DSA & beyond - From Arrays to Graphs : What to Learn

From Arrays to Graphs: What to Learn in DSA & Beyond

📘 A Ranked Learning Table for DS, Algorithms, and CS Concepts

# Newly added for completeness and coverage of foundational topics.

Data Structures	Algorithms (Part 1)	Algorithms (Part 2)	Other (Concepts)	Tools/Systems
Array	Sorting	Counting Sort	Math	Shell
String	Counting	Line Sweep	Design	Database
Stack	Two Pointers	Bucket Sort	Brainteaser	Interactive
Queue	Prefix Sum	Shortest Path	Geometry	Concurrency
Linked List	Sliding Window	Combinatorics	Probability and Statistics	Command Line Tools #
Hash Table	Recursion	Rolling Hash	Game Theory	Version Control (Git) #
Set	Binary Search	Reservoir Sampling	Randomized	Operating Systems Basics #
Matrix	Bit Manipulation	Minimum Spanning Tree	Computational Complexity #	Networking Basics (TCP/IP) #
Binary Tree	Greedy	Strongly Connected Component	Memory Models #	HTTP / DNS / Web Basics #
Tree	Simulation	Eulerian Circuit	Distributed Systems #	Security Basics (Hashing, etc) #
Doubly-Linked List	Depth-First Search (DFS)	Radix Sort	Machine Learning Basics #	Compilers and Parsing #
Ordered Set	Breadth-First Search (BFS)	Rejection Sampling	Cryptography #	Software Engineering Principles #
Heap (Priority Queue)	Backtracking	Biconnected Component
Trie	Divide and Conquer	KMP Algorithm #
Union Find	Dynamic Programming	Z-Algorithm #
Binary Search Tree	Memoization	Network Flow (Ford–Fulkerson) #
Hash Function	String Matching	Convex Hull Algorithm #
Segment Tree	Enumeration	Maximum Bipartite Matching #
Binary Indexed Tree	Number Theory	Linear Programming #
Suffix Array	Bitmask	Fast Fourier Transform (FFT) #
Monotonic Stack	Topological Sort
Monotonic Queue	Merge Sort
Data Stream	Quickselect
Iterator
Graph
Skip List #
Deque #
Bloom Filter #

---

Full table

From Arrays to Graphs: What to Learn in DSA & Beyond

📘 A Ranked (Easy on Top to Hard at bottom) Learning Table for Data Structures, Algorithms, CS Concepts, and Tools

