Why doesn't std::sort use my operator< implementation

Question

Why doesn't std::sort use my operator< implementation in this code

#include <iostream>
#include <vector>
#include <tuple>
#include <algorithm>
using namespace std;

bool operator<(
    const tuple<int, int>& t1,
    const tuple<int, int>& t2
) {
    return get<1>(t1) > get<1>(t2);// `>` so that it gets sorted in reverse
}

int main() {
    vector<tuple<int, int>> v;
    for (int i = 0; i < 10; ++i) {
        v.push_back(make_tuple(0, i));
    }
    cout << "before sort: ";
    for (auto& x : v) { cout << get<1>(x) << ", "; }
    cout << endl;

    auto v2 = v;
    sort(v2.begin(), v2.end());
    cout << "after sort(begin, end): ";
    for (auto& x : v2) { cout << get<1>(x) << ", "; }
    cout << endl;

    sort(v.begin(), v.end(), [](auto& t1, auto& t2) {
        return get<1>(t1) > get<1>(t2);// `>` so that it gets sorted in reverse
    });
    cout << "after sort(begin, end, comparator): ";
    for (auto& x : v) { cout << get<1>(x) << ", "; }
    cout << endl;

    return 0;
}

The output is:

before sort: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 
after sort(begin, end): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 
after sort(begin, end, comparator): 9, 8, 7, 6, 5, 4, 3, 2, 1, 0,

The output I expected is:

before sort: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 
after sort(begin, end): 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 
after sort(begin, end, comparator): 9, 8, 7, 6, 5, 4, 3, 2, 1, 0,

Answer 1

This has to do with how name lookup works in function templates (commonly referred to as two-phase lookup). std::sort is defined in <algorithm>, and the lookup for < will find those names in scope at the point of the template definition (which yours is not) and those names in the associated namespaces of the dependent function arguments (which for std::tuple would be namespace std, which also does not include yours).

Since the arguments in question are in namespace std, it's actually undefined behavior to add your overload into that namespace. So your options are to either stick with the default behavior (which would be lexicographical <) or to provide your own custom comparator (as you do in your question).