I tried to teach GPT about an algorithm I come up with to run a sequence of min-heap operations in O(n) (instead of O(n log n)). But I could not make it understand. But that was also a brand new concept built on top of some pretty niche literature (Chazelle's Soft Heap); so GPT would have to actually 'think', instead of just regurgitate papers.

My prompt was: (and it gave me the right answer)

"I have to formulate an MIP. I have a list of items i \in I each belong to groups g \in G. They are related by a static parameter G_{ig} which says if i in g, then 1 else 0. I want each item i to be freely and independently assigned to slots c \in C. However I want to keep items i together with other items in the same group if possible -- it's a soft preference.

How do i write the mathematical MIP formulation?"