Proof of O(1) solution to I would walk 500 miles

Does anyone know how to prove the math solution for I would walk 500 miles?
solution link:

The two lowest-weight edges of the MST are (N-1,N) and (N-2,N). Can you figure it out from there?


Hi, would you mind explaining a bit further? Can’t quite wrap my mind around it.

What other edges are part of the MST? (If you don’t know, perhaps write a program to print them out.)

Hi, I have since written up a full editorial for the \mathcal{O}(1) solution:
Hope it can be of some use!