Doubly Linked Lists

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CSE 331- Lecture 14
Chapter 9 Doubly Linked Lists API Implementation
Header Node Circular Form Chapter 10 Tree
Terminology node, leaf, root, parent, child,
height Binary Tree
Return Midterm Exam Answer questions
about Maze Search Program
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Abstract Model of a List Object
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Circular Doubly Linked Lists

• Implemented on a Computer it might look something
  like this.

The 4 node is the front() node the 2 node is
the back() node begin() returns an iterator to
the 4 node end() returns an iterator to he header
node
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Updating a Doubly Linked List
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Inserting a Node at a Position
// insert newNode before curr newNode-gtprev
curr-gtprev newNode-gtnext curr curr-gtprev-gtnext
newNode curr-gtprev newNode
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Deleting a Node at a Position
// unlink the node (curr) from the
list curr-gtprev-gtnext curr-gtnext curr-gtnext-gtp
rev curr-gtprev delete curr
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Tree Structures
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Tree Structures
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Tree Structures
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Tree Terminology

• Node location containing value(s)
• Parent node 1 link above here in tree
• Child node 1 link below here in tree
• Root top (first) node in tree
• Leaf A node without any children
• Interior node any non-leaf node
• Ancestor any node on a path between root and
  here
• Descendent any node reachable by a path from
  here downward in tree
• Level number of links traversed from root to
  here
• Height (depth) length of longest path from root
  to any leaf
• Subtree Any node (chosen as root) along with
  all of its descendents

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Tree Node Level and Path Length
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Binary Tree Definition

• A binary tree T is a finite set of nodes with one
  of the following properties
• (a) T is a tree if the set of nodes is empty.
  (An empty tree is a tree.)
• (b) The set consists of a root, R, and exactly
  two distinct binary trees, the left
  subtree TL and the right subtreeTR.
  The nodes in T consist of node R and all
  the nodes in TL and TR.

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Binary Tree Nodes
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Tree Node Level and Path Length Depth Discussion
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Tree Node Level and Path Length Depth Discussion
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Tree Node Level and Path Length Depth Discussion
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Tree Node Level and Path Length Depth Discussion
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Summary Slide 1
- Doubly linked lists - provide the most
flexible implementation for the sequential
list. - Its nodes have pointers to the next
and the previous node, so the program can
traverse a list in either the forward or
backward direction. - Traverse a list by
starting at the first node and follow the
sequence of next nodes until you arrive back
at the header. - To traverse a list in reverse
order, start at the last node and follow the
sequence of previous nodes until arriving back
at the header.
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Summary Slide 2
- trees - hierarchical structures that place
elements in nodes along branches that
originate from a root. - Nodes in a tree are
subdivided into levels in which the topmost
level holds the root node. - Any node in a
tree may have multiple successors at the
next level. Hence a tree is a non-linear
structure. - Tree terminology with which you
should be familiar parent child
descendents leaf node interior node
subtree.
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Summary Slide 3
- Binary Trees - Most effective as a storage
structure if it has high density - ie
data are located on relatively short paths from
the root. - A complete binary tree has
the highest possible density - an n-node
complete binary tree has depth int(log2n).
- At the other extreme, a degenerate binary tree
is equivalent to a linked list and exhibits
O(n) access times.