Arrays and Dynamic Arrays
Push, pop, resize, and amortized analysis with the accounting method on a worked example.
Computer Science Foundations
Implementation, Big-O analysis, and JUnit edge-case tests for every structure from arrays through graphs. A common cause of failed autograder submissions in data structures coursework is iterator invalidation after a mid-traversal mutation, the exact failure mode our tutors annotate inline. Verified CS graduates, starting at $20 per task, 12-hour average turnaround.
Why Data Structures
Data structures form the load-bearing column of every CS curriculum. Before a student writes a single Dijkstra implementation or a B-tree page split, the same 8 categories of containers, arrays, linked lists, stacks, queues, trees, heaps, hash tables, and graphs, get implemented, traced, profiled, and tested under increasingly hostile rubrics.
Topics covered
Push, pop, resize, and amortized analysis with the accounting method on a worked example.
Insert, delete, and traversal with explicit prev pointer updates and head and tail edge cases.
Bidirectional traversal, mid-list deletion, and Valgrind-clean memory handling in C and C++.
Josephus problem patterns, sentinel node tricks, and termination guards on traversal loops.
Array-backed and linked implementations, expression evaluation, and balanced-bracket checking.
Ring buffers, two-stack queues, and deque-based sliding window patterns from LeetCode hard.
Full overview
Data structures form the load-bearing column of every CS curriculum. Before a student writes a single Dijkstra implementation or a B-tree page split, the same 8 categories of containers, arrays, linked lists, stacks, queues, trees, heaps, hash tables, and graphs, get implemented, traced, profiled, and tested under increasingly hostile rubrics. A typical data structures II course requires AVL rotations, hash table resizing with quadratic probing, and graph traversal across 6 project milestones.
Intro courses cover tries and hash tables in a spell-check assignment. Contracts-based courses grade data structure invariants with formal preconditions and postconditions. The skill compounds: a confident understanding of pointer-based linked structures builds recursion patterns; comfort with hash tables builds dynamic programming with memoization; graph traversal builds every problem in an algorithms course and most of LeetCode hard.
The assessment landscape splits roughly 60-40 between implementation projects (graded by autograders against held-out test inputs) and written exams (graded by hand for complexity proofs, invariant statements, and ASCII pointer diagrams). Both halves reward the same underlying skill, structuring code around explicit invariants and proving each operation preserves them, but require different artifacts: working code with passing tests on one side, hand-written proofs and worked examples on the other. CSHH tutor matching for this subject draws from CS graduates with depth in either Java with JUnit, Python with pytest, or C and C++ with Valgrind plus Google Test for systems-leaning data structures.
Our tutors deliver implementations with explicit Big-O annotations on every operation, drawn invariant diagrams for tree and heap operations, and JUnit or pytest suites that include the boundary cases graders love to mark: empty container, single element, duplicate keys, capacity-1 resize, and adversarial inputs that trigger worst-case collisions. Languages supported in this subject: Java, Python, C++, C, JavaScript, Assembly.
Where Students Get Stuck
Students reach for the first container they remember, then pay performance penalties on every operation. HashMap vs TreeMap vs LinkedHashMap is the most common confusion in Java; dict vs OrderedDict vs collections.Counter is the Python analog. We map the operation profile (insert frequency, lookup frequency, ordered iteration, range queries) to the structure that meets the Big-O budget, with the tradeoff written out.
The classic bug: free(curr) before updating prev.next leaves a dangling pointer that segfaults on the next traversal. The variant: deleting the head node requires special handling because there is no prev. We draw 4-state ASCII diagrams (before, intermediate, after, edge case) and write helper functions that handle head, tail, and middle deletions with shared invariant assertions.
Self-balancing trees require 4 rotation cases (LL, LR, RL, RR) on insert and 6 cases on delete. Textbooks publish 2 as pseudocode; students reinvent the other 4 incorrectly. Our solutions implement all 10 cases with a unified rotation helper, plus invariant checks after every operation that print the violated property when a test fails.
Open addressing (linear, quadratic, double hashing) competes with chaining. Linear probing suffers primary clustering above load factor 0.5; quadratic probing only finds a free slot if the table size is prime and the load factor is below 0.5; chaining tolerates higher load but adds pointer overhead. We pick the strategy based on key distribution and amortized cost per operation.
The standard delete-min implementation has a subtle bug: when computing the index of the last child of a parent at index i (left = 2i + 1, right = 2i + 2 in 0-indexed; left = 2i, right = 2i + 1 in 1-indexed), students mix conventions and read off the end of the array. The structure looks correct, but ExtractMin silently returns the wrong value on heaps of certain sizes.
Adjacency matrix is O(V squared) space and O(V squared) BFS. Adjacency list is O(V plus E) space and O(V plus E) BFS. Students declare a list but iterate with i, j double-loops, paying matrix complexity on a list representation. We commit to one representation per assignment and write traversal in idiomatic form (iterator-based for lists, range-based for matrices).
Assignment Types
Singly, doubly, and circular linked lists in Java, Python, C, or C++ with insert, delete, and traversal across head, tail, and middle cases. Named pitfall: freeing curr before updating prev.next, which leaves a dangling pointer that segfaults on the next pass.
Binary search trees, AVL trees, and red-black trees with every rotation case handled and an invariant check after each operation. Named pitfall: implementing only the 2 textbook rotation cases and reinventing the other cases on delete incorrectly.
Chaining and open-addressing tables with load-factor tuning, resize logic, and the equals plus hashCode contract enforced. Named pitfall: linear probing above load factor 0.5 that degrades to O(n) lookup under primary clustering.
Binary heaps, d-ary heaps, and priority queues with sift-up, sift-down, and decrease-key for Dijkstra-ready use. Named pitfall: a last-leaf index miscalculation in sift-down that silently returns the wrong value from delete-min.
Adjacency-list and adjacency-matrix graphs with BFS, DFS, and shortest-path traversals at the right complexity for each representation. Named pitfall: declaring an adjacency list but iterating with an i, j double loop, paying O(V squared) matrix cost on a list.
Written complexity analysis for each operation, including amortized bounds for dynamic arrays and Fibonacci heaps via the accounting and potential methods. Named pitfall: reading worst-case O(n) per push and concluding n pushes cost O(n squared), missing the amortized result.
Disjoint Set Union with union-by-rank and path compression, plus segment trees with lazy propagation for range queries. Named pitfall: skipping path compression, which inflates amortized cost well above the near-constant inverse-Ackermann bound.
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