排序--插入排序
上学的时候学数据结构，没有意识到它的重要性，而如今工作了，也积累了一些项目经验，回过头来再看数据结构，才感觉出那看似“基础”的知识，其中蕴含着最简单，也最深刻的道理，所以打算重新系统得复习一下，在此写的文章就算是自己的复习笔记了。
今天先从排序开始复习，我所了解的排序有内排序和外排序之分，假如整个排序过程不需要访问外存的话便能实现排序，则此类排序称为内排序，反之，若参加排序的记录数非常大，内存是无法容纳这些记录的，就得需要外部存储设备来进行排序，则称此类排序为外部排序。
学习数据结构最重要的是掌握它的一些思想精华，排序算法就很有代表性，排序算法大致可分为：插入排序，选择排序，交换排序，归并排序等。今天首先来复习插入排序，插入排序的主要思想是不断地将待排序的元素插入到有序序列中，使有序序列不断扩大，直至所有元素都被插入有序序列中。插入排序算法比较典型的有直接插入排序和希尔排序。
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一.直接插入排序（Straight Insertion Sort）
排序的过程如下：给定无需序列：（3，6，9，7，1，8，2，4）
① 3，6，9，7，1，8，2，4 （将6插入到有序序列3中）
② 3，6，9，7，1，8，2，4 （将9插入到有序序列3，6中）
③ 3，6，9，7，1，8，2，4 （将7插入到有序序列3，6，9中）
④ 3，6，7，9，1，8，2，4 （将1插入到有序序列3，6，7，9中）
⑤ 1，3，6，7，9，8，2，4 （将8插入到有序序列1，3，6，7，9中）
⑥ 1，3，6，7，8，9，2，4 （将2插入到有序序列1，3，6，7，8，9中）
⑦ 1，2，3，6，7，8，9，4 （将4插入到有序序列1，2，3，6，7，8，9中）
⑧ 1，2，3，4，6，7，8，9 (排序成功)
using System;
namespace SortAlgorithm
{
/// <summary>
/// 直接插入算法
/// </summary>
class Program
{
public static void Main(string[] args)
{
//j指针用于查找插入位置，temp用于记录当前要插入元素
int j,temp;
//待排序数组
int[] array={3,6,5,9,7,1,8,2,4};
//第一个元素默认有序，所以i从1开始，既拿第二个元素开始插入
for(int i=1;i<array.Length;i++)
{
//将待插入元素保存在temp中
temp=array[i];
j=i-1;
while(j>=0&&temp<array[j])
{
array[j+1]=array[j];//向后移动元素
j--;
}
array[j+1]=temp;//将待插入元素插入到所查找好的位置
}
//打印已排好的元素
foreach(int i in array)
{
Console.Write(i+" ");
}
Console.ReadKey(true);
}
}
}
以上代码中的while(j>=0&&temp<array[j])需要进行两次比较，这里可以做一些改进，可以通过设置监视哨减少循环中的比较次数。所谓监视哨就是利用数组的某个元素来存放当前待排序的元素，从而达到避免数组越界和减少比较次数的目的，这里使用array[0]来作为监视哨，改进后的代码如下：
using System;
namespace InsertionSort
{
class Program
{
public static void Main(string[] args)
{
//待排序数组
int[] array={0,3,6,5,9,7,1,8,2,4};
//j指针用于查找插入位置
int j;
for(int i=1;i<array.Length;i++)
{
array[0]=array[i];
j=i-1;
while(array[0]<array[j])
{
array[j+1]=array[j];
j--;
}
array[j+1]=array[0];
}
foreach(int i in array)
{
Console.Write(i+" ");
}
Console.ReadKey(true);
}
}
}
注意
：使用监视哨的前提是array[0]元素不能存在于排序序列中，只作为辅助变量
直接插入排序算法最好情况的时间复杂度：O（n)，最坏情况为：o(n²)
二.希尔排序
希尔排序(Shell Sort)又称缩小增量排序，它是对直接插入排序的一种改进方法，直接插入排序适合于数据量较少的排序，
当待排序记录序列接近正序时，其时间复杂度为O（n)，希尔排序正是依此对直接排序进行的改进算法，其基本思想是将待
排序的元素分组，从而减少参与直接插入排序的数据量，当经过几次分组后，元素的排列已经基本有序，这时再对所有元素
实施直接插入排序，算法如下：
using System;
namespace ShellSort
{
/// <summary>
/// 希尔排序
/// </summary>
class Program
{
public static void Main(string[] args)
{
//待排序数组
int[] array={3,6,5,9,7,1,8,2,4};
int j,temp;
//d为步长
for(int d=array.Length/2;d>=1;d=d/2)
{
for(int i=d;i<array.Length;i++)
{
temp=array[i];
j=i-d;
while(j>=0&&temp<array[j])
{
array[j+1]=array[j];
j=j-d;
}
array[j+d]=temp;
}
}
foreach(int i in array)
{
Console.Write(i+" ");
}
Console.ReadKey(true);
}
}
}
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