
// 对每组进行直接插入排序
for (int i = 0; i < n - gap; i++)  // i控制“每组的起始位置”，避免end+gap越界
{
    int end = i;  // end：当前组“已排序部分”的最后一个元素下标
    int tmp = arr[end + gap];  // tmp：当前要插入的“未排序元素”（组内下一个元素）

    while (end >= 0)
    {
        if (arr[end] > tmp)  // 已排序元素比tmp大 → 往后挪gap位
        {
            arr[end + gap] = arr[end];
            end -= gap;  // 组内往前跳gap位，继续比较
        }
        else  // 找到插入位置，退出循环
        {
            break;
        }
    }
    arr[end + gap] = tmp;  // 把tmp插入到组内的正确位置
}
}
}

void Swap(int* x, int* y)
{
	int tmp = *x;
	*x = *y;
	*y = tmp;
}
//直接选择排序
void SelectSort(int* arr, int n)
{
	int begin = 0, end = n - 1;
	while (begin < end)
	{
		int maxi = begin;
		int mini = begin;
		for (int i = begin + 1; i <= end; i++)
		{
			if (arr[i] < arr[mini])
			{
				mini = i;
			}
			if (arr[i] > arr[maxi])
			{
				maxi = i;
			}
		}
		if (maxi == begin)
		{
			maxi = mini;
		}
		Swap(&arr[mini], &arr[begin]);
		Swap(&arr[maxi], &arr[end]);
		begin++;
		end--;
	}
}

void AdjustDown(HPDataType* arr, int parent, int n)
{
	int child = parent * 2 + 1;//左孩子
	while (child < n)
	{
		//大堆：<
		//小堆：>
		if (child + 1 < n && arr[child] < arr[child + 1])
		{
			child++;
		}
		//大堆: >
		//小堆：<
		if (arr[child] > arr[parent])
		{
			//调整
			Swap(&arr[child], &arr[parent]);
			parent = child;
			child = parent * 2 + 1;
		}
		else {
			break;
		}
	}
}
void HPPop(HP* php)
{
	assert(!HPEmpty(php));
	// 0 php->size-1
	Swap(&php->arr[0], &php->arr[php->size - 1]);
	--php->size;
	//向下调整
	AdjustDown(php->arr, 0, php->size);
}
// 排升序，建⼤堆
// 排降序，建⼩堆
// O(N*logN)
void HeapSort(int* a, int n)
{
 // a数组直接建堆 O(N)
 for (int i = (n-1-1)/2; i >= 0; --i)
 {
 AdjustDown(a, n, i);
 }
 // O(N*logN)
 int end = n - 1;
 while (end > 0)
 {
 Swap(&a[0], &a[end]);
 AdjustDown(a, end, 0);
 --end;
 }
 }

void Swap(int* x, int* y)
{
	int tmp = *x;
	*x = *y;
	*y = tmp;
}
//冒泡排序
void BubbleSort(int* arr, int n)
{
	for (size_t end = n; end > 0; --end)
	{
		int exchange = 0;
		for (size_t i = 1; i < end; ++i)
		{
			if (arr[i - 1] > arr[i])
			{
				Swap(&arr[i - 1], &arr[i]);
				exchange = 1;
			}
		}
		if (exchange == 0)
			break;
	}
}

//快速排序
 void QuickSort(int* a, int left, int right)
 {
 if (left >= right) {
 return;
 }
 //_QuickSort⽤于按照基准值将区间[left,right)中的元素进⾏划分
 int meet = _QuickSort(a, left, right);
 QuickSort(a, left, meet - 1);
 QuickSort(a, meet + 1, right);
 }
 //将区间中的元素进⾏划分的_QuickSort⽅法主要有以下⼏种实现⽅式：

//快速排序
void QuickSort(int* arr, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	//找基准值
	int keyi = _QuickSort(arr, left, right);
	//left keyi right
	//左序列[left,keyi-1]     右序列[keyi+1,right]
	QuickSort(arr, left, keyi - 1);
	QuickSort(arr, keyi + 1, right);
}
//hoare版本
int _QuickSort1(int* arr, int left, int right)
{
	int keyi = left;
	++left;
	while (left <= right)
	{
		//right：从右往左走，找比基准值要小的
		while (left <= right && arr[right] > arr[keyi])
		{
			right--;
		}
		//left：从左往右走，找比基准值要大的
		while (left <= right && arr[left] < arr[keyi])
		{
			left++;
		}
		//right left 
		if (left <= right)
		{
			Swap(&arr[left++], &arr[right--]);
		}
	}	
	Swap(&arr[keyi], &arr[right]);
	return right;
}//right:从右往左走,找比基准值要小的数据left:从左往右走,找比基准值要大的数据left<= right找到之后，让left和right交换当left>right,keyi和right数据交换,当基准值和left/right相等,也要交换

