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Conversion Error when passing arguments to lambda comparator

I have a sorted vector of structures and I am trying to find the index of element that has the queried value in its member attribute. For this I am trying to use lower_bound, but I am having problems with the comparator lambda function. Here is a simplified version of my code:

#include <iostream>
#include <vector>
#include <algorithm>

struct Student
{
    int id;
};

std::vector<Student> Students;

int main()
{
    Student Ann = {1};
    Student Bob = {3};
    Student Alice = {4};
    Students = {Ann, Bob, Alice};
    int id_query = 3;
    auto index_ptr = std::lower_bound(Students.begin(), Students.end(), id_query, [](const int a, const Student s) -> bool {return a < s.id;});
}

g++ with std=17 gives me the following

Starting build...
/bin/g++ -g /home/aram/dev/cpp/coverages/stack_overflow.cpp -std=c++17 -o /home/aram/dev/cpp/coverages/stack_overflow
In file included from /usr/include/c++/9/bits/stl_algobase.h:71,
                 from /usr/include/c++/9/bits/char_traits.h:39,
                 from /usr/include/c++/9/ios:40,
                 from /usr/include/c++/9/ostream:38,
                 from /usr/include/c++/9/iostream:39,
                 from /home/aram/dev/cpp/coverages/stack_overflow.cpp:1:
/usr/include/c++/9/bits/predefined_ops.h: In instantiation of ‘bool __gnu_cxx::__ops::_Iter_comp_val<_Compare>::operator()(_Iterator, _Value&) [with _Iterator = __gnu_cxx::__normal_iterator<Student*, std::vector<Student> >; _Value = const int; _Compare = main()::<lambda(int, Student)>]’:
/usr/include/c++/9/bits/stl_algobase.h:979:14:   required from ‘_ForwardIterator std::__lower_bound(_ForwardIterator, _ForwardIterator, const _Tp&, _Compare) [with _ForwardIterator = __gnu_cxx::__normal_iterator<Student*, std::vector<Student> >; _Tp = int; _Compare = __gnu_cxx::__ops::_Iter_comp_val<main()::<lambda(int, Student)> >]’
/usr/include/c++/9/bits/stl_algo.h:2032:32:   required from ‘_FIter std::lower_bound(_FIter, _FIter, const _Tp&, _Compare) [with _FIter = __gnu_cxx::__normal_iterator<Student*, std::vector<Student> >; _Tp = int; _Compare = main()::<lambda(int, Student)>]’
/home/aram/dev/cpp/coverages/stack_overflow.cpp:21:142:   required from here
/usr/include/c++/9/bits/predefined_ops.h:177:11: error: no match for call to ‘(main()::<lambda(int, Student)>) (Student&, const int&)’
  177 |  { return bool(_M_comp(*__it, __val)); }
      |           ^~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/9/bits/predefined_ops.h:177:11: note: candidate: ‘bool (*)(int, Student)’ <conversion>
/usr/include/c++/9/bits/predefined_ops.h:177:11: note:   candidate expects 3 arguments, 3 provided
/home/aram/dev/cpp/coverages/stack_overflow.cpp:21:83: note: candidate: ‘main()::<lambda(int, Student)>’
   21 |     auto index_ptr = std::lower_bound(Students.begin(), Students.end(), id_query, [](const int a, const Student s) -> bool {return a < s.id;});
      |                                                                                   ^
/home/aram/dev/cpp/coverages/stack_overflow.cpp:21:83: note:   no known conversion for argument 1 from ‘Student’ to ‘int’

Build finished with error(s).
The terminal process failed to launch (exit code: -1).

The comparator of std::lower_bound is supposed to take the object dereferenced from the iterator, ie the element as the 1st parameter, the value to be compared as the 2nd parameter.

The type Type1 must be such that an object of type ForwardIt can be dereferenced and then implicitly converted to Type1 . The type Type2 must be such that an object of type T can be implicitly converted to Type2 .

You need to change the order of the parameters, eg

auto index_ptr = std::lower_bound(Students.begin(), Students.end(), id_query, [](const Student s, const int a) -> bool {return s.id < a;});

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