Week 3 Lecture Analysis: Search, Sorting & Complexity
Section 1: The Philosophy of Search & Complexity
David Malan introduces the Week 3 lecture by returning to the foundational demonstration of tearing the phone book in half. However, in this iteration, the conceptual narrative transitions into rigorous mathematical formalization for Linear Search and Binary Search.
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SEARCH ALGORITHMS COMPARATIVE EXECUTION MATRIX
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[ Linear Search (Unsorted/Sorted) ]
[ 1 ] ──> [ 2 ] ──> [ 3 ] ──> ... ──> [ N ] ──> Time Complexity: O(N)
[ Binary Search (Requires Sorted Array) ]
[ 1 ... N/2 ... N ] ──> Cut in half ──> [ 1 ... N/4 ] ──> Time Complexity: O(log N)
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- Linear Search: Inspecting the buffer page by page. Simplest to implement, worst performant O(N).
- Binary Search: Halving the search space directly at the midpoint O(log N).
- Asymptotic Notation: Big O defines the upper bound, Big Omega defines the lower bound, and Big Theta represents exact bounds.
Section 2: Sorting Mechanics & Comparative Engineering
Deploying human volunteers on stage, Malan visualizes physical sorting mechanics across Bubble Sort and Selection Sort.
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BUBBLE SORT STEP-BY-STEP SWAP LOGIC
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Pass 1: [ 5, 2, 8, 1, 9 ] ──> (5 > 2) Swap ──> [ 2, 5, 8, 1, 9 ]
[ 2, 5, 8, 1, 9 ] ──> (8 > 1) Swap ──> [ 2, 5, 1, 8, 9 ]
[ 2, 5, 1, 8, 9 ] ──> (8 < 9) OK ──> [ 2, 5, 1, 8, 9 ] (9 Locked)
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- Bubble Sort Mechanics: Comparing adjacent pairs and swapping them if they violate monotonic ordering O(n^2).
- Selection Sort Mechanics: Iterating across the unsorted partition to identify the absolute minimum element Theta(n^2).
Section 3: Recursion & Divide-and-Conquer Architecture
Recursion represents the architectural capability of a function to invoke itself, leading to the apex sorting routine: Merge Sort.
- Anatomy of Recursion: Enforcing a strict Base Case to prevent stack overflow, alongside the recursive decrement step.
- Merge Sort Architecture: Deploying the canonical divide-and-conquer paradigm to achieve O(n log n) runtime complexity.