Importance of sorting

#1

If we are checking every possible configuration for boy to get paired then whats significance of sorting here ?

#2

we are actually not checking every permutation! hence sorting is necessary!
try this if n=5 and m=5
1 2 3 4 5
5 4 3 2 1

#3

at every point either we are selecting a girl or not selecting it so how its not checking every configuration?

#4

We don’t take every permutation (as there are N! permutations), instead we take every possible selection!
think this way : let n=2,m=3
then possible inputs are ; 1,2 and 1,2,3
or 1,2 and 2,1,3
or 2,1 and 3,2,1
or …
now when you sort both arrays, all these inputs become equivalent!
Hence sorting is necessary.
If your doubt is cleared mark it as resolved