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. 2 - Tree & Binary Tree
  2. 2.8 Advanced Trees

2.8.6 - M-Way Search Tree

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Last updated 6 years ago

m: Tree's Degree

主要用於external search及sort，因為通常資料量很大的時候，無法一次全部置於Memory中進行搜尋，需藉助外部儲存記憶體來保存Data(通常使用樹狀結構來保存)，再分批載入Memory中search。

Tree的高度 = Disk I/O次數，若要降低樹的高度最有效的作法就是加大樹的Degree。

若一m-way search tree高度為h，求其最多節點數、最多資料數。

m0+m1+m1+...+mh−2+mh−1=mh−1m−1個節點mh−1m−1∗(m−1)=mh−1筆資料m^{0}+m^{1}+m^{1}+...+m^{h-2}+m^{h-1}=\frac{m^h-1}{m-1}個節點\\ \frac{m^h-1}{m-1}*(m-1)=m^{h}-1筆資料m0+m1+m1+...+mh−2+mh−1=m−1mh−1​個節點m−1mh−1​∗(m−1)=mh−1筆資料