Data Structures Algorithms
The course teaches core data structures—arrays, linked lists, stacks, queues, hash tables, trees, and graphs—and algorithmic techniques such as complexity analysis, dynamic programming, and graph traversal, preparing learners for technical interviews.
Who Should Take This
Computer science undergraduates, recent graduates, and early‑career software engineers who have basic programming knowledge benefit from this curriculum. They aim to solidify fundamentals, master interview‑style problem solving, and build confidence in designing efficient solutions for real‑world coding challenges. The course’s focus on practical implementation and analytical reasoning equips them to excel in technical assessments and contribute effectively to engineering teams.
What's Included in AccelaStudy® AI
Adaptive Knowledge Graph
Practice Questions
Lesson Modules
Console Simulator Labs
Exam Tips & Strategy
20 Activity Formats
Course Outline
60 learning goals
1
Complexity Analysis
2 topics
Big-O Notation
- Describe Big-O notation including O(1), O(log n), O(n), O(n log n), O(n^2), and O(2^n) growth rates and explain how Big-O characterizes worst-case algorithmic performance
- Implement Big-O analysis for code snippets by identifying loop nesting, recursive call trees, and dominant terms to determine time and space complexity classifications
- Analyze the difference between best-case, average-case, and worst-case complexity and evaluate how amortized analysis applies to operations like dynamic array resizing
Space Complexity
- Describe space complexity including auxiliary space, input space, and call stack space for recursive algorithms and explain how to measure total memory consumption
- Analyze time-space trade-offs in algorithm design and evaluate when additional memory usage (memoization, hash tables) is justified by proportional time complexity improvements
2
Linear Data Structures
3 topics
Arrays and Dynamic Arrays
- Describe array memory layout including contiguous allocation, index-based O(1) access, and the time complexity of insertion, deletion, and search operations
- Implement two-pointer and sliding window techniques on arrays for problems including pair sum, removing duplicates, and maximum subarray sum
- Analyze dynamic array resizing strategies including doubling and geometric growth and evaluate how amortized O(1) append is achieved despite periodic O(n) copy operations
Linked Lists
- Describe singly and doubly linked list node structure including data fields, next/prev pointers, and the time complexity differences from arrays for insertion, deletion, and access
- Implement linked list operations including insertion at head/tail/position, deletion by value/position, reversal, and cycle detection using Floyd's tortoise and hare algorithm
- Analyze when to use linked lists versus arrays based on access patterns, insertion frequency, memory overhead, and cache locality considerations
Stacks and Queues
- Describe stack LIFO and queue FIFO semantics including push, pop, peek, enqueue, and dequeue operations and their O(1) time complexity guarantees
- Implement stack-based algorithms for balanced parentheses checking, expression evaluation (postfix notation), and monotonic stack for next greater element problems
- Implement queue-based algorithms including BFS traversal, task scheduling, and circular buffer patterns using array-backed and linked-list-backed queue implementations
3
Hash-Based Data Structures
2 topics
Hash Maps and Hash Sets
- Describe hash function properties including determinism, uniform distribution, and the relationship between hash table size, load factor, and collision probability
- Describe collision resolution strategies including separate chaining with linked lists and open addressing with linear probing, quadratic probing, and double hashing
- Implement hash map solutions for frequency counting, two-sum problems, anagram grouping, and substring search to achieve O(1) average-case lookup performance
- Analyze hash map performance degradation under high collision rates and evaluate how load factor thresholds trigger rehashing to maintain amortized O(1) operations
Advanced Hash Applications
- Implement hash set-based algorithms for duplicate detection, intersection and union of collections, and sliding window distinct element counting
- Implement LRU cache using a hash map combined with a doubly linked list to achieve O(1) get and put operations with least-recently-used eviction policy
4
Trees
4 topics
Binary Trees and BSTs
- Describe binary tree terminology including root, leaf, height, depth, parent, child, subtree, complete tree, and full tree and explain the relationship between height and node count
- Implement binary tree traversals including in-order, pre-order, post-order (recursive and iterative), and level-order (BFS) and explain the output ordering of each traversal type
- Describe the binary search tree property and explain how it enables O(log n) search, insertion, and deletion in balanced trees versus O(n) worst case in degenerate trees
- Implement BST operations including search, insertion, deletion (handling three cases), finding min/max, and in-order successor for ordered data retrieval
Balanced Trees
- Describe AVL tree self-balancing properties including balance factor, left rotation, right rotation, and left-right/right-left double rotations for maintaining O(log n) height
- Analyze how unbalanced BSTs degenerate to linked lists and evaluate how self-balancing trees guarantee O(log n) operations regardless of insertion order
Heaps and Priority Queues
- Describe heap properties including the complete binary tree structure, min-heap and max-heap ordering invariants, and array-based storage with parent-child index relationships
- Implement heap operations including insert (sift-up), extract-min/max (sift-down), heapify for array-to-heap conversion, and priority queue operations using a heap
- Implement heap-based solutions for top-K elements, median finding with two heaps, and merge K sorted lists using priority queue selection
Trie Data Structure
- Describe the trie (prefix tree) data structure including node structure, character-based edges, and how tries enable O(m) prefix lookup where m is the word length
