Doubt in video lecture segment tree 02-query

#1

In case of complete overlap
qs-----------qe
ss-----se
how it is possible because if i want to know about min element of range (1,4) qs=1 and qe=4
and my node range is (2,3) then how it gives correct answer .please help.

#2

you have the min value fro (2,3) in node of range (2,3). since you have queried for (1,4) its answer is the min of range in (1) ,(2,3) ,(4) so when the complete overlap occur in these three cases we just return the ans of this range.