How to insert integers of an array of 0 to n^5-1 into an AVL tree?

Question

Given n distinct integers in the range 0, 1, ··· , n^5 − 1, design a worst-case linear-time algorithm to construct an AVL tree on these integers.

I think the idea is to shrink the problem basically meaning change the base from n^5 -1 to N and then inserting it into an AVL tree. But dont know how to do it though!

An AVL tree is just a self-balancing binary search tree. But, because you know all of the numbers ahead of time, you can add the numbers to the tree in [level order](https://en.wikipedia.org/wiki/Tree_traversal#Breadth-first_search), which avoids the need for searching and re-balancing. You *do* have to compute the balance factors correctly. — user3386109, Aug 28 '19 at 16:28
Possible duplicate of [Balanced Binary Search Tree for numbers](https://stackoverflow.com/questions/16766159/balanced-binary-search-tree-for-numbers) — user3386109, Aug 28 '19 at 16:36

score 2 · Answer 1 · answered Aug 28 '19 at 16:36

The "n^5" gives it away: Sort the integers with radix sort, using n as the radix. This will take O(n) time (5 passes) and O(n) space. Then build a balanced binary tree.

See https://en.wikipedia.org/wiki/Radix_sort, and Building Red-Black Tree from sorted array in linear time

How to insert integers of an array of 0 to n^5-1 into an AVL tree?

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