排序算法中平均时间复杂度

作业排序 (Job sequencing)

Job sequencing is the set of jobs, associated with the job i where deadline di >= 0 and profit pi > 0. For any job i the profit is earned if and only if the job is completed by its deadline. To complete a job, one has to process the job on a machine for one unit of time. Only one machine is available for processing the jobs.

作业排序是与作业i相关联的一组作业，其中期限di> = 0且利润pi> 0 。 对于任何工作， 我当且仅当作业被其限期完成利润赚。 为了完成一项工作，必须在一台机器上在一个单位时间内处理该工作。 仅一台机器可用于处理作业。

Steps for performing job sequencing with deadline using greedy approach is as follows:

使用贪婪方法在截止日期之前执行作业排序的步骤如下：

1. Sort all the jobs based on the profit in an increasing order.

   根据利润按升序对所有作业进行排序。

2. Let α be the maximum deadline that will define the size of array.

   令α为将定义数组大小的最大截止日期。

3. Create a solution array S with d slots.

   创建具有d个插槽的解决方案数组S。

4. Initialize the content of array S with zero.

   用零初始化数组S的内容。

5. Check for all jobs.

   检查所有作业。

   1. If scheduling is possible a lot i^th slot of array s to job i.
   2. 如果调度是可能很多我阵列的^个时隙s到工作我 。
   3. Otherwise look for location (i-1), (i-2)...1.
   4. 否则寻找位置(i-1)，(i-2)... 1 。
   5. Schedule the job if possible else reject.

6. Return array S as the answer.

   返回数组S作为答案。

7. End.

   结束。

作业排序算法 (Algorithm for job sequencing)

Input: A is the array of jobs with deadline and profit S array will be the output.

输入： A是具有截止日期的职位数组，而利润S数组将是输出。

    1. Begin
2. Sort all the jobs based on profit Pi so
3. P1 > P2 > P3 …………………………….>=Pn
4. d = maximum deadline of job in A
5. Create array S[1,…………………,d]
6. For i=1 to n do
7. Find the largest job x
8. For j=i to 1
9. If ((S[j] = 0) and (x deadline<= d))
10. Then 
11. S[x] = i;
12. Break;
13. End if
14. End for
15. End for
16. End

时间复杂度 (Time complexity)

Job sequencing problems has the time complexity of O(n2).

作业排序问题的时间复杂度为O(n2)。

Example:

例：

Given a set of 9 jobs where each job has a deadline and profit associated to it .Each job takes 1 unit of time to complete and only one job can be scheduled at a time. We earn the profit if and only if the job is completed by its deadline. The task is to find the maximum profit and the number of jobs done.

给定一组9个工作，每个工作都有一个截止日期和与之相关的利润。每个工作需要1个时间单位才能完成，并且一次只能安排一个工作。 当且仅当工作在截止日期之前完成时，我们才能赚取利润。 任务是找到最大的利润和完成的工作数量。

    Jobs	 Profit	  Deadline
J1	        85	        5
J2	        25	        4
J3	        16	        3
J4	        40	        3
J5	        55	        4
J6	        19	        5
J7	        92	        2
J8	        80	        3
J9	        15	        7

Step 1:

第1步：

Step 2:

第2步：

Step 3:

第三步：

Step 4:

第4步：

Step 5:

步骤5：

Step 6:

步骤6：

So, the maximum profit = 40 + 92 + 80 + 55 + 85 + 15 = 367

因此，最大利润= 40 + 92 + 80 + 55 + 85 + 15 = 367

翻译自: https://www.includehelp.com/operating-systems/job-sequencing.aspx

排序算法中平均时间复杂度