📐 Unit 1: Asymptotic Time Complexity Analysis (Big O Curves)

In slides 94 through 99 of lecture0.pdf, David Malan introduces the visual graphs that form the bedrock of algorithmic comparison in computer science. In enterprise systems engineering, we define this rigorous evaluation as Asymptotic Computational Complexity.

Time to Solve
  ^
  |   / n (Linear - 1 by 1)
  |  /  n/2 (Linear - 2 by 2)
  | /
  |/_______________________ log2(n) (Logarithmic Search)
  +---------------------------------------------> Size of Problem (n)

🔬 Architectural Deconstruction of the Three Curves

• O(n) Curve - Step-by-Step Linear Search: Flipping through a phone book page by page. Represents a pure 1:1 linear correlation. Architecturally unsustainable for massive enterprise databases.
• O(n/2) Curve - Two-by-Two Page Skipping: Flipping two pages at a time. While solving the problem in half the operations, the growth order remains linear O(n). Introduces the engineering risk of overshooting the target.
• O(log2 n) Curve - Binary Search: The "Holy Grail" of computer science. No matter how massively the data set scales into billions of records, the time curve remains nearly horizontal. For 4 billion pages, the processor locates the precise target in a mere 32 execution steps!

🏛️ Unit 2: The C vs Scratch Rosetta Stone

In slides 110 and 111, Malan provides a direct historical comparison—a computational "Rosetta Stone"—translating visual Scratch execution blocks directly into bare-metal C syntax.

#include <stdio.h>

int main(void)
{
    printf("hello, world\n");
}