Best fit
Students who completed AP Computer Science A or already know Java, Python, or C++ basics
DSA Course
Data Structures & Algorithms Course
A structured DSA path through arrays, strings, stacks, queues, hashing, trees, graphs, sorting, dynamic programming, and runtime reasoning.
This course is for students moving beyond introductory programming into the concepts that power advanced computer science, contests, college courses, and technical interviews. Students learn each data structure as a usable problem-solving tool, then practice implementation, tracing, edge cases, and Big-O explanations.
Starting point
Comfort with one programming language such as Java, Python, or C++
Session style
Concept lessons
Student outcome
Choose appropriate data structures for common problem types and explain the tradeoff
DSA Student Menu
Study guide and practice links
Course Overview
A complete bridge from AP Computer Science A to college-level DSA
Students move from coding fluency into the deeper habits of computer science: choosing structures, proving an approach with traces, testing edge cases, and explaining the cost of a solution as input grows.
Topic-by-topic library
Each major DSA topic has an original Code Scholars page with key ideas, practice prompts, and enrollment links.
Pattern-first practice
Students learn arrays, strings, prefix sums, two pointers, sliding windows, recursion, graphs, and dynamic programming as reusable patterns.
Implementation and analysis
Lessons combine code, diagrams, test cases, runtime reasoning, and short written explanations.
Custom pacing
The course can run as AP CSA enrichment, Advanced Topics in CS support, USACO growth, college DSA help, or interview-style prep.
Student Fit
Who this course is for
- Students who completed AP Computer Science A or already know Java, Python, or C++ basics
- Advanced high school students taking data structures, algorithms, or Advanced Topics in CS
- Students preparing for USACO Silver growth, PClassic, ACSL programming, or harder contest problems
- College students in intro data structures or algorithms courses who need ethical concept support
- Students preparing for technical interviews, coding clubs, research projects, or stronger portfolio work
Prerequisites
What students should know before starting
- Comfort with one programming language such as Java, Python, or C++
- Understanding of loops, methods/functions, arrays/lists, and basic classes
- Willingness to draw diagrams, trace code, test edge cases, and explain time complexity
- AP Computer Science A completion is helpful, but a bridge track is available for motivated students
Curriculum
Data structures and algorithms curriculum
The sequence is original to Code Scholars and can be taught in Java, Python, or C++ depending on school, contest, college, or interview goals.
1
Foundations and Algorithm Analysis
Students learn what algorithms and data structures are, why they matter, and how to compare approaches.
- Algorithm design
- Data structure types
- Big-O notation
- Big-Theta and Big-Omega
- Space complexity
- Recurrence intuition
2
Arrays, Strings, and Core Patterns
Students strengthen the practical patterns that appear in AP extensions, contests, and college DSA.
- Arrays
- Strings
- Prefix sums
- Two pointers
- Sliding window
- Linear and binary search
3
Stacks, Queues, Deques, and Linked Lists
Students study access-order rules and reference-based structures with diagrams and edge-case tests.
- Stack
- Queue
- Circular queue
- Priority queue
- Deque
- Linked-list operations
4
Hashing, Maps, Heaps, and Priority Processing
Students learn fast lookup, collision reasoning, heap invariants, priority queues, and Huffman coding.
- Hash tables
- Sets and maps
- Frequency counting
- Heap structure
- Heap sort
- Huffman coding
5
Trees and Balanced Search Structures
Students learn tree vocabulary, traversal, search ordering, balancing, and advanced index structures.
- Binary trees
- Tree traversal
- Binary search trees
- AVL trees
- Red-black trees
- B trees and B+ trees
6
Graphs and Network Algorithms
Students model relationships and solve traversal, connectivity, shortest-path, spanning-tree, and flow problems.
- Adjacency lists and matrices
- DFS and BFS
- Strongly connected components
- Dijkstra
- Bellman-Ford
- Kruskal and Prim
7
Sorting and Searching Algorithms
Students compare comparison sorts, non-comparison sorts, search strategies, stability, memory, and runtime.
- Bubble sort
- Selection sort
- Insertion sort
- Merge sort
- Quicksort
- Counting, radix, bucket, and shell sort
8
Advanced Algorithm Design
Students practice greedy choices, dynamic programming, backtracking, string matching, and optional contest structures.
