Consider this test

5
00101
00101
11001
00001
11110

your comparator:

comp = [&bs,&n](int u, int v)  {
    if(v==u) return false;
    return bs[(u-1)*n+v-1]==0;
}

comp(2, 1) = true

comp(1, 2) = true

Which order is correct — 1<2 or 2<1? std::stable_sort will leave 2<1 (i think stable_sort would change the order of two elements if both comp(x, y) and comp(y, x) are true)

shuffling before sorting would ruin your solution

both comp(x, y) and comp(y, x) being true is UB. https://codeforces.me/blog/entry/72525