C++ functors behavior - c++

Question

#include <iostream>
#include <vector>
#include <set>
#include <algorithm>
using namespace std;
struct cmp {
bool operator()(const int& i, const int& j) const{
return false;
}
} ;
struct cmp2 {
bool operator()(const int& i, const int& j) const{
return false;
}
} cmp2_item;
class Solution {
public:
vector<int> smth(vector<int> arr, int k) {
// nth_element(arr.begin(), arr.begin()+k, arr.end(), cmp); #ERROR
// nth_element(arr.begin(), arr.begin()+k, arr.end(), cmp()); #WORKS
// nth_element(arr.begin(), arr.begin()+k, arr.end(), cmp2_item); # WORKS
// sort(arr.begin(), arr.end(), cmp); #ERROR
// sort(arr.begin(), arr.end(), cmp()); #WORKS
// set<int, cmp> s; # WORKS
// set<int, cmp2_item> s; # ERROR
return {};
}
};
int main() {
// your code goes here
Solution s;
s.smth({}, 1);
return 0;
}
I want to understand why this code behaves in this way.
for nth_element we expect a functor so it makes sense to include like cmp(), but why does it start working without the (), when i instantiate the struct and use that?
Similar in sort
while when using it for a comparator for a set, it only works if the struct is not instantiated and without the ()
Can someone please clarify using the signatures why this is so?
nth_element: template< class RandomIt, class Compare > void nth_element ( RandomIt first, RandomIt nth, RandomIt last, Compare comp );
sort
void sort (RandomAccessIterator first, RandomAccessIterator last, Compare comp);
set:
class Compare = less<T>, // set::key_compare/value_compare
class Alloc = allocator<T> // set::allocator_type
> class set;

Answer 1

One part of this is that cmp2_item is not a type, its an instance of the type cmp2. So you can't pass that as a class type. You might be able to do:
set<int, cmp> s; //# WORKS
set<int, decltype(cmp2_item)> s2; //# NOW WORKS
For these:
// Not ok because cmp is not a function comparison object, its a type
nth_element(arr.begin(), arr.begin()+k, arr.end(), cmp); #ERROR
// Ok because this is effectively passing a functor (and not just a type)
// I believe this takes a copy of the functor type (by construction), I
// am not quite so clear on the inner workings of the compiler in this
// case. I guess its by type comparison, but possible compiler
// implementation specific?
nth_element(arr.begin(), arr.begin()+k, arr.end(), cmp()); #WORKS
// This is ok because it passes an actual comparison object (that has
// operator () defined).
nth_element(arr.begin(), arr.begin()+k, arr.end(), cmp2_item); # WORKS
Basically you have to look more closely at what you are passing: a type, an object or a function - and what the specific STL accepts as a parameter.
Note:
comparison function object (i.e. an object that satisfies the requirements of Compare) which returns ​true if the first argument is less than (i.e. is ordered before) the second.
See here: enter link description here