数据结构与算法（七）排序c语言实现

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#数据结构 #算法 #快速排序 #插入排序 #排序算法

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本文介绍了三种排序算法：直接插入排序通过逐个比较插入元素的位置，二分插入排序利用二分查找优化插入过程，希尔排序则通过间隔递减的方式改进排序效率。详细展示了每种排序方法的实现细节和应用场景。

数据结构与算法（七）排序

直接插入排序

void DInsertSort(SqList* Sq)//直接插入排序
{
	int i, j;
	for (i = 2; i <= Sq->length; ++i)
	{
		Sq->r[0].key = Sq->r[i].key;
		for (j = i-1; Sq->r[0].key<Sq->r[j].key; j--)
		{
			Sq->r[j + 1].key = Sq->r[j].key;
		}
		Sq->r[j + 1].key = Sq->r[0].key;
	}
}

二分法插入排序

void BInsersort(SqList* Sq)//二分插入排序
{
	int i, j;
	for (i = 2; i <= Sq->length; ++i)
	{
		Sq->r[0].key = Sq->r[i].key;
		int low = 1;
		int high = i-1;
		while (low <= high)
		{
			int mid = (low + high) / 2;
			if (Sq->r[0].key < Sq->r[mid].key)
				high = mid - 1;
			else
				low = mid + 1;
		}
		for (j = i - 1; j >= high + 1; --j)
			Sq->r[j + 1].key = Sq->r[j].key;
		Sq->r[high + 1].key = Sq->r[0].key;
	}
}

希尔排序

void ShellInsert(SqList* Sq, int delta)//希尔排序，插入部分
{
	int i, j;
	for (i = 1 + delta; i <= Sq->length; ++i)
	{
		if (Sq->r[i].key < Sq->r[i - delta].key)
		{
			Sq->r[0].key = Sq->r[i].key;
			for (j = i - delta; j > 0 && Sq->r[0].key < Sq->r[j].key; j = j - delta)
			{
				Sq->r[j + delta].key = Sq->r[j].key;
			}
			Sq->r[j + delta].key = Sq->r[0].key;
		}
	}
}

void ShellSort(SqList* Sq)//希尔排序，循环部分
{
	int i = 0;
	int delta[3] = { 5,3,1 };
	for (i = 0; i < 3; ++i)
	{
		ShellInsert(Sq,delta[i]);
	}
}

冒泡排序

void BubbleSort(SqList* Sq)//冒泡排序
{
	int i, j;
	for (i = 1; i <= Sq->length - 1; ++i)
	{
		for (j = 1; j <= Sq->length - i; ++j)
		{
			if (Sq->r[j].key > Sq->r[j + 1].key)
			{
				int t = Sq->r[j].key;
				Sq->r[j].key = Sq->r[j + 1].key;
				Sq->r[j + 1].key = t;
			}
		}
	}
}

快速排序

int Partition(SqList* Sq, int low, int high)//快速排序，定位函数
{
	Sq->r[0].key = Sq->r[low].key;
	int pivotkey = Sq->r[low].key;
	while (low < high)
	{
		while (low < high && Sq->r[high].key >= pivotkey)
			high--;
		Sq->r[low].key = Sq->r[high].key;
		while (low < high && Sq->r[low].key <= pivotkey)
			low++;
		Sq->r[high].key = Sq->r[low].key;
	}
	Sq->r[low].key = Sq->r[0].key;
	return low;
}

void QSort(SqList* Sq, int low, int high)//快速排序，排序函数
{
	int pivotloc;
	if (low < high)
	{
		pivotloc = Partition(Sq,low,high);
		QSort(Sq,low,pivotloc-1);
		QSort(Sq, pivotloc + 1,high);
	}
}

完整代码

#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>

#define MAX 20

typedef struct
{
	int key;
	int other;
}RedType;

typedef struct
{
	RedType r[MAX+1];
	int length;
}SqList;

