Topological sorting using std::sort

Question

Note: While writing this question, I think I already found the answer. Feel free to ammend or append it with a better version. I thought it might be nice to

Answer 1

Consider the values

pair
    x{0, 1},
    y{2, 0},
    z{1, 2};

Here,

!tpc(x, y) && !tpc(y, x);
!tpc(y, z) && !tpc(z, y);

However,

tpc(x, z);

Thus your comparator does not impose a strict weak ordering, and behavior is undefined if you use it with std::sort or in any other role where a strict weak ordering is required.

A comparator that is strict weak and is a refinement of your comparator would be:

struct refined_comparator {
    bool operator()(const pair &p, const pair &q) const { return p.a + p.b < q.a + q.b; }
} rc;