# Newly added for completeness and coverage of foundational topics.

Data Structures	Algorithms	Core CS Concepts	Tools/Systems
Array	Linear Search	Primitive Data Types	Shell / Command Line Basics
String	Basic Array Operations	Math (Arithmetic, Basic Algebra)	Programming Language(s) (Pick One)
Stack	String Manipulation Basics	Time/Space Complexity (Big O)	IDE / Text Editor
Queue	Palindrome Checking	Abstract Data Types (ADT)	Debugger / REPLs
Deque	Push, Pop, Peek Operations	Pointers / References	Version Control (Git)
Linked List	Enqueue, Dequeue Operations	OOP Basics (Classes, Objects)	Markdown / Basic Documentation
Doubly-Linked List	Add/Remove Front/Back	Recursion	Testing Basics (Unit Tests)
Hash Table	Parentheses Matching	Hash Function	API Basics (What is an API?)
Set	Traversal, Insertion, Deletion (Linked List)	Algorithm Design Paradigms (Intro) (e.g., Brute Force)	Operating Systems Basics
Matrix	Reversing a Linked List	Discrete Math Basics (Sets, Logic)	Networking Basics (TCP/IP, HTTP, DNS)
Tree (General Concept)	Bidirectional Operations (Doubly LL)	Memory Models (Stack, Heap)	Web Basics (Client-Server)
Binary Tree	Insert, Delete, Search (Hash Table)	Graph Theory Basics	Database (Relational, SQL Intro)
Binary Search Tree (BST)	Two Sum Problem / Anagrams	Greedy Algorithms (Intro)	Security Basics (e.g., Hashing)
Heap (Priority Queue)	Add, Remove, Contains (Set)	Divide and Conquer	Command Line Tools (grep, find, awk, sed etc.)
Graph	Finding Duplicates	Dynamic Programming (Concept of Memoization/Tabulation)	Software Engineering Principles (DRY, KISS, SOLID)
Union Find	Matrix Traversal, Transposition	Pathfinding Concepts	Concurrency (Threads, Mutexes, Processes)
Ordered Set (concept, often via Balanced BST)	Spiral Traversal	Amortized Analysis	REST APIs (Design, Implementation)
Trie	Recursion (for Tree Traversal)	Randomized (Algorithms Concept)	Compilers and Parsing
Monotonic Stack	Tree Traversals (Pre, In, Post)	Bitmask (with DP)	Distributed Systems (Concepts: CAP Theorem, etc.)
Monotonic Queue	Tree Construction from Traversals	Iterator Pattern	Cloud Computing (IaaS, PaaS, SaaS, Basic Services)
AVL Tree	Tree Diameter / Height	String Matching (Concept)	Containerization (e.g., Docker)
Red-Black Tree	Search, Insert, Delete in BST	Combinatorics	CI/CD Tools (e.g., Jenkins, GitHub Actions)
Segment Tree	Validate BST / LCA in BST	Probability and Statistics	System Design (Advanced: Scalability, Microservices, etc.)
Binary Indexed Tree (BIT)	Heapify, Insert, Extract-Min/Max	Number Theory (GCD, Primes, Modulo)	Advanced Security Concepts (Encryption, AuthN/AuthZ deeper dive)
Suffix Array	Graph Representation	Computational Complexity (P vs NP, NP-Completeness)	Web APIs (Advanced: GraphQL, gRPC, WebSockets)
Skip List	Basic Sorting (Bubble, Insertion)	Data Stream (Concept/Problem Type)
Bloom Filter	Binary Search (on sorted array)	Caching Strategies
B-Tree / B+Tree	Two Pointers	Information Theory
LRU Cache (as a structure combining others)	Sliding Window	Data Compression
Suffix Tree (often learned with Suffix Arrays but more complex)	Prefix Sum	Cryptography
	Bit Manipulation	Geometric Algorithms (Line Sweep, Convex Hull Concepts)
	Breadth-First Search (BFS)	Probabilistic Data Structures (Concept)
	Depth-First Search (DFS)	Suffix Tree (DS Concept)
	Merge Sort	Machine Learning Basics
	Quick Sort	AI/ML Algorithms (General concept of their existence/types)
	Heap Sort	Deep Learning (Intro)
	Quickselect	Quantum Computing (Intro)
	Sliding Window Min/Max (Intro)	Sustainability (in Computing)
	Backtracking (e.g., N-Queens)
	Dynamic Programming (Intro, Memoization)
	Path Compression, Union by Rank (Union Find)
	Cycle Detection (Undirected Graph)
	(Balanced BST based operations) (For Ordered Set)
	Range Queries (Basic)
	Insert, Search, Prefix Matching (Trie)
	Word Break Problem (Trie approach)
	Next Greater/Smaller Element (Monotonic Stack)
	Largest Rectangle in Histogram
	Sliding Window Maximum/Minimum (Monotonic Queue)
	Rotations, Balancing (AVL/Red-Black Tree)
	Counting Sort
	Radix Sort
	Bucket Sort
	Range Queries, Updates (Segment Tree)
	Lazy Propagation
	Range Queries, Updates (BIT)
	2D BIT
	Suffix Array Construction (Intro)
	LCP Array
	Search, Insert, Delete (Skip List)
	Add, Check Membership (Bloom Filter)
	(Database Indexing Operations) (B-Tree)
	Get, Put Operations (LRU Cache)
	LRU Cache (Core DS Logic)
	Simulation
	Enumeration
	Topological Sort
	Rolling Hash (Technique)
	Shortest Path (Dijkstra’s)
	Minimum Spanning Tree (Prim’s, Kruskal’s)
	Bellman-Ford Algorithm
	Strongly Connected Components (SCC)
	Biconnected Components
	KMP Algorithm
	Z-Algorithm
	Aho-Corasick Algorithm
	Eulerian Circuit/Path
	Network Flow (Ford–Fulkerson)
	Maximum Bipartite Matching
	Johnson’s Algorithm
	Convex Hull Algorithm
	Fast Fourier Transform (FFT)
	Linear Programming
	Max Flow Min Cut variants

---

# Newly added for completeness and coverage of foundational topics.