Hello ,
i was reading the editorial for Exptree i was not able to understand the proof mentioned by @gil_vegliach in the commments, as he mentioned that for any two vertices v1 and v2 in [1…n] in tree T1 , T2 resp., if we remove (parent[v1],v1) and (parent[v2],v2) will lead to same tree only if T1 = T2 initially but i came up with a counter example of 7 nodes
(T1) (T2)
0 and 0
/ \ / \
0 0 0 0
/ \ \
( 0 ) 0 0
/ \ / \
0 0 0 0
\
( 0 )
v1 is the vertex marked with () in T1 and v2 is the vertex marked with () in T2 , now if i remove the edge between v1 and it’s parent , and remove the edge between v2 and it’s parent then i get the same tree but T1 != T2. Now i am not able to understand wheather the proof is wrong or i have understood it incorrectly