int _QuickSort(int* a, int left, int right)
 {
 int hole = left;
 int key = a[hole];
 while (left < right)
 {
 while (left < right && a[right] >= key)
 {
 --right;
 }
 a[hole] = a[right];
 hole = right;
 while (left < right && a[left] <= key)
 {
 ++left;
 }
 a[hole] = a[left];
 hole = left;
 }
 a[hole] = key;
 return hole;
 }

void Swap(int* x, int* y)
{
	int tmp = *x;
	*x = *y;
	*y = tmp;
}
//lomuto前后指针法
int _QuickSort(int* arr, int left, int right)
{
	int keyi = left;
	int prev = left, cur = prev + 1;
	while (cur <= right)
	{
		if (arr[cur] < arr[keyi] && ++prev != cur)
		{
			Swap(&arr[prev], &arr[cur]);
		}
		cur++;
	}
	Swap(&arr[keyi], &arr[prev]);
	return prev;
}

//非递归版本的快速排序——栈
void QuicSortNoR(int* arr, int left, int right)
{
	ST st;
	StackInit(&st);
	StackPush(&st, left);
	StackPush(&st, right);
	while (!StackEmpty(&st))
	{
		//取栈顶两次
		int end = StackTop(&st);
		StackPop(&st);
		int begin = StackTop(&st);
		StackPop(&st);
		//[begin,end]找基准值
		int keyi = begin;
		int prev = begin, cur = prev + 1;
		while (cur <= end)
			{
		if (arr[cur] < arr[keyi] && ++prev != cur)
		{
			Swap(&arr[prev], &arr[cur]);
		}
		cur++;
	}
	Swap(&arr[keyi], &arr[prev]);
	keyi = prev;
	//begin keyi end
	//左序列：[begin,keyi-1]  右序列：[keyi+1,end];
	if (keyi + 1 < end)
	{
		StackPush(&st, keyi + 1);
		StackPush(&st, end);
	}
			if (begin < keyi - 1)
		{
			StackPush(&st, begin);
			StackPush(&st, keyi - 1);
		}
	}
	StackDestroy(&st);
}//关于栈部分的代码前面文章内容里面有,这里就不展示了

//归并排序
void _MergeSort(int* arr, int left, int right, int* tmp)
{
	if (left >= right)
	{
		return;
	}
	//[left,right]
	int mid = (left + right) / 2;
	//根据mid划分左右两个序列：[left,mid] [mid+1,right]
	_MergeSort(arr, left, mid, tmp);
	_MergeSort(arr, mid + 1, right, tmp);

	//合并两个有序的序列
	int begin1 = left, end1 = mid;
	int begin2 = mid + 1, end2 = right;
	int index = begin1;

	//[begin1,end1]  [begin2,end2]
	while (begin1 <= end1 && begin2 <= end2)
	{
	if (arr[begin1] < arr[begin2])
	{
		tmp[index++] = arr[begin1++];
	}
	else {
		tmp[index++] = arr[begin2++];
	}
}
while (begin1 <= end1)
{
	tmp[index++] = arr[begin1++];
}
while (begin2 <= end2)
{
	tmp[index++] = arr[begin2++];
}
//tmp中有序的数据导入到原数组
//[left,right]
	for (int i = left; i <= right; i++)
	{
		arr[i] = tmp[i];
	}
}
void MergeSort(int* arr, int n)
{
	int* tmp = (int*)malloc(sizeof(int) * n);
	_MergeSort(arr, 0, n - 1, tmp);
	free(tmp);
	tmp = NULL;
}

//计数排序
void CountSort(int* arr, int n)
{
	//找最大和最小值
	int min = arr[0], max = arr[0];
	for (int i = 1; i < n; i++)
	{
		if (arr[i] < min)
		{
			min = arr[i];
		}
		if (arr[i] > max)
		{
			max = arr[i];
		}
	}
		//max-min+1确定count数组的大小
	int range = max - min + 1;
	int* count = (int*)malloc(sizeof(int) * range);
	if (count == NULL)
	{
		perror("malloc fail!");
		exit(1);
	}
	//初始化用calloc
	memset(count, 0, sizeof(int) * range);
	for (int i = 0; i < n; i++)
	{
		count[arr[i] - min]++;
	}
	//将count数组还原到原数组中，使其有序
	int index = 0;
		for (int i = 0; i < range; i++)
	{
		while (count[i]--)
		{
			arr[index++] = i + min;
		}
	}
}

