we have a permutation p of size `N`.<br>↵
<br>↵
we iterate on this permutation and insert elements into a Binary Search Tree.<br>↵
<br>↵
Prove that each sub-tree will consists of all elements from some `l` to `r`.<br>↵
<br>↵
In other words, prove that elements of each sub-tree form continuous subarray of identity permutation (if written is sorted order).<br>↵
<br>↵
`identity permutation` -> `1, 2, 3, 4 ... N`.
<br>↵
we iterate on this permutation and insert elements into a Binary Search Tree.<br>↵
<br>↵
Prove that each sub-tree will consists of all elements from some `l` to `r`.<br>↵
<br>↵
In other words, prove that elements of each sub-tree form continuous subarray of identity permutation (if written is sorted order).<br>↵
<br>↵
`identity permutation` -> `1, 2, 3, 4 ... N`.
