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BST Search Time

  • Includes, LowerBound, Upperbound, Insert, Put, Get, Erase
    1. Dominated by BST Search
    2. Runtime is O(h), where h = height of tree
  • How does h related to n = size of tree?
  • From basic theory: log n <= h < n
  • Worst Cases (h = n - 1)
    1. Insert items in sorted order
    2. Insert items in reverse sorted order
  • Best Cases (h = log n) - Insert in "level order"
  • Random Case
    1. Theorem: If items are inserted in random order, h = O(log n)
    2. Problem: World is often not random. Data tends to be ordered, or mostly ordered

?? Need better BST algorithms ??


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