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Functional Specifications
 Tree Basics
 Traversal Techniques
 Wire Fame
 User’s Conceptual Model
 Designer’s model
 Flow of Control
The Tree Basics
Tree is a non-linear, two-dimensional data structure. It is called a tree
because of its shape when represented
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Like genealogists draw family trees, computer scientists draw
trees from the root node down - unlike nature
After vectors (arrays) and lists, probably the most commonly
encountered data structure used in computer algorithms
Used frequently in everyday life, egs: family trees, organization
of sports tournaments, organizational charts, parse tree of
language sentence.
Tree Terms
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A tree is a non-empty collection of vertices (nodes) that can
have a name and other associated data to be stored and edges
that connect between two vertices.
Root node: first node in the tree
Parent node: node that points to other nodes
Child node: node pointed to by parent
Leaf node: node with no children
Path: is the list of nodes connected by the edges - the defining
property of a tree is that there is exactly one path between the
root and each of the other nodes in the tree.
Binary tree: tree whose nodes all contain two links (to none,
one or two children).
Subtree: portion of the tree structure usually referred to as left
or right subtree
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Depth: the longest path from the root to any node
Forest: a set of trees!
Basically all genealogical terms (siblings, descendants, etc.) are used
with computer tree structures too.
Binary Tree
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Is a finite set of nodes that is either empty of consists of a root
and two disjoint binary trees calls a left subtree and a right
subtree
The Binary Search Tree
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The binary search tree: the most common form of binary tree, is
created by inserting items according to some order
Tree traversal
Definition: A technique for processing the nodes of a tree in some order.
in-order traversal, postorder traversal, tree traversal, level-order traversal.
What I've just called ``scanning through'' a tree is actually called traversing a tree.
General Definition: to traverse a data structure is to process, however you like, every
node in the data structure exactly once.
Note: You may ``pass through'' a node as many times as you like but you
must only process the node once.
E.g. we can talk about ``traversing a list'', which means going through the list and
processing every node once. We had a special name for this: map.
For a specific data structure, we talk about the different orders in which it might be
traversed. For a list there are two common traversal orders: first-to-last (the most
common) and last-to-first.
The general recursive pattern for traversing a (non-empty) binary tree is this: At node N
you must do these three things:
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(L) recursively traverse its left subtree. When this step is finished you are back at
N again.
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(R) recursively traverse its right subtree. When this step is finished you are back
at N again.
(N) Actually process N itself.
We may do these things in any order and still have a legitimate traversal. If we do (L)
before (R), we call it left-to-right traversal, otherwise we call it right-to-left traversal.
Pre-Order Traversal
do (N) before anything else.
Post-Order Traversal
do (N) after everything else.
In-Order, or Infix Order, Traversal
do (N) in between the two subtrees.
E.g. let us look at what order the nodes will get processed given this tree:
Using Left-To-Right traversal:
WireFrame
User’s Conceptual Model
What is all about – here we will talk about concepts of tress and traversals
New Tree
User selects an option New Tree to start a tree. The first number entered becomes
the root of the tree. The subsequent numbers entered become its children .
There is no limit on the size of tree (Hardware of user is only constraint of limit )
Load
A pre-saved tree can be loaded into the program to view it. Only one tree can be
loaded as the user can save one tree only.
Add a node
User selects the option “Add” to add a new node. On clicking the Add option the
user gets a prompt to enter a number of his choice (The new number should follow the
rules listed below)
Rules for a valid input node
 The value entered should be an Integer (No alphabets e.g. a,b,t,z ;No Alpha
numeric e.g. a12,we22 or r3r And No Special Characters eg.*,$,&)
 The number entered should be an integer (No Real or exponential numbers are
allowed e.g. 10.1 , 10e10),number should be in the range?? To??.
 Numbers should not be repeated.
Delete a node
User selects the option “Delete” to delete a node from tree.On selectin the
option the user gets a prompt to enter a number(node) to be deleted .
Rules for deleting a node
 The selected number (node) should be a number existing in the tree.
 Number once deleted can be repeated again.
 All the numbers follow the rules defined for a valid number
 On selecting an non-existing number the user get a prompt.
Find
User can check for existence of an number by selecting an option “Find”
This gives the user a prompt to enter a number.
User gets a keyboard shortcut to perform the operations.
Rules for selecting a number to Find
 The selected number should be a member of tree.
 The input to the prompt should abide to the rules of Valid input..
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Multiple searches are allowed on a node.
Save
User can save the latest tree he is viewing. Only one tree can be saved. The tree
gets a default name specified by the program.
o The saved tree can be viewed only through the applet.
o If Save operation can be committed on a tree with changes done to it.
o Save can be done to commit changes done to pre-saved tree.
Clear
User can use the option Clear to tree loaded to the applet.
It should be used to start a New tree or load a saved tree.
Traversal Menu
Pre-Order, In-Order and Post-Order Traversal.
User can traverse in different orders using options Pre-Order, In-Order and PostOrder from menu.
Designer’s Model
User inputs different values and selects different options to traverse the tree.
Flow of control
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User Selects from menu to either Travers or open Help
The user get an option to open new or load a saved tree.
The Menu of IN/PRE/POST ORDER Traversal is given to user.
The user can start adding new nodes.
User can delete a node from tree.
The user can find a node
The user can save the tree.
User can clear the tree ,and the control goes back to option to either load or create new tree
From here WE will describe the working using screen shots..
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Load/New Tree
Add/Delete a node
Save/Clear a tree.
Help
Traversing(IN/PRE/POST ORDER)