Trees

Expression Trees Explained

Learn what expression trees are, how the compiler builds them from lambdas, and how providers like EF Core walk them to generate SQL.

Domains, Trees, and Forests

How Active Directory organizes multiple domains into trees and forests to model organizational and trust boundaries.

AVL Trees

A self-balancing binary search tree that maintains O(log n) height via rotations after every insertion and deletion.

Binary Search Trees

A binary tree variant that maintains an ordering invariant, enabling fast search, insert, and delete operations.

Binary Trees

A hierarchical data structure where each node has at most two children, forming the foundation for many advanced tree structures.

Fenwick Trees (Binary Indexed Trees)

A compact array-based structure using the lowbit trick to compute prefix sums and point updates in O(log n).

Segment Trees

A binary tree over an array that answers range queries (sum, min, max) and supports point/range updates in O(log n).

Recursion Trees and Recurrence Relations

Model the runtime of recursive algorithms as recurrence relations and solve them by drawing recursion trees.

Decision Trees

Covers how decision trees split data recursively using impurity measures like Gini and entropy to produce interpretable, rule-based predictions.

What is a Binary Search Tree (BST)?

A binary search tree is a binary tree where every node’s left subtree holds smaller keys and its right subtree holds larger keys, enabling search, insertion, a…

What is a Red-Black Tree?

A red-black tree is a self-balancing binary search tree that colors each node red or black and enforces balancing rules so the longest root-to-leaf path is nev…