Prerequisites for Data Structures

Comfort with basic programming is essential before implementing nontrivial data structures.

Data structures are defined not only by stored values but also by the operations and invariants maintained by code.

• Trace assignments, conditionals, loops, and method calls.
• Write methods with parameters and return values.
• Understand local variables and scope.
• Read nested loops and estimate how many times they execute.

Data-structure connections: Traversal, insertion, deletion, search, and update operations.

The course uses Java implementations, so classes, objects, fields, constructors, and methods should already be familiar.

Most data structures are implemented as classes whose internal representation is hidden behind operations.

• Distinguish a class from an object.
• Create objects with new and use constructors.
• Understand instance fields, local variables, and this.
• Recognize encapsulation, access modifiers, and static versus instance members.

Data-structure connections: Node classes, container classes, ADTs, and encapsulated invariants.

Linked structures depend on references that connect objects dynamically.

Understanding references is critical for linked lists, trees, graphs, and object-based structures.

• Understand that object variables store references rather than embedded copies.
• Recognize that two variables may refer to the same object.
• Use null safely and understand what it represents.
• Distinguish changing an object from reassigning a reference.

Data-structure connections: Next links, child references, graph nodes, and structural updates.

Arrays are the foundation for dynamic arrays, heaps, hash tables, adjacency matrices, and many internal representations.

Constant-time indexed access makes arrays one of the most important building blocks in data-structure design.

• Use zero-based indexing correctly.
• Iterate over arrays and distinguish indices from stored values.
• Understand shifting during insertion and deletion.
• Distinguish physical capacity from logical size.

Data-structure connections: ArrayList, binary heaps, hash-table buckets, and adjacency matrices.

Tree and graph algorithms are frequently expressed recursively.

Recursion provides a natural way to process hierarchical structures by solving the same problem on substructures.

• Identify a terminating base case.
• Trace recursive calls and returns.
• Understand stack depth and infinite recursion.
• Recognize recursive patterns in tree traversal and depth-first search.

Data-structure connections: Tree traversals, DFS, recursive insertion/deletion, and divide-and-conquer reasoning.

Data structures are compared by the cost of their operations as input size grows.

Big-O provides the language for explaining why one representation scales better than another.

• Recognize O(1), O(log n), O(n), O(n log n), and O(n²).
• Estimate nested-loop costs.
• Understand why repeated halving produces logarithmic behavior.
• Compare time and space trade-offs rather than relying on a single metric.

Data-structure connections: Operation tables for arrays, lists, trees, heaps, hash tables, and graphs.

Being able to trace an algorithm by hand is one of the most useful skills for understanding a data structure.

Tracing exposes how pointers, indices, stacks, queues, and tree links change from one step to the next.

• Track variable and structure state after each operation.
• Follow loops and recursive calls in execution order.
• Check whether structural invariants remain true after updates.
• Use small examples to reason about edge cases.

Data-structure connections: Simulator use, debugging, correctness checks, and exam-style reasoning.

A small amount of discrete mathematics supports reasoning about sets, trees, graphs, and complexity.

Mathematical notation helps express relationships, bounds, connectivity, and structural properties precisely.

• Be comfortable with sets, membership, union, intersection, and difference.
• Understand simple relations and graph-style connections.
• Use powers and logarithms when reasoning about balanced trees and repeated halving.
• Read simple summations and inequalities when comparing algorithm costs.

Data-structure connections: Sets, graph connectivity, tree height, and asymptotic analysis.

Data-structure bugs often come from incorrect links, indices, boundary conditions, or broken invariants.

Systematic debugging is more reliable than repeatedly changing code until the output looks correct.

• Test empty, single-element, and boundary cases.
• Inspect intermediate states instead of only final output.
• Use assertions or explicit checks for invariants.
• Separate input errors from structural logic errors.

Data-structure connections: Linked-list updates, rotations, heap order, hash-table resizing, and graph traversal.