Binary Search

Description

Demonstrates binary search on a sorted array of 16 numbers searching for the value 42. Each step highlights the middle element, eliminates half the array, and a step counter shows the logarithmic efficiency versus linear search.

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Phases

#	Phase Name	Duration	Description
1	Title Card	3s	Title fades in
2	Array Setup	4s	16 sorted boxes appear with values
3	Linear Search Contrast	5s	Brief: linear scans all 16 cells
4	Binary Search Step 1	5s	Mid = index 7 (value 35), 42 > 35, eliminate left half
5	Binary Search Step 2	5s	Mid = index 11 (value 55), 42 < 55, eliminate right
6	Binary Search Step 3	5s	Mid = index 9 (value 42), FOUND!
7	Step Counter Comparison	5s	3 steps (binary) vs 16 steps (linear) shown
8	O(log n) Formula	4s	MathTex O(log n) explanation
9	Outro	2s	Fade out

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Layout

+------------------------------------------------------+
|                 Binary Search                       |
+------------------------------------------------------+
|                                                      |
|  Sorted array (16 elements):                        |
|  [ 2| 5| 9|14|18|23|29|35|42|49|55|61|68|74|81|90]|
|   [0][1][2][3][4][5][6][7][8][9]...                 |
|                                                      |
|  Step 1: mid=7, arr[7]=35, target=42 → go RIGHT    |
|  ████████[mid=35]░░░░░░░░░░░░░░░░░░░░              |
|                                                      |
|  Step 2: mid=11, arr[11]=55, target=42 → go LEFT   |
|              ░░░░[mid=55]████████████              |
|                                                      |
|  Step 3: mid=9, arr[9]=42 → FOUND! ✓              |
|                                                      |
|  Steps: 3       vs    Linear: up to 16             |
|  O(log n)              O(n)                         |
+------------------------------------------------------+

Area Descriptions

• Top: Title
• Center: Array row; eliminated halves are dimmed/greyed
• Below array: Step description text
• Bottom: Complexity comparison and formula

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Assets & Dependencies

• Fonts: LaTeX / sans-serif
• Manim version: ManimCE 0.19.1

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Notes

• Eliminated cells fade to dim grey
• Active search range has bright borders
• Middle element flashes orange when evaluated
• "FOUND!" cell turns green with a pop animation