Binary Search Trees

1
Lecture 22

• Binary Search Trees

2
Inorder Traversal

• Traverse the tree as LEFT- ROOT- RIGHT
• void print(Node ptr)
• if (ptr ! null)
• print(ptr.left)
• cout ltlt ptr.data
• print(ptr.right)
• How does this work?

8
12
6
14
10
4
7
3
Preorder Traversal

• Traverse the tree as ROOT-LEFT-RIGHT
• void print(Node ptr)
• if (ptr ! null)
• cout ltlt ptr.data
• print(ptr.left)
• print(ptr.right)

4
Postorder Traversal

• Traverse the tree as LEFT-RIGHT-ROOT
• void print(Node ptr)
• if (ptr ! null)
• print(ptr.left)
• print(ptr.right)
• cout ltlt ptr.data

5
Deleting a node

• Delete algorithm
• 3 cases
• - leaf
• - make parent's Left or
  Right (as appropriate) NULL
• - delete me
• - internal node, 1 child
• - make parent's Left or
  Right point to my single child
• - delete me
• - internal node, 2
  children
• - go left, then as far
  right as possible to find node
• with maximal value in
  left subtree (MLS)
• - swap MLS data into
  original node to be deleted (me)
• - make MLS's parent's
  Right point to MLS's left
• - delete MLS

6
Deleting a Node

• void Remove(Tree root, string s)
• Tree pos
• Tree prev
• Tree deadnode
• if (root nulll)
• System.out.println( " " s " is not
  in the tree.)
• else if (s lt root.myStr)
• Remove(root.left, s)
• else if (s gt root.myStr)
• Remove(root.right, s)
• ctd...

7
Deleting a Node ctd..

• else // found the node to remove
• deadnode root // deadnode could be
  overwritten later
• if (root.left null)
• root root.right
• else if (root.right null)
• root root.left // will
  actually delete at end
• else // the node to delete has two
  children
• // go left once, then as far right
  as possible
• pos root.left
• while (pos-gtright ! null)
• prev pos
• pos pos.right
• root.myStr pos.myStr
• deadnode pos // deadnode no
  longer root

8
Searching a tree

• bool Search(Node t, string val)
• if (t null) return false
• if ( val t.data)
• return true
• if (val lt t.data)
• Search( t.Left,val)
• else
• Search( t.Right, val )
• return true