algorithm - Calculating height of tree provided condition on height of left tree and height of right tree -


suppose denote leftheight(u) , rightheight(u) heights of left , right subtrees of node u.

now if have constant c > 0 such nodes u in tree t, have 

leftheight(u) ≤ rightheight(u) + c

what can said height of such tree ? o(log n) or ?

also, if condition had been changed :

leftheight(u)−c ≤ rightheight(u) ≤ leftheight(u) + c

how affect height of tree ?

to answer first pat of question, height not o(log n). consider tree n nodes degenerated a list by; every node u, left subtree empty , each node (except single leaf) has nonempty right subtree, in following sketch.

   \    b     \      c

the inequality

leftheight(u) ≤ rightheight(u) + c

holds every constant c, yet height of tree n.


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