Data Structures & Algorithms curriculum

A data structures and algorithms path from complexity and linear structures through trees, heaps, graphs, dynamic programming, and implementation audits.

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Intermediate CS / AP CSA bridge / intro college CS2

Data Structures & Algorithms curriculum

A data structures and algorithms path from complexity and linear structures through trees, heaps, graphs, dynamic programming, and implementation audits.

Pacing

10 units, 20-30 weeks self-paced

Units

10 unit sequence

Practice

40 checked answers

Support

Self-paced or tutor-guided

Outcomes

Choose data structures based on operations, invariants, and tradeoffs.
Analyze algorithms with Big-O reasoning and edge-case tests.
Implement classic structures and algorithms in a deterministic, testable style.

Unit sequence

Built for independent progress first, then tutor support where the student gets stuck.

01
Algorithm analysis and Big-O
- Estimate time and space complexity.
- Separate best, average, and worst cases.
Practice: Analyze three implementations of the same task and justify their asymptotic costs.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Complexity
What is the Big-O for scanning every item in a list of n items once?
Algorithm analysis
Which input should be checked when evaluating worst-case behavior?
only the easiest casean adversarial or largest relevant caseonly n=1a screenshot
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Algorithm analysis and Big-O"?
Compare contiguous arrays, dynamic arrays, and linked lists.Estimate time and space complexity.Separate best, average, and worst cases.Use invariants for insertion and deletion.
Practice artifact
Which practice artifact should you produce for "Algorithm analysis and Big-O" before asking a tutor for help?
Skip the unit and start a new subject.Memorize vocabulary without checking any examples.Analyze three implementations of the same task and justify their asymptotic costs.Watch videos without writing or solving anything.
02
Arrays, lists, and linked structures
- Compare contiguous arrays, dynamic arrays, and linked lists.
- Use invariants for insertion and deletion.
Practice: Implement a small list abstraction and test empty, one-item, and many-item cases.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Arrays
In a zero-indexed array, what is the index of the first item?
Linked lists
A linked list is strongest when you need:
random indexingfrequent insertions after a known nodeGPU renderingSQL joins
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Arrays, lists, and linked structures"?
Estimate time and space complexity.Compare contiguous arrays, dynamic arrays, and linked lists.Separate best, average, and worst cases.Use invariants for insertion and deletion.
Practice artifact
Which practice artifact should you produce for "Arrays, lists, and linked structures" before asking a tutor for help?
Implement a small list abstraction and test empty, one-item, and many-item cases.Memorize vocabulary without checking any examples.Watch videos without writing or solving anything.Skip the unit and start a new subject.
03
Stacks, queues, and deques
- Use LIFO and FIFO abstractions.
- Model call stacks, scheduling, buffering, and undo.
Practice: Build a balanced-symbol checker and a queue simulation.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Stacks
A stack uses which access pattern: FIFO or LIFO?
Queues
A normal queue uses which access pattern?
LIFOFIFOrandomrecursive only
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Stacks, queues, and deques"?
Separate best, average, and worst cases.Estimate time and space complexity.Compare contiguous arrays, dynamic arrays, and linked lists.Use LIFO and FIFO abstractions.
Practice artifact
Which practice artifact should you produce for "Stacks, queues, and deques" before asking a tutor for help?
Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Build a balanced-symbol checker and a queue simulation.Skip the unit and start a new subject.
04
Recursion and divide-and-conquer
- Write base cases and recursive cases deliberately.
- Trace recursion trees and combine steps.
Practice: Solve recursive search, tree, and divide-and-conquer problems with trace tables.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Recursion
Every correct recursive algorithm needs a base case. Type the missing phrase: base ____.
Divide and conquer
Merge sort splits the input, sorts parts, then:
encrypts themmerges sorted partsdrops duplicates alwaysuses a queue only
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Recursion and divide-and-conquer"?
Estimate time and space complexity.Separate best, average, and worst cases.Trace recursion trees and combine steps.Compare contiguous arrays, dynamic arrays, and linked lists.
Practice artifact
Which practice artifact should you produce for "Recursion and divide-and-conquer" before asking a tutor for help?
Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Solve recursive search, tree, and divide-and-conquer problems with trace tables.Skip the unit and start a new subject.
05
Searching and sorting
- Implement linear search, binary search, selection, insertion, merge, and quicksort.
- Explain stability, in-place behavior, and comparison bounds.
Practice: Benchmark sorts on already-sorted, reverse-sorted, and random data.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Binary search
Binary search on 64 sorted items needs at most how many halvings to reach one item?
Sorting
Which sort has typical O(n log n) time and stable merge behavior?
selection sortmerge sortbogosortlinear scan
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Searching and sorting"?