- Greedy algorithms
- Dynamic programming
- Longest common subsequence
- Backtracking
- Rabin-Karp
- Union-find, tries, and segment trees
Topic Library
Original DSA lesson pages
Use these topic pages as a guided map through the course. Each page includes original Code Scholars notes, practice prompts, and links to contact or enroll.
DSA Foundations
Students begin with the language of algorithms, data structures, growth rates, and problem decomposition.
FoundationsGetting Started with DSAA student-friendly entry point into data structures and algorithms: what the field studies, how lessons build on one another, and how to practice without feeling buried by terminology.FoundationsWhat Is an Algorithm?Algorithms are precise problem-solving procedures. Students learn how to describe steps clearly, check correctness, and compare multiple ways to solve the same task.FoundationsData Structure TypesStudents survey linear, hierarchical, hashed, and graph-based structures and learn that each one organizes access in a different way.FoundationsWhy Learn DSA?DSA helps students write programs that are not only correct, but also scalable, explainable, and easier to debug when inputs grow.AnalysisAsymptotic NotationsStudents learn Big-O, Big-Omega, and Big-Theta as a vocabulary for describing how runtime and memory change as inputs grow.AnalysisMaster TheoremThe Master Theorem gives students a shortcut for many divide-and-conquer recurrences once they understand what the recurrence is measuring.Algorithm DesignDivide and ConquerStudents learn to split a problem into smaller independent pieces, solve each piece, and combine the results into a full answer.Algorithm DesignRecursionRecursion becomes manageable when students can name the base case, the smaller problem, and the value returned by each call.
Arrays, Strings, and Pattern Techniques
These practical techniques are essential for AP CSA extensions, USACO growth, and college DSA readiness.
Linear StructuresArraysArrays teach indexed access, fixed-size storage, traversal, mutation, and the importance of careful loop bounds.Linear StructuresStringsString problems combine indexing, character processing, immutability concerns, and pattern recognition.Pattern TechniquesPrefix SumsPrefix sums precompute running totals so range-sum questions can be answered quickly after one setup pass.Pattern TechniquesTwo PointersTwo-pointer methods use two moving indices to scan sorted arrays, strings, or windows without unnecessary nested loops.Pattern TechniquesSliding WindowSliding windows maintain information about a contiguous segment while expanding and shrinking the segment efficiently.SearchingLinear SearchLinear search checks items one at a time and is often the simplest correct approach when data is unsorted or small.SearchingBinary SearchBinary search repeatedly halves a sorted search space, but only works when the preconditions and bounds are handled carefully.String AlgorithmsRabin-Karp AlgorithmRabin-Karp introduces rolling hashes for efficient pattern matching across a longer string.
Stacks, Queues, and Linked Structures
Students learn access-order rules, node references, and how implementation choices change performance.
Linear ADTsStackStacks use last-in, first-out access. Students connect push, pop, and peek to call stacks, undo history, and expression processing.Linear ADTsQueueQueues use first-in, first-out access and model waiting lines, scheduling, buffering, and breadth-first traversal.Linear ADTsTypes of QueueStudents compare ordinary queues, circular queues, priority queues, and deques based on how items enter and leave.Linear ADTsCircular QueueCircular queues reuse array space by wrapping indices around instead of shifting items after every removal.Linear ADTsPriority QueuePriority queues remove the most urgent item first instead of the oldest item first, usually with heap-backed efficiency.Linear ADTsDequeA deque supports adding and removing from both ends, making it useful for window algorithms, undo-redo patterns, and flexible queues.Linked StructuresLinked ListLinked lists store data in nodes connected by references, which makes insertion flexible but random access slower.Linked StructuresLinked List OperationsStudents implement search, insert, delete, update, and reverse operations while handling empty, first-node, and last-node cases.Linked StructuresTypes of Linked ListSingly, doubly, and circular linked lists provide different navigation and update tradeoffs.
Hash Tables, Heaps, and Priority Structures
This section focuses on fast lookup, collision reasoning, heap invariants, and advanced priority structures.
