Algorithms, Data Structures, and Complexity: A Complexity-First Pedagogical Framework

Algorithms and Data Structures (ADS) constitute a foundational pillar of computer science education; however, traditional instruction often emphasizes functional correctness while leaving scalability reasoning implicit or secondary. This paper proposes a pedagogical reframing termed ADSC (Algorithms, Data Structures, and Complexity) , in which multi-layered cost models become the central explanatory lens for algorithmic understanding. The ADSC framework introduces the concept of Scalability Literacy , defined as the learner’s ability to anticipate feasibility limits, empirically validate efficiency claims, and detect complexity leaks hidden within high-level abstractions or AI-generated code. Sorting algorithms are employed as a didactic laboratory through which algorithmic cost is operationalized using complementary metrics: comparison counts (C), element movements (M), theoretical auxiliary memory usage (S _peak ), and large-scale execution time (up to n = 2 x 10 ⁶ ). This multidimensional evaluation enables students to systematically distinguish between (i) asymptotic growth behavior, (ii) implementation-dependent constant factors, and (iii) paradigm-specific cost models, including allocation and memory management penalties characteristic of functional programming styles. Validated through sustained university-level teaching practice, the ADSC approach shifts learning from the mechanical reproduction of algorithmic templates toward algorithmic auditing . By foregrounding explicit cost reasoning, the framework equips future software engineers with the analytical rigor required to design, evaluate, and trust scalable systems in an ecosystem increasingly shaped by automated and AI-assisted code generation.