Data Structures and Algorithm Design Expert

I need an expert in data structures and algorithm design to help me with a two-part project involving performance comparisons and AVL tree implementations. 1. Performance Comparison You will need to: - Understand and analyze Abstract Data Types (ADTs) and investigate the time complexities and performances for specific data structures. - Explain the searching time complexities of a List, Binary Search Tree (BST), and AVL Tree, detailing how each structure achieves its specific performance level. - Explain the sorting time complexities for List-based Sorting, Priority Queue (PQ)-Sorting, and Heap Sorting, with an emphasis on how each achieves its performance. - Create two distinct algorithms for AVL tree-based sorting (using PQ-sorting and AVL tree traversal), write their pseudocode, and explain their time complexities. 2. AVL Tree Implementation You will modify the AVL class to store balance factors instead of subtree heights. - Implement specific methods in AVL.py including left_height, right_height, recompute_balanceFactor, _recompute_balanceFactor_singleNode, and _isbalanced. - Ensure to only modify and submit the AVL.py file with necessary comments. Ideal Skills and Experience: - Deep understanding of data structures, especially AVL trees, Binary Search Trees, and lists. - Proficient in algorithm design and writing pseudocode. - Python programming skills, particularly with AVL tree implementations. - Ability to clearly explain complex concepts in a succinct manner.