// 测试排序的性能对⽐
 void TestOP()
 {
 srand(time(0));
 const int N = 100000;
 int* a1 = (int*)malloc(sizeof(int)*N);
 int* a2 = (int*)malloc(sizeof(int)*N);
 int* a3 = (int*)malloc(sizeof(int)*N);
 int* a4 = (int*)malloc(sizeof(int)*N);
 int* a5 = (int*)malloc(sizeof(int)*N);
 int* a6 = (int*)malloc(sizeof(int)*N);
 int* a7 = (int*)malloc(sizeof(int)*N);
 for (int i = 0; i < N; ++i)
 {
 a1[i] = rand();
 a2[i] = a1[i];
 a3[i] = a1[i];
 a4[i] = a1[i];
 a5[i] = a1[i];
 a6[i] = a1[i];
 a7[i] = a1[i];
 }
 int begin1 = clock();
 InsertSort(a1, N);
 int end1 = clock();
 int begin2 = clock();
 ShellSort(a2, N);
 int end2 = clock();
 int begin3 = clock();
 SelectSort(a3, N);
 int end3 = clock();
 int begin4 = clock();
 HeapSort(a4, N);
 int end4 = clock();
 int begin5 = clock();
 QuickSort(a5, 0, N-1);
 int end5 = clock();
 int begin6 = clock();
 MergeSort(a6, N);
 int end6 = clock();
 int begin7 = clock();
 BubbleSort(a7, N);
 int end7 = clock();
 printf("InsertSort:%d\n", end1 - begin1);
 printf("ShellSort:%d\n", end2 - begin2);
 printf("SelectSort:%d\n", end3 - begin3);
 printf("HeapSort:%d\n", end4 - begin4);
 printf("QuickSort:%d\n", end5 - begin5);
 printf("MergeSort:%d\n", end6 - begin6);
 printf("BubbleSort:%d\n", end7 - begin7);
 free(a1);
 free(a2);
 free(a3);
 free(a4);
 free(a5);
 free(a6);
 free(a7);
 }

#include"sort.h"
#include"Stack.h"
//直接插入排序
void InsertSort(int* arr, int n)
{
	for (int i = 0; i < n - 1; i++)
	{
		int end = i;
		int tmp = arr[end + 1];
		while (end >= 0)
		{
			if (arr[end] > tmp)
			{
				arr[end + 1] = arr[end];
				end--;
			}
			else {
				break;
			}
		}
		arr[end + 1] = tmp;
	}
}
//希尔排序
void ShellSort(int* arr, int n)
{
	int gap = n;
	while (gap > 1)
	{
		gap = gap / 3 + 1;//3 2 1 
		//对每组进行直接插入排序
		for (int i = 0; i < n - gap; i++)
		{
			int end = i;
			int tmp = arr[end + gap];
			while (end >= 0)
			{
				if (arr[end] > tmp)
				{
					arr[end + gap] = arr[end];
					end -= gap;
				}
				else {
					break;
				}
			}
			arr[end + gap] = tmp;
		}
	}
}
void Swap(int* x, int* y)
{
	int tmp = *x;
	*x = *y;
	*y = tmp;
}
//冒泡排序
void BubbleSort(int* arr, int n)
{
	for (size_t end = n; end > 0; --end)
	{
		int exchange = 0;
		for (size_t i = 1; i < end; ++i)
		{
			if (arr[i - 1] > arr[i])
			{
				Swap(&arr[i - 1], &arr[i]);
				exchange = 1;
			}
		}
		if (exchange == 0)
			break;
	}
}
//选择排序
void SelectSort(int* arr, int n)
{
	int begin = 0, end = n - 1;
	while (begin < end)
	{
		int maxi = begin;
		int mini = begin;
		for (int i = begin + 1; i <= end; i++)
		{
			if (arr[i] < arr[mini])
			{
				mini = i;
			}
			if (arr[i] > arr[maxi])
			{
				maxi = i;
			}
		}
		//mini begin
		//maxi end
		if (maxi == begin)
		{
			maxi = mini;
		}
		Swap(&arr[mini], &arr[begin]);
		Swap(&arr[maxi], &arr[end]);
		begin++;
		end--;
	}
}
//向下调整算法
void AdjustDown(int* arr, int parent, int n)
{
	int child = parent * 2 + 1;//左孩子
	while (child < n)
	{
		//大堆：<
		//小堆：>
		if (child + 1 < n && arr[child] < arr[child + 1])
		{
			child++;
		}
		//大堆: >
		//小堆：<
		if (arr[child] > arr[parent])
		{
			//调整
			Swap(&arr[child], &arr[parent]);
			parent = child;
			child = parent * 2 + 1;
		}
		else {
			break;
		}
	}
}
//排升序--- 建大堆
//排降序--- 建小堆
//堆排序
void HeapSort(int* arr, int n)
{
	//建堆——向下调整算法建堆
	for (int i = (n - 1 - 1) / 2; i >= 0; i--)
	{
		AdjustDown(arr, i, n);
	}
	//堆排序
	int end = n - 1;
	while (end > 0)
	{
		Swap(&arr[0], &arr[end]);
		AdjustDown(arr, 0, end);
		end--;
	}
}
//hoare版本
int _QuickSort1(int* arr, int left, int right)
{
	int keyi = left;
	++left;
	while (left <= right)
	{
		//right：从右往左走，找比基准值要小的
		while (left <= right && arr[right] > arr[keyi])
		{
			right--;
		}
		//left：从左往右走，找比基准值要大的
		while (left <= right && arr[left] < arr[keyi])
		{
			left++;
		}
		//right left 
		if (left <= right)
		{
			Swap(&arr[left++], &arr[right--]);
		}
	}
	Swap(&arr[keyi], &arr[right]);
	return right;
}
//lomuto前后指针法
int _QuickSort(int* arr, int left, int right)
{
	int keyi = left;
	int prev = left, cur = prev + 1;
	while (cur <= right)
	{
		if (arr[cur] < arr[keyi] && ++prev != cur)
		{
			Swap(&arr[prev], &arr[cur]);
		}
		cur++;
	}
	Swap(&arr[keyi], &arr[prev]);
	return prev;
}
//快速排序
void QuickSort(int* arr, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	//找基准值
	int keyi = _QuickSort(arr, left, right);
	//left keyi right
	//左序列[left,keyi-1]     右序列[keyi+1,right]
	QuickSort(arr, left, keyi - 1);
	QuickSort(arr, keyi + 1, right);
}
//非递归版本的快速排序——栈
void QuicSortNoR(int* arr, int left, int right)
{
	ST st;
	StackInit(&st);
	StackPush(&st, left);
	StackPush(&st, right);
	while (!StackEmpty(&st))
	{
		//取栈顶两次
		int end = StackTop(&st);
		StackPop(&st);
		int begin = StackTop(&st);
		StackPop(&st);

		//[begin,end]找基准值
		int keyi = begin;
		int prev = begin, cur = prev + 1;
		while (cur <= end)
		{
			if (arr[cur] < arr[keyi] && ++prev != cur)
			{
				Swap(&arr[prev], &arr[cur]);
			}
			cur++;
		}
		Swap(&arr[keyi], &arr[prev]);
		keyi = prev;
		//begin keyi end
		//左序列：[begin,keyi-1]  右序列：[keyi+1,end];
		if (keyi + 1 < end)
		{
			StackPush(&st, keyi + 1);
			StackPush(&st, end);
		}
		if (begin < keyi - 1)
		{
			StackPush(&st, begin);
			StackPush(&st, keyi - 1);
		}
	}
	StackDestroy(&st);
}
//归并排序
void _MergeSort(int* arr, int left, int right, int* tmp)
{
	if (left >= right)
	{
		return;
	}
	//[left,right]
	int mid = (left + right) / 2;
	//根据mid划分左右两个序列：[left,mid] [mid+1,right]
	_MergeSort(arr, left, mid, tmp);
	_MergeSort(arr, mid + 1, right, tmp);
	//合并两个有序的序列
	int begin1 = left, end1 = mid;
	int begin2 = mid + 1, end2 = right;
	int index = begin1;
	//[begin1,end1]  [begin2,end2]
	while (begin1 <= end1 && begin2 <= end2)
	{
		if (arr[begin1] < arr[begin2])
		{
			tmp[index++] = arr[begin1++];
		}
		else {
			tmp[index++] = arr[begin2++];
		}
	}
	while (begin1 <= end1)
	{
		tmp[index++] = arr[begin1++];
	}
	while (begin2 <= end2)
	{
		tmp[index++] = arr[begin2++];
	}
	//tmp中有序的数据导入到原数组
	//[left,right]
	for (int i = left; i <= right; i++)
	{
		arr[i] = tmp[i];
	}
}
void MergeSort(int* arr, int n)
{
	int* tmp = (int*)malloc(sizeof(int) * n);
	_MergeSort(arr, 0, n - 1, tmp);
	free(tmp);
	tmp = NULL;
}
//计数排序
void CountSort(int* arr, int n)
{
	//找最大和最小值
	int min = arr[0], max = arr[0];
	for (int i = 1; i < n; i++)
	{
		if (arr[i] < min)
		{
			min = arr[i];
		}
		if (arr[i] > max)
		{
			max = arr[i];
		}
	}
	//max-min+1确定count数组的大小
	int range = max - min + 1;
	int* count = (int*)malloc(sizeof(int) * range);
	if (count == NULL)
	{
		perror("malloc fail!");
		exit(1);
	}
	//初始化用calloc
	memset(count, 0, sizeof(int) * range);
	for (int i = 0; i < n; i++)
	{
		count[arr[i] - min]++;
	}
	//将count数组还原到原数组中，使其有序
	int index = 0;
	for (int i = 0; i < range; i++)
	{
		while (count[i]--)
		{
			arr[index++] = i + min;
		}
	}
}

