This is regarding 144D - Missile Silos. The problem gives an weighted undirected graph and asks us to calculate all points (not just vertices, they can be points on edges as well ) which have shortest distance equal to some given value.

I realise this is a simple Djikstra, but I am unable to understand the three cases that are given here Editorial .

I am having a real hard time understanding it(I tried reading others code, but still couldn't get it), Could someone please explain it to me. Thanks. Much appreciated.