For 2 million characters, the difference will be as follows

Time taken by regex function: 12066 ms
Time taken by set function: 2837 ms
Time taken by erase function: 123 ms

Argh ! I thought i can't add a include file...

I didn't remove it, it wasn't part of the template when I did this kata.

You deleted "const" from function - this is bad.

programming is cheating! Pen&paper for life!!

I don't recall anything having a reference to &str in the details of this, but if we want to discuss the details of the task:

Your task is to write a function that takes a string and return a new string with all vowels removed.

It states that you are taking a string, and returning a new string. So modifying the existing string and returning it is not the same as returning a new string, as described in the assignment. If there is a by reference involved in the solution's template, that may be an update to the kata from the time this, and many other solutions were written. But in any event, the details of the task tell you to return a new string, not the one that was sent to the function.

/shrug

If the take in parameter is marked '&str' (as it is in the assignment. '&' is removed in this solution) you are supposed to use the original string directly through reference. This reduces memory usage and increases speed =)
Anyway this is how i see it. Correct if am wrong.

for loop is cheating.

I don't see how the string is being passed by reference, as you need to specify by reference in the function parameters, and would change how we access the data within the string. But regex_replace creates an empty result string, and then populates and returns it based on the regex rules against the original string. It is not modifying the original string.

removing stuff from the assignment is bad practice imo
the str is passed as reference
otherwise well done and thank you for showing this

how so?

regex is cheating Bozo

See https://stackoverflow.com/questions/1452721/why-is-using-namespace-std-considered-bad-practice

I know python but I am new to c++, just a simple question why most people don't use using namespace std ! ?
Can some plesae explain !