#pragma once
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<time.h>
//
void InsertSort(int* arr, int n);
//
void ShellSort(int* arr, int n);
//
void BubbleSort(int* arr, int n);
//
void QuickSort(int* arr, int left, int right);
void QuicSortNoR(int* arr, int left, int right);
//
void SelectSort(int* arr, int n);
//
void HeapSort(int* arr, int n);
//
void MergeSort(int* arr, int n);
//
void CountSort(int* arr, int n);

#include"sort.h"
void arrprint(int* arr, int n)
{
	for (int i = 0; i < n; i++)
	{
		printf("%d ", arr[i]);
	}
	printf("\n");
}
void test01()
{
	//int a[] = { 5, 3, 9, 6, 2, 4, 7, 1, 8 };
	int a[] = { 100,101,109,105,101,105 };
	int n = sizeof(a) / sizeof(a[0]);
	printf("排序之前：");
	arrprint(a, n);
	//InserSort(a, n);
	//ShellSort(a, n);
	//SelectSort(a, n);
	//QuickSort(a, 0, n - 1);
	//QuicSortNoR(a, 0, n - 1);
	//MergeSort(a, n);
	CountSort(a, n);
	printf("排序之后：");
	arrprint(a, n);
}
// 测试排序的性能对⽐
void TestOP()
{
	srand(time(0));
	const int N = 100000;
	int* a1 = (int*)malloc(sizeof(int) * N);
	int* a2 = (int*)malloc(sizeof(int) * N);
	int* a3 = (int*)malloc(sizeof(int) * N);
	int* a4 = (int*)malloc(sizeof(int) * N);
	int* a5 = (int*)malloc(sizeof(int) * N);
	int* a6 = (int*)malloc(sizeof(int) * N);
	int* a7 = (int*)malloc(sizeof(int) * N);
	for (int i = 0; i < N; ++i)
	{
		a1[i] = rand();
		a2[i] = a1[i];
		a3[i] = a1[i];
		a4[i] = a1[i];
		a5[i] = a1[i];
		a6[i] = a1[i];
		a7[i] = a1[i];
	}
	int begin1 = clock();
	InsertSort(a1, N);
	int end1 = clock();

	int begin2 = clock();
	ShellSort(a2, N);
	int end2 = clock();

	int begin3 = clock();
	SelectSort(a3, N);
	int end3 = clock();

	int begin4 = clock();
	HeapSort(a4, N);
	int end4 = clock();

	int begin5 = clock();
	QuickSort(a5, 0, N - 1);
	int end5 = clock();

	int begin6 = clock();
	MergeSort(a6, N);
	int end6 = clock();

	int begin7 = clock();
	BubbleSort(a7, N);
	int end7 = clock();
	printf("InsertSort:%d\n", end1 - begin1);
	printf("ShellSort:%d\n", end2 - begin2);
	printf("SelectSort:%d\n", end3 - begin3);
	printf("HeapSort:%d\n", end4 - begin4);
	printf("QuickSort:%d\n", end5 - begin5);
	printf("MergeSort:%d\n", end6 - begin6);
	printf("BubbleSort:%d\n", end7 - begin7);
	free(a1);
	free(a2);
	free(a3);
	free(a4);
	free(a5);
	free(a6);
	free(a7);
}
int main()
{
	//test01();
	TestOP();
	return 0;
}