Compare contiguous arrays, dynamic arrays, and linked lists.Estimate time and space complexity.Implement linear search, binary search, selection, insertion, merge, and quicksort.Separate best, average, and worst cases.
Practice artifact
Which practice artifact should you produce for "Searching and sorting" before asking a tutor for help?
Memorize vocabulary without checking any examples.Skip the unit and start a new subject.Benchmark sorts on already-sorted, reverse-sorted, and random data.Watch videos without writing or solving anything.
06
Hash tables, maps, and sets
- Use hashing, collision handling, load factors, and resizing.
- Choose maps and sets for membership and counting tasks.
Practice: Implement a frequency table and explain collision behavior.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Hash tables
If two keys map to the same bucket, that event is called a what?
Sets
A set is best when the main operation is:
membership testingpixel drawingaudio recordingCSS styling
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Hash tables, maps, and sets"?
Separate best, average, and worst cases.Estimate time and space complexity.Compare contiguous arrays, dynamic arrays, and linked lists.Choose maps and sets for membership and counting tasks.
Practice artifact
Which practice artifact should you produce for "Hash tables, maps, and sets" before asking a tutor for help?
Skip the unit and start a new subject.Implement a frequency table and explain collision behavior.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
07
Trees, heaps, and priority queues
- Use binary trees, BSTs, traversals, heaps, and priority queues.
- Maintain ordering and heap invariants.
Practice: Implement traversal methods and a priority queue test suite.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Trees
In a binary search tree, values less than a node usually go to which side?
Heaps
A priority queue is commonly implemented with a:
heapparagraphCSS gridvideo stream
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Trees, heaps, and priority queues"?
Estimate time and space complexity.Separate best, average, and worst cases.Compare contiguous arrays, dynamic arrays, and linked lists.Use binary trees, BSTs, traversals, heaps, and priority queues.
Practice artifact
Which practice artifact should you produce for "Trees, heaps, and priority queues" before asking a tutor for help?
Implement traversal methods and a priority queue test suite.Skip the unit and start a new subject.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
08
Graphs and traversal
- Represent graphs with adjacency lists and matrices.
- Use BFS, DFS, shortest paths, and topological ordering.
Practice: Model a course-prerequisite graph and detect whether an ordering exists.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Graphs
In an unweighted graph, BFS finds shortest paths by number of what?
Traversal
DFS is naturally implemented using recursion or which structure?
stackqueue onlyspreadsheethash collision
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Graphs and traversal"?
Estimate time and space complexity.Use BFS, DFS, shortest paths, and topological ordering.Separate best, average, and worst cases.Compare contiguous arrays, dynamic arrays, and linked lists.
Practice artifact
Which practice artifact should you produce for "Graphs and traversal" before asking a tutor for help?
Watch videos without writing or solving anything.Skip the unit and start a new subject.Memorize vocabulary without checking any examples.Model a course-prerequisite graph and detect whether an ordering exists.
09
Dynamic programming and greedy algorithms
- Identify overlapping subproblems and optimal substructure.
- Compare greedy choices with DP recurrences.
Practice: Solve coin change or knapsack with a recurrence table and edge cases.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Dynamic programming
Dynamic programming stores solutions to overlapping subproblems in a table called a what?
Optimization
DP is appropriate when a problem has optimal substructure and:
overlapping subproblemsonly one inputno recurrenceno state
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Dynamic programming and greedy algorithms"?
Identify overlapping subproblems and optimal substructure.Compare contiguous arrays, dynamic arrays, and linked lists.Estimate time and space complexity.Separate best, average, and worst cases.
Practice artifact
Which practice artifact should you produce for "Dynamic programming and greedy algorithms" before asking a tutor for help?
Solve coin change or knapsack with a recurrence table and edge cases.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Skip the unit and start a new subject.
10
Implementation capstone
- Design an algorithmic module with tests and complexity notes.
- Document preconditions, invariants, and failure cases.
Practice: Ship a small pathfinding, scheduler, search, or compression project with a correctness note.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Capstone
A correct algorithm write-up should include complexity, proof idea, and what kind of cases?
Implementation audit
Which is strongest evidence that an algorithm is ready?
passes examples and edge-case testsuses a fancy namehas no comments anywhereruns once by luck
Unit readiness
Which target best matches the Data Structures & Algorithms unit "Implementation capstone"?
Estimate time and space complexity.Separate best, average, and worst cases.Document preconditions, invariants, and failure cases.Compare contiguous arrays, dynamic arrays, and linked lists.
Practice artifact
Which practice artifact should you produce for "Implementation capstone" before asking a tutor for help?
Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Ship a small pathfinding, scheduler, search, or compression project with a correctness note.Skip the unit and start a new subject.