Data Structure
  • 資料結構自學筆記
  • 1 - Stack & Queue
    • 1.1 - Stack
    • 1.2 - Queue
    • 1.3 - Stack and Queue
  • 2 - Tree & Binary Tree
    • 2.1 - Tree
    • 2.2 - Binary Tree
    • 2.3 - Binary Tree Traversal
    • 2.4 - Binary Search Tree
    • 2.5 - Heap
    • 2.6 - Thread Binary Tree
    • 2.7 - Tree and Binary Tree Conversion
    • 2.8 Advanced Trees
      • 2.8.1 - Min-Max Heap
      • 2.8.2 - Deap
      • 2.8.3 - Symmetric Min-Max Heap
      • 2.8.4 - Extended Binary Tree
      • 2.8.5 - AVL Tree
      • 2.8.6 - M-Way Search Tree
      • 2.8.7 - B Tree
      • 2.8.8 - Red-Black Tree
      • 2.8.9 - Optimal Binary Search Tree
      • 2.8.10 - Splay Tree
      • 2.8.11 - Leftest Heap
      • 2.8.12 - Binomial Heap
  • 3 - Search & Sort
    • 3.1 - Searching
    • 3.2 - Elementary Sorting
      • 3.2.1 - Insertion Sort
      • 3.2.2 - Selection Sort
      • 3.2.3 - Bubble Sort
      • 3.2.4 - Shell Sort
    • 3.3 - Sophisticated Sorting
      • 3.3.1 - Quick Sort
      • 3.3.2 - Merge Sort
      • 3.3.3 - Heap Sort
      • 3.3.4 - Radix Sort
      • 3.3.5 - Bucket Sort
      • 3.3.6 - Counting Sort
    • 3.4 - Summary
  • 4 - Graph
    • 4.1 - Intro
    • 4.2 - Graph Traversal
    • 4.3 - Spanning Tree
      • 4.3.1 - Kruskal's algorithm
      • 4.3.2 - Prim's algorithm
      • 4.3.3 - Sollin's algorithm
    • 4.4 - Shortest Path Length
      • 4.4.1 - Dijkstra's algorithm
      • 4.4.2 - Bellman-Ford algorithm
      • 4.4.3 - Floyd-Warshall algorithm
    • 4.5 - AOV Network
    • 4.6 - AOE Network
    • 4.7 - Others
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  • 1. 定義
  • 2. Insert
  • 3. 範例
  1. 2 - Tree & Binary Tree
  2. 2.8 Advanced Trees

2.8.8 - Red-Black Tree

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Last updated 6 years ago

1. 定義

是一棵Binary Search Tree且滿足:

  1. 節點的顏色非黑即紅

  2. 紅色節點的兩個子點的顏色一定要是黑色(任何路徑上不可出現連續的紅色節點)

  3. NULL是為黑色節點

  4. Root一律是黑色節點

  5. Root到不同的Leaf上的路徑皆具有相同的黑色節點數目

2. Insert

  1. 尋找x適合插入的位置

  2. 尋找的過程中，若發生節點的兩個子點是紅色的則必須做顏色轉換(做完後需檢查有無連續的紅色節點存在，若有必須做Rotation)

  3. 置入x且標為紅色節點

  4. 檢查是否有連續紅色節點，若有必須做Rotation

  5. (將Root改為黑色節點)

Rotation：與AVL Tree相似

  • LL

  • LR

  • RL

  • RR

3. 範例

{2, 7, 8, 1, 5, 6, 4}建立一個Red-Black Tree