Quicksort — Pivot Partitioning

Description

Demonstrates the quicksort algorithm on an unsorted array using in-place pivot partitioning. Shows the two-pointer sweep with elements being classified relative to the pivot, the pivot landing in its final sorted position, and recursive application to subarrays. Displays both average and worst-case complexities.

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Phases

#	Phase Name	Duration	Description
1	Intro	3s	Title and unsorted array displayed
2	Pivot Selection	4s	Last element chosen as pivot, highlighted in gold
3	Partition Pass 1	12s	Two-pointer sweep: left finds element > pivot, right finds element < pivot; elements swap
4	Pivot Placement	4s	Pivot moves to its final sorted position
5	Recursion	16s	Visualize recursive calls on left and right subarrays
6	Complexity	5s	Average O(n log n) and worst O(n²) displayed
7	Outro	4s	Fully sorted array highlighted

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Layout

+--------------------------------------------------+
|  Title: Quicksort — Pivot Partitioning           |
+--------------------------------------------------+
|                                                  |
|  [6][3][8][1][9][2][7][4]   <- array row         |
|   i               j  [P]   <- pointer labels     |
|                                                  |
|  Partition step visualized with arrows           |
|                                                  |
|  Recursion depth shown below main array          |
|                                                  |
|  Complexity box:                                 |
|  Avg: O(n log n)   Worst: O(n²)   bottom-right   |
+--------------------------------------------------+

Area Descriptions

• Top strip: Title text
• Center: Main array with pointer annotations below each element
• Bottom: Subarray recursion visualization
• Bottom right: Complexity comparison panel

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Assets & Dependencies

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

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Notes

• Pivot highlighted in gold throughout
• Elements smaller than pivot colored cyan (left partition), larger colored orange (right partition)
• Once sorted position determined, pivot shown in bright green
• Show left pointer (i) and right pointer (j) with labeled arrows