- Implement trie operations including insert, search, and startsWith prefix matching for autocomplete and dictionary word validation applications
- Analyze trie space complexity and compare tries versus hash sets for string prefix search operations and evaluate memory optimization using compressed tries
5
Graphs
4 topics
Graph Representation and Traversal
- Describe graph terminology including vertices, edges, directed/undirected, weighted/unweighted, cyclic/acyclic, connected components, and degree and explain adjacency list versus adjacency matrix trade-offs
- Implement breadth-first search using a queue for shortest path in unweighted graphs, level-order traversal, and connected component discovery
- Implement depth-first search using recursion and explicit stack for cycle detection, topological sorting, and path finding in directed and undirected graphs
- Analyze BFS versus DFS trade-offs including memory usage, optimality for shortest path, and suitability for different graph structures and problem types
Shortest Path Algorithms
- Implement Dijkstra's algorithm using a priority queue for single-source shortest path in weighted graphs with non-negative edges and explain its greedy approach
- Describe the Bellman-Ford algorithm for shortest paths with negative edge weights and explain how it detects negative cycles through V-1 relaxation iterations
- Analyze the time complexity differences between Dijkstra O((V+E) log V) and Bellman-Ford O(VE) and evaluate algorithm selection based on graph properties and edge weight constraints
Topological Sort and MST
- Implement topological sorting using DFS and Kahn's algorithm (BFS with in-degree) for DAG ordering and explain applications in build systems and task scheduling
- Describe minimum spanning tree algorithms including Prim's greedy vertex-addition approach and Kruskal's edge-sorting with union-find approach and explain their O(E log V) complexity
Union-Find
- Describe the Union-Find (disjoint set) data structure including find with path compression and union by rank for near-constant time connected component operations
- Implement Union-Find for cycle detection in undirected graphs, Kruskal's MST algorithm, and dynamic connectivity queries in network problems
6
Sorting and Searching
2 topics
Sorting Algorithms
- Implement merge sort using divide-and-conquer with recursive splitting and merging and explain its O(n log n) guaranteed time complexity and O(n) space overhead
- Implement quicksort with partition logic including pivot selection strategies (first, last, median-of-three, random) and explain its O(n log n) average versus O(n^2) worst-case behavior
- Implement heap sort using in-place heapification and repeated extract-max operations and explain its O(n log n) worst-case guarantee with O(1) auxiliary space
- Analyze sorting algorithm selection criteria including stability, in-place requirement, best/average/worst case behavior, and input characteristics that favor each algorithm
Binary Search
- Implement binary search on sorted arrays including iterative and recursive approaches with proper boundary handling to achieve O(log n) lookup performance
- Implement binary search variants including finding first/last occurrence, search insert position, and binary search on rotated sorted arrays
- Analyze binary search on answer problems where the search space is a range of possible answers and evaluate how to apply binary search to minimize/maximize optimization problems
7
Algorithm Design Paradigms
3 topics
Dynamic Programming
- Describe dynamic programming principles including optimal substructure, overlapping subproblems, and the distinction between top-down memoization and bottom-up tabulation approaches
- Implement classic 1D dynamic programming solutions including Fibonacci, climbing stairs, coin change, and longest increasing subsequence with state transition recurrences
- Implement 2D dynamic programming solutions including longest common subsequence, edit distance, unique paths in grid, and 0/1 knapsack problem
- Analyze DP state space optimization techniques including rolling arrays for space reduction and evaluate how to identify DP problems by recognizing optimal substructure and overlapping subproblems
Greedy Algorithms
- Describe the greedy algorithm paradigm including the greedy choice property and optimal substructure requirements and explain when greedy approaches yield globally optimal solutions
- Implement greedy solutions for interval scheduling, activity selection, Huffman coding, and fractional knapsack problems with correctness justification
- Analyze when greedy algorithms fail to produce optimal solutions and evaluate how to prove greedy correctness using exchange arguments or contradiction proofs
Recursion and Backtracking
- Describe recursion including base cases, recursive cases, call stack behavior, and how to derive recurrence relations for recursive algorithms
- Implement backtracking solutions for constraint satisfaction problems including N-Queens, Sudoku solver, permutations, and subset generation with pruning
- Analyze the time complexity of backtracking solutions using decision tree analysis and evaluate how pruning strategies reduce the effective search space from exponential worst case
Scope
Included Topics
- Fundamental data structures including arrays, linked lists (singly and doubly), stacks, queues, deques, hash maps, hash sets, binary search trees, AVL trees, heaps (min and max), priority queues, and graph representations (adjacency list and adjacency matrix)
- Core algorithms including sorting (merge sort, quick sort, heap sort, counting sort), searching (binary search, linear search), graph traversal (BFS, DFS), shortest path (Dijkstra, Bellman-Ford), and minimum spanning tree (Prim, Kruskal)
- Algorithm design paradigms including dynamic programming (memoization and tabulation), greedy algorithms, divide and conquer, recursion and backtracking, Big-O time and space complexity analysis, and amortized analysis fundamentals
Not Covered
- Advanced competitive programming techniques and contest math
- NP-hard and NP-complete problem theory
- Advanced data structures (B-trees, red-black trees, segment trees, Fenwick trees)
- String matching algorithms (KMP, Rabin-Karp, Aho-Corasick)
- Computational geometry algorithms
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