Trees emphasis on Binary Search Trees

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Trees (emphasis on Binary Search Trees)

• Reading 8.1 8.5
• Motivation
• search is a really important problem
• binary search is an incredibly powerful tool to
  do it
• Issues
• binary search through an array is easy to
  implement
• the main reason arrays work well is that it is
  easy to isolate the "left half" and "right half"
  of the array
• but arrays have their problems with insertion,
  deletion, resizing, and so on
• and these problems will be especially bad in
  binary search situations, since adds and removes
  will almost always be to the middle of the array,
  to keep it in sorted order
• linked structures solve some of those problems,
  but you lose the ability to isolate portions of
  the list effectively
• The solution
• who says a LinkedList has to have a single next
  pointer?

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Arrays and LinkedLists are "Linear" Structures
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A (Binary) Search Tree Structure
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Why Is This A Binary Search Tree?

• It's a tree rather than a list, because a tree
  node has multiple "out" or "child" pointers

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Tree Not a Graph

• It's a tree rather than a graph because there
  cannot be two paths to the same node (a node has
  at most one parent, and every node has a parent
  except for the root node

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Binary Tree

• It's a binary tree because every node has at most
  two children

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Binary Search Tree

• It is a search tree because every node in the
  tree has the following property
• the node's data value is greater than or equal to
  the data value of every node in the left subtree
• the node's data value is less than or equal to
  the data value of every node in the right subtree
• (so how would you search for thevalue 62, or
  1001, in this tree?)

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8
Sorted Collections

• This is one implementation a sorted collection
  (recall the assignment on SortedLinkedList)
  because all the elements in the list can be
  compared to each other (using compareTo), and the
  list is maintained in sorted order
• why?
• So the standard operations are
• contains does the collection contain this value
• add add a new value in order
• remove remove the first (or all) occurrences of
  this value
• iterator return an iterator that will produce
  all values in the collection in ascending order
• Our task implement BinarySearchTree
• where should we start?