快速排序算法详解：hoare、挖坑法、lomuto前后指针与非递归实现

#pragma once
#include<stdio.h>
#include<time.h>
#include<stdlib.h>

//插入排序
//1）直接插入排序n^2
void InsertSort(int* arr, int n);
//2）希尔排序n^1.3
void ShellSort(int* arr, int n);

//选择排序
//1）直接选择排序n^2
void SelectSort(int* arr, int n);
//2）堆排序 nlogn
void HeapSort(int* arr, int n);

//交换排序
//1）冒泡排序
void BubbleSort(int* arr, int n);
//2）快速排序
void QuickSort(int* arr, int left, int right);
//非递归版本快速排序
void QuickSortNorR(int* arr, int left, int right);

#pragma once
#include<stdio.h>
#include<stdlib.h>
#include<stdbool.h>
#include<assert.h>

//定义栈的结构
typedef int STDataType;
typedef struct Stack {
	STDataType* arr;
	int top; //指向栈顶的位置---刚好就是栈中有效数据个数
	int capacity;//栈的空间大小
}ST;

//初始化
void STInit(ST* ps);
//销毁
void STDesTroy(ST* ps);

//入栈——栈顶
void STPush(ST* ps, STDataType x);
//出栈———栈顶
void STPop(ST* ps);
//取栈顶元素
STDataType STTop(ST* ps);


//栈是否为空
bool STEmpty(ST* ps);
//获取栈中有效元素个数
int STSize(ST* ps);

#define _CRT_SECURE_NO_WARNINGS 666
#include"Sort.h"
#include"Stack.h"

//1）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;
		for (int i = 0; i < n - gap; i++)
		{
			int end = i;
			//当前组的下一个位置数据
			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;
}

//向下调整算法 logn
void AdjustDown(int* arr, int parent, int n)
{
	int child = parent * 2 + 1;
	while (child < n)
	{
		//建大堆：<
		//建小堆: >
		if (child + 1 < n && arr[child] < arr[child + 1])
		{
			child++;
		}
		//孩子和父亲比较
		//建大堆：>
		//建小堆:<
		if (arr[child] > arr[parent])
		{
			Swap(&arr[child], &arr[parent]);
			parent = child;
			child = parent * 2 + 1;
		}
		else {
			break;
		}
	}
}

//堆排序————使用的是堆结构的思想 n * logn
void HeapSort(int* arr, int n)
{
	//向下调整算法——建堆n
	for (int i = (n - 1 - 1) / 2; i >= 0; i--)
	{
		AdjustDown(arr, i, n);
	}

	////向上调整算法建堆n*logn
	//for (int i = 0; i < n; i++)
	//{
	//	AdjustUp(arr, i);
	//}

	//n*logn
	int end = n - 1;
	while (end > 0)
	{
		Swap(&arr[0], &arr[end]);
		AdjustDown(arr, 0, end);//logn
		end--;
	}
}

//冒泡排序
void BubbleSort(int* arr, int n)
{
	int exchange = 0;
	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j < n - i - 1; j++)
		{
			if (arr[j] > arr[j + 1])
			{
				exchange = 1;
				Swap(&arr[j], &arr[j + 1]);
			}
		}
		//经历一次循环exchange没有改变，没有发生交换
		//说明数组本身有序，此时时间复杂度达到最好（n）
		if (exchange == 0)
		{
			break;
		}
	}
}

////1）直接选择排序
//void SelectSort(int* arr, int n)
//{
//	//找最小值
//	for (int i = 0; i < n; i++)
//	{
//		int mini = i;
//		for (int j = i + 1; j < n; j++)
//		{
//			if (arr[j] < arr[mini])
//			{
//				mini = j;
//			}
//		}
//		//遍历完一遍后找到了最小值mini
//		//将其放到下标为0的位置...
//		Swap(&arr[mini], &arr[i]);
//	}
//}

//1）直接选择排序
void SelectSort(int* arr, int n)
{
	int begin = 0, end = n - 1;
	while (begin < end)
	{
		//初始情况假定最大最小在下标为0的位置
		int mini = begin;
		int maxi = begin;
		//在begin和end的范围内找最大和最小
		for (int i = begin + 1; i <= end; i++)
		{
			if (arr[i] < arr[mini])
			{
				mini = i;
			}
			if (arr[i] > arr[maxi])
			{
				maxi = i;
			}
		}
		//特殊情况处理，当maxi和begin在同一位置时
		if (maxi == begin)
		{
			maxi = mini;
		}
		//找到最小最大值，和begin和end位置交换
		Swap(&arr[begin], &arr[mini]);
		Swap(&arr[end], &arr[maxi]);
		begin++;
		end--;
	}
}

