Prerequisites for Data Structures

You need to be comfortable with basic programming before implementing a real data structure.

A data structure is defined not only by the values it stores but by the operations it offers and the invariants its code maintains.

• Trace assignments, conditionals, loops, and method calls step by step.
• Write methods that take parameters and return values.
• Understand local variables and scope.
• Read nested loops and estimate how many times they run.

Where it shows up: Traversal, insertion, deletion, search, and update operations.

The course implements everything in Java, so classes, objects, fields, constructors, and methods should already be familiar.

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

• Tell a class from an object.
• Create objects with new and use constructors.
• Understand instance fields, local variables, and the this keyword.
• Know encapsulation, access modifiers, and the difference between static and instance members.
• Throw and catch exceptions, for example when someone tries to remove an element from an empty structure.
• Read interfaces and generic types such as List<Integer>; Chapter 1 revisits both.

Where it shows up: Node classes, container classes, ADTs, and encapsulated invariants.

Linked structures rely on references that connect objects at run time.

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

• Know that an object variable holds a reference to the object, not a copy of it.
• Recognize that two variables can refer to the same object (aliasing).
• Use null safely and know what it represents.
• See the difference between modifying an object and assigning a new value to a reference.

Where it shows up: Next-node links, child references, graph vertices, and structural updates.

Arrays underlie dynamic arrays, heaps, hash tables, adjacency matrices, and many internal representations. Basic array use is assumed. Chapter 3 covers arrays and array algorithms in detail; how ArrayList grows as a dynamic array is in Chapter 6.

Constant-time access by index makes the array one of the most important building blocks of data structure design.

• Use zero-based indexing correctly.
• Traverse an array and tell an index from the value stored there.
• Declare, fill, and print one- and two-dimensional arrays.
• Avoid out-of-bounds indices and know when ArrayIndexOutOfBoundsException is thrown.

Where it shows up: ArrayList, binary heaps, hash table buckets, and adjacency matrices.

Tree and graph algorithms are usually written recursively. Chapter 4 revisits recursion before trees and graphs put it to use.

Recursion is the natural way to process hierarchical structures: solve the same problem on each substructure.

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

Where it shows up: Tree traversals, DFS, recursive insertion and deletion, and divide and conquer.

Data structures are compared by how the cost of their operations grows with the input. Chapter 2 introduces the notation formally; knowing the common growth rates beforehand makes that chapter easier.

Big O is 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 the cost of nested loops.
• Understand why repeated halving gives logarithmic behavior.
• Weigh time against space instead of relying on a single measure.

Where it shows up: Cost tables for arrays, lists, trees, heaps, hash tables, and graphs.

Tracing an algorithm by hand is one of the most useful skills for understanding a data structure.

A trace shows how pointers, indices, stacks, queues, and tree links change from one step to the next.

• Follow the state of the variables and the structure after every operation.
• Trace loops and recursive calls in execution order.
• Check whether structural invariants still hold after an update.
• Think through edge cases on small examples.

Where it shows up: Using the simulators, debugging, checking correctness, and reasoning through exam questions.

A little discrete mathematics makes it easier to reason about sets, trees, graphs, and complexity.

Mathematical notation lets you state relationships, bounds, connectivity, and structural properties precisely.

• Be comfortable with sets, membership, union, intersection, and difference.
• Understand simple relations and connections such as those in a graph.
• Use exponents and logarithms when thinking about balanced trees and repeated halving.
• Read simple sums and inequalities when comparing algorithm costs.

Where it shows up: Sets, graph connectivity, tree height, and asymptotic analysis.

Many results in the course, such as bounds on tree height, the correctness of recursive algorithms, and probe sequences in hash tables, are established with short proofs, mostly by induction or contradiction.

A proof shows that a structure keeps its promised bound on every input; trying a few examples cannot give that guarantee.

• Set up the base case and the inductive step, and see where the inductive hypothesis is used.
• Follow an induction on a quantity such as the number of nodes, the height, or the rank.
• Recognize proof by contradiction: assume the opposite and derive a contradiction.
• Know divisibility, prime numbers, and common divisors.

Where it shows up: Correctness of recursion, relations between node count and height in binary trees, height bounds for red-black trees and disjoint-set trees, and why quadratic probing and double hashing try distinct slots.

Data structure bugs usually come from wrong links, wrong indices, boundary conditions, or broken invariants.

Systematic debugging is more reliable than changing code by trial and error until the output looks right.

• Test empty, single-element, and boundary cases.
• Look at intermediate states, not just the final output.
• Use assert statements or explicit checks for invariants.
• Separate bad input from logic errors in the structure.

Where it shows up: Linked list updates, rotations, heap order, hash table resizing, and graph traversal.