transform_reduce to fix count implementation

[vug]

Hi! while watching your talk on YouTube ran this logic on a small example and it didn't give me the correct result.

https://en.cppreference.com/w/cpp/algorithm/reduce says the binary operation has to be associative and commutative. I think a + (b == val) is not. Because the way reduce goes over a vector {a, b, c, d} with init is: R(R(R(a, b), R(c, d)), init), NOT R(R(R(R(init, a), b), c), d). :-O I realized this when I saw the diagram for reduce in https://blog.tartanllama.xyz/accumulate-vs-reduce/.

I watched further into your talk and learned about transform_reduce. ^_^ Using that we can make the binary op of reduce part of transform_reduce commutative and associative.

Also I'm not an export. The way reduce goes over a vector could be compiler, platform dependent. Here is a Compiler Explorer comparison of reduce and transform_reduce versions: https://godbolt.org/z/r66M4cYsb

Have a nice day!

[vug]

This might break the flow of your presentation though. :-( Your favorite algorithm transform_reduce should come later in the presentation. :-)
Also, I created this pull request using the editor in GitHub's web interface. Might have written something wrong. Please check twice. ^_^

[vug]

By the way, one other thing I've tried before switching to transform_reduce was to force reduce to operate like R(R(R(R(init, a), b), c), d), and used std::reduce(std::execution::seq, ... explicitly, but that didn't help either. (You can see that in the compiler explorer link above).