Binary trees in one shot complete dsa in java dsa in java

okay, let's dive into binary trees in java, covering the core concepts, implementation, common algorithms, and how they fit into the broader landscape of data structures and algorithms. this will be a comprehensive guide with code examples.

**i. introduction to binary trees**

a **binary tree** is a hierarchical data structure where each node has at most two children, referred to as the *left child* and the *right child*. the topmost node in a tree is called the *root*. a node with no children is a *leaf* node.

**key concepts:**

* **node:** the fundamental building block of a tree. contains data and references (pointers) to its left and right children.
* **root:** the top-most node in the tree. has no parent.
* **left child:** the node directly below and to the left of a parent node.
* **right child:** the node directly below and to the right of a parent node.
* **parent:** the node directly above another node.
* **sibling:** nodes that share the same parent.
* **leaf:** a node with no children (both left and right children are null).
* **edge:** the connection between a parent node and its child node.
* **path:** a sequence of nodes and edges connecting a node to a descendant.
* **level:** the distance of a node from the root (root is at level 0).
* **height:** the length of the longest path from the root to a leaf. the height of an empty tree is typically defined as -1. the height of a tree with just one node is 0.
* **depth:** the distance from the root to a specific node.

**types of binary trees:**

* **full binary tree:** every node has either 0 or 2 children.
* **complete binary tree:** all levels are completely filled except possibly the last level, which is filled from left to right.
* **perfect binary tree:** all internal nodes have two children, and all leaves are at the same level. a perfect binary tree of height `h` has `2^(h+1) - 1` nodes.
* **balanced binary tree:** the height difference between the left and ...

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Binary Trees
DSA in Java
Java Data Structures
Tree Traversal
Binary Search Tree
Depth First Search
Breadth First Search
Tree Algorithms
Node Insertion
Node Deletion
Balanced Trees
AVL Trees
Red-Black Trees
Tree Height
Leaf Nodes