For traversing binary trees there are standard ways like,
 - In order
 - Pre Order
 - Post Order

Questions Are:
The construction of the data as a binary tree is upto us. Am I right?
(I read somewhere 2n-n combinations are possible)

Is there any thing like it should be always ordered or sorted?

Just to validate my understanding, making data into binary tree format
helps us in traversing, sometimes treating data in binary tree format
is natural. Am I right?

Why In Donald Knuth's TAOCP Vol1 he says the binary trees dealt there
are ordered tress? Is there any significance for ordered trees?
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