# A fast algorithm for constructing balanced binary search trees

## TL;DR

This paper introduces a non-recursive, efficient algorithm for constructing minimal-height binary search trees from sorted arrays, with potential for parallelization and minimal memory use.

## Contribution

The paper presents a novel non-recursive algorithm for building minimal-height binary search trees with linear time complexity and constant memory, enabling efficient parallelization.

## Key findings

- Algorithm operates in O(N) time for sorted arrays
- Constructed trees have minimal height
- Algorithm can be transformed into a complete binary search tree in O(log N) time

## Abstract

We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of minimal height and can be transformed to a complete binary search tree (retaining minimal height) with $O(\log N)$ time and $O(1)$ memory. The algorithm allows simple and effective parallelization.