Question

嘿所以我试图验证一些排序算法。

插入排序
归并
使用“三个中位数”分区和截止值为10的Quicksort（使用小数组部分的插入排序）

分析：
插入排序的最坏情况运行时间被讨论为O（n ²），实际运行时间为O（n），用于排序输入（只要内部循环被正确编码）。对于所有输入，Mergesort被讨论为O（n log n）。对于所有输入，使用“三个中值”分区和合理截止的Quicksort被讨论为O（n Log（n）），但在实践中比Mergesort更快。您的计时是否验证了这些计算？

注意N = Max / 2，2N = MAX

运行程序后，我找到了

The diff for insertion sorted with sorted max/2 is 0.000307083129882812
The diff for insertion sorted with sorted max is 0.000623941421508789
The diff for insertion reverse with sorted max/2 is 0.000306129455566406
The diff for insertion reverse with sorted max is 0.000745058059692383
The diff for insertion random with sorted max/2 is 2.39158606529236
The diff for insertion random with sorted max is 9.72073698043823
The diff for merge sort with sorted max/2 is 0.00736188888549805
The diff for merge sort with sorted max is 0.0154471397399902
The diff for merge reverse with sorted max/2 is 0.00730609893798828
The diff for merge reverse with sorted max is 0.0154309272766113
The diff for merge random with sorted max/2 is 0.0109999179840088
The diff for merge random with sorted max is 0.0232758522033691
The diff for quick sorted with sorted max/2 is 3.10367894172668
The diff for quick sorted with sorted max is 12.5512340068817
The diff for quick reverse with sorted max/2 is 3.09689497947693
The diff for quick reverse with sorted max is 12.5547797679901
The diff for quick random with sorted max/2 is 0.0112619400024414
The diff for quick random with sorted max is 0.0221798419952393

我知道插入排序正常工作，因为对于随机，我做了9.72073698043823 / 2.39158606529236~ = 4 = 2 ² = O（n ²）

但我不知道如何验证其他的是否是O（n Log（n））。请帮忙

Answer 1

让我提醒你，f（n）= O（n）意味着当n增长很大时f（n）/ n =＆gt;恒定

什么没说：

那个常数可能很大
对于小值，它意味着某些东西：例如： 10 ^ 9 / n + n是O（n）但是对于n = 1，它是10 ^ 9 + 1; - ）
O（某事物）不是参数杀手，数据的拓扑结构可能会在某种程度上影响算法（例如：“几乎”排序的数据，冒泡排序表现良好）

如果你想得出结论，使用与你的应用相关的大样本运行测试，不要过早得出结论（注意现代CPU可能会欺骗你使用缓存，流水线和多核如果你使用它（你能做什么）分选）

帮助验证Big O.

1 个答案: