Welcome back, aspiring algorithm experts! In our quest to build efficient programs, we've explored linear structures like arrays and linked lists. Now, we're stepping into a new dimension: hierarchical structures. Imagine organizing information like a family tree or a filing cabinet – that's the essence of trees.
A tree, in computer science, is a non-linear data structure that consists of nodes connected by edges. It's defined recursively: a tree is either empty or a node (called the root) with a collection of disjoint subtrees, each of which is also a tree. This recursive definition is key to understanding how trees work.
graph TD;
A[Root] --> B(Child 1);
A --> C(Child 2);
B --> D(Grandchild 1);
B --> E(Grandchild 2);
C --> F(Grandchild 3);
Let's break down the terminology:
- Node: A fundamental unit of a tree, holding data and references (pointers) to other nodes.
- Root: The topmost node in a tree. It has no parent.
- Parent Node: A node that has one or more child nodes.
- Child Node: A node that is directly connected to a parent node.
- Edge: A connection between two nodes.
- Leaf Node: A node with no children. These are the 'endpoints' of the tree.
- Subtree: A tree formed by a node and all of its descendants.
- Height: The length of the longest path from the root to a leaf node.
- Depth: The length of the path from the root to a particular node.
Trees excel at representing hierarchical relationships and are particularly powerful for efficient searching, insertion, and deletion operations, especially when compared to linear structures in certain scenarios. Think about searching for a word in a dictionary – a tree-like structure would allow you to quickly narrow down your search space.
One of the most common and fundamental types of trees is the Binary Tree. In a binary tree, each node can have at most two children, typically referred to as the left child and the right child. This constraint makes binary trees highly predictable and amenable to efficient algorithms.
graph TD;
A[Node] --> B(Left Child);
A --> C(Right Child);