HashingHash TableHash tables support fast average-case lookup by turning keys into array positions and resolving collisions carefully.HeapsHeap Data StructureBinary heaps store a complete tree in an array while maintaining a parent-child priority invariant.SortingHeap SortHeap sort uses heap structure to repeatedly select the next largest or smallest item with predictable O(n log n) behavior.Advanced HeapsFibonacci HeapFibonacci heaps are advanced priority queues designed for efficient amortized operations in certain graph algorithms.Advanced HeapsDecrease Key and Delete Node in a Fibonacci HeapStudents study how changing priorities and deleting nodes work in a lazy heap structure without rebuilding the entire heap.Greedy AlgorithmsHuffman CodingHuffman coding builds an efficient prefix code by repeatedly combining the least frequent symbols.
Trees and Balanced Search Structures
Students move from tree vocabulary into traversal, search, balancing, and database-style tree families.
TreesTree Data StructureTrees model hierarchy with roots, children, parents, leaves, subtrees, height, and depth.TreesTree TraversalTraversal strategies visit tree nodes in different orders, each useful for a different kind of task.TreesBinary TreeBinary trees restrict each node to at most two children, making them a foundation for searches, heaps, expression trees, and recursion practice.TreesFull Binary TreeA full binary tree is shaped so each node has either zero or two children, a useful property for reasoning about certain recursive structures.TreesPerfect Binary TreePerfect binary trees have all leaves at the same level and every internal node filled, producing a highly regular shape.TreesComplete Binary TreeComplete binary trees fill levels from left to right, which is why heaps can be stored compactly in arrays.TreesBalanced Binary TreeBalanced trees keep height controlled so search, insert, and delete operations do not degrade into long linked-list behavior.TreesBinary Search TreeBinary search trees organize values so left subtrees hold smaller values and right subtrees hold larger values.Balanced TreesAVL TreeAVL trees maintain strict height balance through rotations after insertions or deletions.Balanced TreesRed-Black TreeRed-black trees use color rules to maintain approximate balance with efficient updates.Balanced TreesRed-Black Tree InsertionInsertion in a red-black tree combines ordinary BST insertion with recoloring and rotations to repair color-rule violations.Balanced TreesDeletion From a Red-Black TreeDeletion is the most complex red-black operation because removing a black node can disturb the black-height rule.Balanced TreesB TreeB trees store multiple keys per node and keep height small, making them important for database and file-system indexing.Balanced TreesInsertion in a B-treeB-tree insertion adds a key into a leaf and splits nodes when they exceed their allowed capacity.Balanced TreesDeletion from a B-treeB-tree deletion removes a key while borrowing or merging nodes when a child falls below the minimum size.Balanced TreesB+ TreeB+ trees keep records or record pointers in linked leaves while internal nodes guide search.Balanced TreesInsertion on a B+ TreeB+ tree insertion places new data in the leaf layer and splits leaves or internal nodes when capacity is exceeded.Balanced TreesDeletion from a B+ TreeB+ tree deletion keeps leaves sufficiently full through redistribution or merging while preserving search routing.String TreesTrieTries store strings by shared prefixes, making prefix queries and dictionary-style lookups efficient.Range Query StructuresSegment TreeSegment trees answer range queries and point updates efficiently by storing interval information in a tree.
Graphs and Network Algorithms
Students learn graph representations, traversals, connectivity, shortest paths, spanning trees, and flow ideas.
GraphsGraph Data StructureGraphs model relationships between vertices using edges, which can be directed, undirected, weighted, or unweighted.GraphsAdjacency MatrixAn adjacency matrix stores edge information in a grid, making edge checks fast but using more space for sparse graphs.GraphsAdjacency ListAn adjacency list stores each vertex with its neighbors, usually saving space when most vertices connect to only a few others.Graph TraversalDFS AlgorithmDepth-first search explores as far as possible along a path before backtracking.Graph TraversalBreadth-First SearchBreadth-first search explores level by level using a queue and naturally finds shortest paths in unweighted graphs.Graph AlgorithmsStrongly Connected ComponentsStrongly connected components group directed-graph vertices that can all reach one another.Graph AlgorithmsSpanning TreeA spanning tree connects all vertices without cycles; a minimum spanning tree does so with minimum total edge weight.Shortest PathsDijkstra's AlgorithmDijkstra's algorithm finds shortest paths from one source when edge weights are nonnegative.Shortest PathsBellman Ford's AlgorithmBellman-Ford relaxes edges repeatedly, handling negative weights and detecting negative cycles.Shortest PathsFloyd-Warshall AlgorithmFloyd-Warshall computes all-pairs shortest paths by gradually allowing more intermediate vertices.Minimum Spanning TreesKruskal's AlgorithmKruskal's algorithm builds a minimum spanning tree by taking edges in increasing weight order while avoiding cycles.Minimum Spanning TreesPrim's AlgorithmPrim's algorithm grows a minimum spanning tree outward from a starting vertex by repeatedly choosing the cheapest crossing edge.Graph StructuresUnion-FindUnion-find tracks disjoint sets and supports fast connectivity checks through parent links and compression.Graph AlgorithmsTopological SortTopological sort orders directed acyclic graph vertices so every prerequisite appears before the thing that depends on it.Network FlowFord-Fulkerson AlgorithmFord-Fulkerson increases flow through augmenting paths until no more improvement is possible.
