"deterministic linear solution is implemented in C++ standard library as std::nth_elemen"

https://cp-algorithms.com/sequences/k-th.html

but I think the STL implements the nondeterministic one/deterministic nlogn one

https://github.com/gcc-mirror/gcc/blob/9693459e030977d6e906ea7eb587ed09ee4fddbd/libstdc%2B%2B-v3/include/bits/stl_algo.h#L1913,L1933

• looks like kth order on random pivots, then if depth is too large, switch to make heap; pop min element k times