//找基准值 hoare版本
int _QuickSort1(int* arr, int left, int right)
{
	int keyi = left; //初始基准值在数组最左边的位置
	left++; //初始left在基准值右边
	while (left <= right)
	{
		//right:从右往左走找比基准值小的值
		while (left <= right && arr[right] > arr[keyi])
		{
			right--;
		}
		//left:从左往右找比基准值大的值
		while (left <= right && arr[left] < arr[keyi])
		{
			left++;
		}
		//left和right交换
		if (left <= right)
		{
			Swap(&arr[left++], &arr[right--]);
		}
	}
	//right的位置就是基准值的位置
	Swap(&arr[keyi], &arr[right]);
	//返回当前基准值的下标
	return right;
}

//找基准值 挖坑法
int _QuickSort2(int* arr, int left, int right)
{
	int hole = left;
	int key = arr[hole];
	while (left < right)
	{
		//right 从右向左找比基准值小的值
		while (left<right && arr[right]>key)
		{
			--right;
		}
		arr[hole] = arr[right];
		hole = right;
		//left 从左向右找比基准值大的值
		while (left < right && arr[left] < key)
		{
			++left;
		}
		arr[hole] = arr[left];
		hole = left;
	}
	arr[hole] = key;
	return hole;
}

//找基准值 lumoto双指针法
int _QuickSort3(int* arr, int left, int right)
{
	int prev = left, cur = prev + 1;
	int keyi = left;
	while (cur <= right)
	{
		//cur数据和基准值比较
		if (arr[cur] < arr[keyi] && ++prev != cur)
		{
			Swap(&arr[cur], &arr[prev]);
		}
		//cur指向的数据不比基准值要小或prev++之后和cur指向同一个位置
		cur++;
	}
	Swap(&arr[keyi], &arr[prev]);
	return prev;
}

//2)快速排序
void QuickSort(int* arr, int left, int right)
{
	if (left >= right)
	{
		return;
	}
	//找基准值
	int keyi = _QuickSort3(arr, left, 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 QuickSortNorR(int* arr, int left, int right)
{
	ST st;
	STInit(&st);
	STPush(&st, right);
	STPush(&st, left);
	while (!STEmpty(&st))
	{
		//取栈顶两次
		int begin = STTop(&st);
		STPop(&st);
		int end = STTop(&st);
		STPop(&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[prev], &arr[keyi]);
		keyi = prev;
		//begin keyi end
		//左序列[begin,keyi-1]
		//右序列[keyi+1,end]
		if (keyi + 1 < end)
		{
			STPush(&st, end);
			STPush(&st, keyi + 1);
		}
		if (begin < keyi - 1)
		{
			STPush(&st, keyi - 1);
			STPush(&st, begin);
		}
	}
	STDesTroy(&st);
}

#include"Stack.h"

//初始化
void STInit(ST* ps)
{
	ps->arr = NULL;
	ps->top = ps->capacity = 0;

}

//销毁
void STDesTroy(ST* ps)
{
	if(ps->arr)
		free(ps->arr);

	ps->arr = NULL;
	ps->top = ps->capacity = 0;
}

//入栈——栈顶
void STPush(ST* ps, STDataType x)
{
	assert(ps);
	//判断空间是否足够
	if (ps->top == ps->capacity)
	{
		//增容
		int newCapacity = ps->capacity == 0 ? 4 : 2 * ps->capacity;
		STDataType* tmp = (STDataType*)realloc(ps->arr, newCapacity * sizeof(STDataType));
		if (tmp == NULL)
		{
			perror("realloc fail！");
			exit(1);
		}
		ps->arr = tmp;
		ps->capacity = newCapacity;
	}
	//空间足够
	ps->arr[ps->top++] = x;
}
//栈是否为空
bool STEmpty(ST* ps)
{
	assert(ps);
	return ps->top == 0;
}
//出栈———栈顶
void STPop(ST* ps)
{
	assert(!STEmpty(ps));
	ps->top--;
}

//取栈顶元素
STDataType STTop(ST* ps)
{
	assert(!STEmpty(ps));
	return ps->arr[ps->top - 1];
}

//获取栈中有效元素个数
int STSize(ST* ps)
{
	assert(ps);
	return ps->top;
}

#define _CRT_SECURE_NO_WARNINGS 666
#include"Sort.h"

void printArr(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 };
	//int a[] = { 5,3,9,6,2,4,7,1,8 };
	int a[] = { 6,1,2,7,9,3 };
	//用整个数组的大小/单个数据的大小 = 数组中数据个数
	int n = sizeof(a) / sizeof(a[0]);
	printf("排序之前:");
	printArr(a, n);

	//InsertSort(a, n);
	//ShellSort(a, n);
	//SelectSort(a, n);
	//QuickSort(a, 0, n - 1);
	QuickSortNorR(a, 0, n - 1);

	printf("排序之后:");
	printArr(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];
	}
	//在执行排序之前打印程序执行到此处的时间
	int begin1 = clock();
	InsertSort(a1, N);
	//在执行排序之后打印程序执行到此处的时间
	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(a4, 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;
}