SqList* CreateList(int n)
{
	SqList* Sq = (SqList*)malloc(sizeof(SqList)*n);
	if (Sq == NULL)
	{
		exit(-1);
	}
	for (int i = 1; i <= n; ++i)//[0]不放元素，用于后面排序的优化
	{
		printf("请输入元素：");
		scanf_s("%d",&(Sq->r[i].key));
	}
	Sq->length = n;
	return Sq;
}

void show(SqList* Sq)
{
	for (int i = 1; i <= Sq->length; ++i)
	{
		printf("%d\t",Sq->r[i].key);
	}
	printf("\n");
}

void DInsertSort(SqList* Sq)//直接插入排序
{
	int i, j;
	for (i = 2; i <= Sq->length; ++i)
	{
		Sq->r[0].key = Sq->r[i].key;
		for (j = i-1; Sq->r[0].key<Sq->r[j].key; j--)
		{
			Sq->r[j + 1].key = Sq->r[j].key;
		}
		Sq->r[j + 1].key = Sq->r[0].key;
	}
}

void BInsersort(SqList* Sq)//二分插入排序
{
	int i, j;
	for (i = 2; i <= Sq->length; ++i)
	{
		Sq->r[0].key = Sq->r[i].key;
		int low = 1;
		int high = i-1;
		while (low <= high)
		{
			int mid = (low + high) / 2;
			if (Sq->r[0].key < Sq->r[mid].key)
				high = mid - 1;
			else
				low = mid + 1;
		}
		for (j = i - 1; j >= high + 1; --j)
			Sq->r[j + 1].key = Sq->r[j].key;
		Sq->r[high + 1].key = Sq->r[0].key;
	}
}

void ShellInsert(SqList* Sq, int delta)//希尔排序，插入部分
{
	int i, j;
	for (i = 1 + delta; i <= Sq->length; ++i)
	{
		if (Sq->r[i].key < Sq->r[i - delta].key)
		{
			Sq->r[0].key = Sq->r[i].key;
			for (j = i - delta; j > 0 && Sq->r[0].key < Sq->r[j].key; j = j - delta)
			{
				Sq->r[j + delta].key = Sq->r[j].key;
			}
			Sq->r[j + delta].key = Sq->r[0].key;
		}
	}
}

void ShellSort(SqList* Sq)//希尔排序，循环部分
{
	int i = 0;
	int delta[3] = { 5,3,1 };
	for (i = 0; i < 3; ++i)
	{
		ShellInsert(Sq,delta[i]);
	}
}

void BubbleSort(SqList* Sq)//冒泡排序
{
	int i, j;
	for (i = 1; i <= Sq->length - 1; ++i)
	{
		for (j = 1; j <= Sq->length - i; ++j)
		{
			if (Sq->r[j].key > Sq->r[j + 1].key)
			{
				int t = Sq->r[j].key;
				Sq->r[j].key = Sq->r[j + 1].key;
				Sq->r[j + 1].key = t;
			}
		}
	}
}

int Partition(SqList* Sq, int low, int high)//快速排序，定位函数
{
	Sq->r[0].key = Sq->r[low].key;
	int pivotkey = Sq->r[low].key;
	while (low < high)
	{
		while (low < high && Sq->r[high].key >= pivotkey)
			high--;
		Sq->r[low].key = Sq->r[high].key;
		while (low < high && Sq->r[low].key <= pivotkey)
			low++;
		Sq->r[high].key = Sq->r[low].key;
	}
	Sq->r[low].key = Sq->r[0].key;
	return low;
}

void QSort(SqList* Sq, int low, int high)//快速排序，排序函数
{
	int pivotloc;
	if (low < high)
	{
		pivotloc = Partition(Sq,low,high);
		QSort(Sq,low,pivotloc-1);
		QSort(Sq, pivotloc + 1,high);
	}
}

int main()
{
	int n;
	SqList* Sq;
	printf("请输入元素个数： ");
	scanf_s("%d",&n);
	Sq=CreateList(n);
	show(Sq);
	//DInsertSort(Sq);
	//show(Sq);
	//BInsersort(Sq);
	//show(Sq);
	//ShellSort(Sq);
	//show(Sq);
	//BubbleSort(Sq);
	//show(Sq);
	QSort(Sq,1,Sq->length);
	show(Sq);
	return 0;
}

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