Data Structures and Algorithms: Formula Sheet

Data Structures and Algorithms: Formula Sheet

Build a responsible reference sheet of relationships, conditions, units, representations, and decision rules rather than copying unexplained formulas. Studies arrays, linked structures, stacks, queues, trees, graphs, hashing, sorting, and complexity. Course titles, local sequences, grading, safety rules, required tools, and assessment formats vary; align this resource with the current syllabus and instructor directions.

Learning outcomes

• Explain and apply abstract data types, then connect it to trees and graphs using course-appropriate evidence.
• Explain and apply trees and graphs, then connect it to hash tables using course-appropriate evidence.
• Explain and apply hash tables, then connect it to sorting and searching using course-appropriate evidence.
• Explain and apply sorting and searching, then connect it to asymptotic analysis using course-appropriate evidence.
• Explain and apply asymptotic analysis, then connect it to abstract data types using course-appropriate evidence.

Prerequisite readiness

programming fluency, functions, recursion basics, discrete mathematics, and proof reasoning Use a short ungraded check, repair the smallest missing skill, and immediately retest it in a course-level task.

Reference-sheet entries

• abstract data types: record its governing relationship or decision rule, required conditions, units or evidence, one representation, and a common misuse.
• trees and graphs: record its governing relationship or decision rule, required conditions, units or evidence, one representation, and a common misuse.
• hash tables: record its governing relationship or decision rule, required conditions, units or evidence, one representation, and a common misuse.
• sorting and searching: record its governing relationship or decision rule, required conditions, units or evidence, one representation, and a common misuse.
• asymptotic analysis: record its governing relationship or decision rule, required conditions, units or evidence, one representation, and a common misuse.

Use test

Can you choose the right relationship on an unlabeled task and explain why its conditions hold? If not, the sheet is storage rather than understanding.

Reliable method

define required operations, select a representation, state invariants, analyze cost, implement, and test adversarial cases Keep assumptions, intermediate reasoning, units, sources, tool use, and checks visible so another learner can follow the decision process.

Representative application

Compare two data structures for a workload and justify the choice with operation frequency, complexity, and measured behavior. Predict a reasonable result before working, compare the outcome with the prediction, and explain limitations or alternative interpretations.

Error recovery

Watch for memorizing Big-O labels without specifying input size, operation, average or worst case, and implementation assumptions. Mark the first unsupported move, classify the cause, correct the reasoning, and schedule a fresh mixed recheck after a delay.

Accessibility, integrity, and safety

Use approved accommodations and accessible formats. Follow course rules for collaboration, citation, calculators, software, generative tools, laboratories, clinical settings, field activity, privacy, copyright, and human or animal subjects. Never use Exams.fit to obtain protected questions or bypass assessment rules.

Evidence to save

When permitted, preserve an implementation and analysis with invariants, complexity, benchmarks, and edge tests with the prompt, first attempt, feedback, revision, verification, and reflection. Remove restricted assessment content and private or proprietary information.

Open-learning reference

Compare this original Exams.fit resource with the relevant OpenStax collection and MIT OpenCourseWare when they match the local course. Reviewed August 2, 2026. This page does not replace the current syllabus, instructor, institution, or qualified professional.