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Quicksort — Pivot Partitioning

対象: Software Engineerカテゴリ: Computer Science

説明

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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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.

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

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

Assets & Dependencies

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

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