Non-Linear Data Structures

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Non-linear data structures are characterized by their hierarchical or networked organization, where elements are not arranged sequentially. Unlike linear structures, traversal can follow multiple paths, making them ideal for representing complex relationships and hierarchies. Each page includes implementation code in C, C++, Java, and Python to help you understand and apply these concepts.

Hierarchical Structure

Elements are organized in parent-child or node-edge relationships forming hierarchies or networks.

Multiple Paths

Can be traversed through multiple paths, with various traversal algorithms like DFS and BFS.

Complex Relationships

Ideal for representing real-world hierarchies, networks, and complex data relationships.

Explore Non-Linear Data Structures

Tree

A hierarchical data structure with a root node and child nodes forming parent-child relationships.

HierarchicalRoot nodeParent-childRecursive

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Binary Tree

A tree structure where each node has at most two children, referred to as left and right child.

Two children maxLeft-rightLevel orderTraversals

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Binary Search Tree

A binary tree where left child values are less than parent, and right child values are greater.

OrderedFast searchO(log n)Self-balancing variants

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AVL Tree

A self-balancing binary search tree where heights of left and right subtrees differ by at most one.

BalancedRotationO(log n) guaranteedHeight tracking

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Heap

A complete binary tree where parent nodes are either greater (max heap) or smaller (min heap) than children.

Priority queueO(1) peekHeapifyComplete tree

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Directed Graph

A graph where edges have direction (arrows), representing one-way relationships like dependencies or web links.

One-way edgesIn/Out degreeDAGTopological sort

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Undirected Graph

A graph where edges are bidirectional, representing symmetric relationships like friendships or roads.

BidirectionalDegreeConnectivityShortest path

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Trie

A tree-like structure for storing strings where each node represents a character, enabling fast prefix searches.

Prefix searchString storageAutocompleteDictionary

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Set

A collection of unique elements with no duplicates, supporting efficient membership testing and set operations.

Unique elementsFast lookup O(1)Union/IntersectionHash-based

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Dictionary / Map

A collection of key-value pairs where each key is unique, enabling fast data retrieval and association.

Key-value pairsO(1) accessDynamic keysHash table

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Common Operations

Tree Operations

Insertion: Add nodes while maintaining structure properties
Deletion: Remove nodes and restructure as needed
Traversal: Visit nodes in specific order (in-order, pre-order, post-order)
Search: Find specific values or nodes

Graph Operations

Add Vertex/Edge: Expand the graph structure
Remove Vertex/Edge: Modify connections
BFS/DFS: Breadth-first and depth-first traversal
Shortest Path: Find optimal routes (Dijkstra, A*)

Advanced Operations

Balancing: Maintain tree height for optimal performance
Heapify: Convert array to heap structure
Prefix Search: Find words by prefix in tries
Cycle Detection: Identify circular paths in graphs

Real-World Applications

File Systems:Directory hierarchies use tree structures

Social Networks:Graphs represent user connections

Autocomplete:Tries enable fast prefix-based search

Priority Queues:Heaps manage task scheduling efficiently

Route Planning:Graphs find shortest paths in maps

Databases:B-trees and BSTs for indexing