1、希尔排序

希尔排序属于插入排序。

平均时间复杂度：比直接插入低。具体分体非常复杂，有兴趣可自行研究。
平局空间复杂度：O(1)。因为只在交换位置时使用一个辅助空间做暂存记录。

2、C#实现

ShellSort.cs

	public static class ShellSort
    {
        public static void Shell(int[] numbers)
        {
            if (numbers == null || numbers.Length < 2)
            {
                Console.WriteLine("参数数组有误");
                return;
            }

            //存储每次的增量值
            int[] addArray = { 5, 3, 1 };

            for (int i = 0; i < addArray.Length; i++)
            {
                //使用不同增量进行排序
                ShellInsert(numbers, addArray[i]);
            }


        }

        public static void ShellInsert(int[] numbers, int add)
        {
            for (int i = add; i < numbers.Length; i++)
            {
                //这里相当于直接插入排序，每次比较新加入的元素
                //每个组的元素上一个元素index就是 -add
                if (numbers[i] < numbers[i - add])
                {
                    int temp = numbers[i];
                    int j;
                    //要保证数组不会越界
                    for (j = i; j > (i-add) && numbers[j - add] > temp; j -= add)
                    {
                        numbers[j] = numbers[j - add];
                    }
                    numbers[j] = temp;
                }
            }
            for (int k = 0; k < numbers.Length; k++)
            {
                Console.Write(numbers[k] + " ");
            }
            Console.WriteLine();
        }
    }

Program.cs

	class Program
    {
        static void Main(string[] args)
        {
            int[] numbers = { 49, 38, 65, 97, 76, 13, 27, 49 };
            ShellSort.Shell(numbers);

            for (int i = 0; i < numbers.Length; i++)
            {
                Console.Write(numbers[i] + " ");
            }
            Console.WriteLine();

            Console.ReadKey();
        }
    }

3、C++实现

ShellSort.cpp

///希尔排序
class ShellSort
{
public:
    static void Shell(int numbers[],int length);
    static void ShellInsert(int numbers[],int length,int add);
};

void ShellSort::Shell(int numbers[],int length)
{
    if (numbers == NULL || length < 2)
    {
        cout<<"参数数组有误"<<endl;
        return;
    }

    int addArray[] = {5,3,1};

    for(int i=0;i<3;i++){
        ShellInsert(numbers,length,addArray[i]);
    }
}
void ShellSort::ShellInsert(int numbers[],int length,int add)
{
    for(int i=add;i<length;i++){

        if(numbers[i]<numbers[i-add]){
            int temp = numbers[i];
            int j;
            for(j=i;j>(i-add)&&numbers[j-add]>temp;j-=add){
                numbers[j] = numbers[j-add];
            }
            numbers[j] = temp;
        }
    }
    for (int k = 0; k < length; k++)
    {
        cout << numbers[k] << " ";
    }
    cout << endl;
}

main.cpp

int main()
{
    int numbers[] = {49,38,65,97,76,13,27,49};
    int length = sizeof(numbers)/sizeof(numbers[0]);

    ShellSort::Shell(numbers,length);

    for(int i=0;i<length;i++){
        cout<<numbers[i]<<" ";
    }
    cout<<endl;

    return 0;
}

4、lua实现

numbers = {49, 38, 65, 97, 76, 13, 27, 49}

function ShellSort(nums)
	local length = #nums
	if (nums == nil or length < 2) then
		print("参数数组有误")
		return
	end

	local addArray = { 5, 3, 1 }

	for i=1,#addArray,1 do
		ShellInsert(nums, addArray[i])
	end

end

function ShellInsert(nums,add)
	for i=add+1,#nums,1 do

		if (nums[i] < nums[i-add]) then

			local temp = nums[i]
			--这里相当于直接插入排序，每次比较新加入的元素
			--每个组的元素上一个元素index就是 -add
			for j=i,i-add,-add do
				--要保证数组不会越界
				if(j>i-add and nums[j-add]>temp) then
					nums[j] = nums[j-add]
				else
					nums[j] = temp
					break
				end
			end
		end
	end

	for k=1,#nums,1 do
		io.write(nums[k] .. ' ')
	end
	print()
end



ShellSort(numbers)

for i=1,#numbers,1 do
	io.write(numbers[i] .. ' ')
end
print()

--#nums  获取数组长度

排序算法02-希尔排序（用C++、C#、lua实现）

1、希尔排序

2、C#实现

3、C++实现

4、lua实现

5、新知识和疑问