6.006 Introduction to Algorithms, Recitation 1
MIT's 2020 recitation notes connect formal asymptotic bounds to input encoding, a stated Word-RAM model, and code-level operation counts, while several local claims require tighter qualification.
These official MIT 6.006 recitation notes move from problems and correctness to efficiency, formal asymptotic notation, input-size modeling, the course's Word-RAM assumptions, and a worked nested-loop analysis. Their strongest contribution is methodological: an operation count is meaningful only after the data representation and unit-cost model have been stated.
All seven physical pages were read and inspected at full rendered resolution. Pages 1–6 contain the lesson; page 7 is an MIT OpenCourseWare attribution and terms page. The archived PDF has SHA-256 0c1395e3cfbb005b0026dd92ea022d1dabd1a88fddaffe68be2f2b678b141c98. It contains native text and vector typography, with no image objects. Several displayed formulas and the code-cost annotations were checked visually because text extraction changes their layout.
What the notes contribute #
- Pages 1–2 separate a problem specification, an algorithm, correctness, and efficiency, then explain why resource use depends on the computational model.
- Page 3 states eventual witness definitions for , , and , treats them as function classes, and gives examples of input-size models for sequences, graphs, and dense matrices.
- Page 4 defines the course's -bit Word-RAM and makes the unit-cost assumptions behind array access, arithmetic, allocation, and addressing explicit.
- Page 5 demonstrates how representation assumptions and an operation-count sum produce an asymptotic upper bound for nested code.
- Page 6 uses logarithmic, polynomial, exponential, and factorial comparisons to exercise the growth hierarchy.
Source claims audit #
| Source claim or framing | Verdict | GTK treatment |
|---|---|---|
| Efficiency may measure time or space and depends on the algorithm and machine model | current | Begin with an explicit resource and cost model rather than attaching a class directly to source code |
| , , and are eventual function classes | current with a domain convention | State eventual nonnegativity for algorithmic cost and comparison functions and use membership notation |
| A graph's input size is | representation-dependent | Apply it to an explicit adjacency-list-style representation; an adjacency matrix instead has entries |
| Listed arithmetic and memory operations on -bit words cost | valid inside the course model | Present this as a Word-RAM assumption, not equal physical latency or a universal RAM definition |
| Addressing word locations needs | sufficient but not minimal | The exact integer condition is , equivalently |
| The birthday example is quadratic because the displayed sum is | conclusion needs a lower-bound witness | The sum alone establishes an upper bound; a no-match input forces the full nested scan and yields worst-case |
| The nonconstant work occurs on code lines 8, 9, and 11 | editing error | The rendered listing places the corresponding operations on lines 18, 19, and 21 |
| “Sterling's approximation” supports the factorial exercise | naming error | Use the standard name, Stirling's approximation; the displayed asymptotic calculation remains usable |
Visual audit #
The source contains a growth-class table, a structured array interface, an annotated code listing, a displayed operation-count sum, and a page of worked equations. They are information-bearing, but none is clearer as a retained page image than accessible native text, tables, code, and mathematics. GTK therefore keeps no raster excerpt from this source. The source contains no independent plot, diagram, photograph, or remote-image dependency.
Editorial role #
GTK uses these notes for the bridge from input representation and a named Word-RAM model to a cost function. Knuth and modern mathematical references carry the notation semantics; the chapter independently supplies the missing lower-bound witnesses and qualifications recorded above.