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Binary Trees — Insert, Search, AVL Balance

Đối tượng: Software EngineerThể loại: Computer Science

Mô tả

Demonstrates binary search tree operations step by step: inserting nodes to build a BST, searching for a value with left/right comparisons shown, detecting an unbalanced tree, and performing an AVL left rotation to restore balance. Height and balance factor labels update throughout.

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Binary Trees — Insert, Search, AVL Balance

Description

Demonstrates binary search tree operations step by step: inserting nodes to build a BST, searching for a value with left/right comparisons shown, detecting an unbalanced tree, and performing an AVL left rotation to restore balance. Height and balance factor labels update throughout.

Phases

# Phase Name Duration Description
1 Intro 3s Title displayed
2 BST Insert 18s Insert nodes 5,3,7,1,4,6,8 one by one; show comparison path for each
3 BST Search 8s Search for value 4; highlight comparison at each node, path shown in cyan
4 Imbalance Detection 5s Show an unbalanced tree (right-heavy), highlight balance factors in red
5 AVL Rotation 10s Animate left rotation to rebalance; show height labels updating
6 Outro 4s Balanced tree displayed with all balance factors = 0 or ±1

Layout

+--------------------------------------------------+
|  Title: Binary Trees                             |
+--------------------------------------------------+
|                                                  |
|          [5]           <- root                   |
|         /   \                                    |
|       [3]   [7]                                  |
|       / \   / \                                  |
|      [1][4][6][8]                                |
|                                                  |
|  Height labels: h=0 (leaves), h=1, h=2           |
|  Balance factors shown in small text             |
|                                                  |
|  AVL rotation diagram (right side during phase 5)|
+--------------------------------------------------+

Area Descriptions

  • Center: Binary tree visualization with nodes as circles
  • Labels on nodes: Value inside circle, balance factor below
  • Right sidebar: Step-by-step operation description

Assets & Dependencies

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

Notes

  • Nodes fade in along the insertion path
  • Search path highlighted in cyan with step-by-step comparison annotations
  • Rotation shown with arc animation indicating node pivot
  • Balance factors updated after each structural change