Sorting Algorithms
Students compare correctness, stability, memory use, and runtime across classic comparison and non-comparison sorts.
SortingBubble SortBubble sort repeatedly swaps adjacent out-of-order items, making it simple to trace but inefficient for large inputs.SortingSelection SortSelection sort repeatedly selects the next smallest item and places it into its final position.SortingInsertion SortInsertion sort builds a sorted prefix by inserting each new value into its correct place.SortingMerge SortMerge sort recursively sorts halves and merges them, giving predictable O(n log n) behavior with extra memory.SortingQuicksortQuicksort partitions around a pivot and recursively sorts the sides, often fast in practice but sensitive to pivot choices.Non-Comparison SortingCounting SortCounting sort uses counts of known-range integer values to sort without comparing every pair of items.Non-Comparison SortingRadix SortRadix sort processes numbers or strings by digit or character position, often using a stable helper sort at each pass.Non-Comparison SortingBucket SortBucket sort distributes values into ranges, sorts within buckets, and concatenates the results.SortingShell SortShell sort improves insertion sort by comparing elements separated by decreasing gaps before finishing with local insertion behavior.
Advanced Algorithm Design
The final layer covers greedy choices, dynamic programming, backtracking, subsequences, and optimization thinking.
Algorithm DesignGreedy AlgorithmGreedy algorithms make the locally best choice at each step, but students must learn when that local choice is globally valid.Algorithm DesignDynamic ProgrammingDynamic programming solves overlapping subproblems by storing results and building answers from smaller states.Dynamic ProgrammingLongest Common SubsequenceLongest common subsequence is a classic DP problem that compares two sequences while allowing skipped characters.Algorithm DesignBacktracking AlgorithmBacktracking explores choices recursively, abandons paths that cannot work, and returns to try alternatives.Algorithm DesignFloyd-Warshall DP ViewStudents revisit all-pairs shortest paths as a dynamic programming pattern based on which intermediate vertices are allowed.
Practice
DSA practice that builds independent problem solvers
Practice combines implementation, visual tracing, runtime analysis, test design, and problem selection based on the student's goals.
Runtime drills
Array and string patterns
Linked-list tracing
Stack and queue tasks
Hash map problems
Tree and heap traversals
BFS/DFS
Greedy and DP planning
Outcomes
By the end of this course, students will be able to
- Choose appropriate data structures for common problem types and explain the tradeoff
- Implement and trace arrays, strings, lists, stacks, queues, maps, heaps, trees, and graphs
- Analyze time and space complexity at an AP Computer Science A-to-college DSA bridge level
- Explain sorting, searching, recursion, traversal, greedy, dynamic programming, and backtracking strategies
- Design test cases for edge conditions instead of relying only on sample inputs
- Prepare for college DSA, Advanced Topics in CS, USACO growth, or technical interview-style problem solving
Learning Format
How sessions are structured
- Concept lessons
- Live implementation
- Visual tracing
- Complexity review
- Problem-set coaching
- Mock quiz, contest, or interview review
Why Code Scholars
Support that builds real understanding
Guided Topic Pages
Students can review Code Scholars topic pages before or after tutoring sessions to reinforce each concept and practice habit.
Deeper Reasoning
Students learn why an algorithm is appropriate, not just how to code it.
Bridge to College CS
The course fills the gap between AP Computer Science A and college data structures.
Contest and Interview Support
Patterns also support USACO, PClassic, ACSL programming, and interview-style practice.
Language Flexibility
Implementation can be taught in Java, Python, or C++ based on the student's course or goal.
Clear Explanations
Students practice explaining tradeoffs, correctness, edge cases, and runtime clearly.