L7 decision tree & table

Major TopicsMajor Topics

Structured English Flowcharts Decision Tables Decision Trees Decision Criteria

Structured EnglishStructured English Structured English is a

technique used to describe algorithmic procedures and is sometimes considered an alternative to flowcharts.

ExampleExample

IF Hours is greater than 40

THEN Compute Overtime

PayELSE Compute Regular PayENDIF

Y NHours > 40

ComputeOvertime

ComputeRegular

What are Flowcharts?What are Flowcharts?

They describe a procedure or program by specifying the sequence diagrammatically in which individual steps must be executed.

An ideal means for documenting complex algorithms so that users can refer to them as procedural guides.

Flowchart SymbolsFlowchart Symbols

Terminal(Start/Stop)

Process

Flow Line

Input/Output

Decisionor Test

Connector

Simple ExampleSimple Example

Start

Print Headings

Read aNumber

A

A

EOF?

Stop

N

PrintNumber,Square

Procedure reads numbers from afile and produces a Table of the

numbers and their squares.

Procedure reads numbers from afile and produces a Table of the

numbers and their squares.

Decision TablesDecision Tables

A Decision table is a table of rows and columns, separated into four quadrants and is designed to illustrate complex decision rules Condition Stub – upper left quadrant Rules Stub – upper right quadrant Action Stub – bottom left quadrant Entries Stub - bottom right quadrant

Decision Table LayoutDecision Table Layout Standard format used for

presenting decision tables.

DecisionStub

RulesStub

ActionStub

EntriesStub

Decision Table ExampleDecision Table Example

1 2 3 4Like Boss? Y Y N N

20% Pay Raise? Y N Y NStay Another Year X XQuit after 2 Months X

Quit next Week X

Developing Decision Developing Decision TablesTables

Process requires the determination of the number of conditions (inputs) that affect the decision.

The set of possible actions (outputs) must likewise be determined

The number of rules is computed Each rule must specify one or more

actions

Number of RulesNumber of Rules

Each condition generally has two possible alternatives (outcomes): Yes or No

In more advanced tables, multiple outcomes for each condition are permitted

The total number of rules is equal to 2 no. of conditions

Thus, if there are four conditions, there

will be sixteen possible rules

Building the TableBuilding the Table For each rule, select the appropriate

action and indicate with an ‘X’ Identify rules that produce the same

actions and attempt to combine those rules; for example:

Condition 1 Y Y Condition 1 YCondition 2 Y N Condition 2 - Action 1 X X Action 1 X

Cleaning Things UpCleaning Things Up Check the table for any impossible

situations, contradictions, and redundancies and eliminate such rules

Rewrite the decision table with the most reduced set of rules; rearranging the rule order is permissible if it improves user understanding

Decision Table example: Decision Table example: combine and reducecombine and reduce

     Conditions and Actions 1 2 3 4 5 6 7 8

Order from Fall Catalog Y Y Y Y N N N NOrder from Christmas Catalog Y Y N N Y Y N NOrder from Special Catalog Y N Y N Y N Y NMail Christmas Catalog X X X XMail Special Catalog X XMail Both Catalogs X X

The four gray columns canbe combined into a single rule. Note that four each,there was NO order placedfrom the Special Catalog.

In addition, Rules 1&5 andRules 3&7 can be combined.Each pair produces the same

action and each pair shares twocommon conditions.

Decision Table example Decision Table example ~ Final Version~ Final Version

Conditions and Actions 1 2 3

Order from Fall Catalog -- -- --Order from Christmas Catalog Y -- NOrder from Special Catalog Y N YMail Christmas Catalog XMail Special Catalog XMail Both Catalogs X

Eliminates the need to check for every possible case.

Decision Table Decision Table example:example:

checking for completeness and checking for completeness and accuracyaccuracy

    Conditions and Actions 1 2 3 4

Salary > $50,000 per year Y Y N NSalary < $2,000 per month Y N Y NAward Double Bonus XAward Regular Bonus XAward no Bonus X

Although the Y-N Combinations suggest a rule, in this case, it is impossible for conditions 1 & 2 to

existsimultaneously. They are in complete

contradiction with each other. In the final version of the table,

Rule 1 will disappear and Rules -4 will become Rules 1-3.

Importance of Decision Importance of Decision TablesTables

Aids in the analysis of structured decisions

Ensures completeness Checks for possible errors (impossible

situations, contradictions, and redundancies, etc.)

Reduces the amount of condition testing that must be done

Decision Trees Decision Trees

Decision trees are useful when multiple branching occurs in a structured decision process, although they can be quite effective when only two decision paths are called for.

They are helpful when necessary to maintain a certain order for a series of decisions.

DrawingDrawing Decision Trees Decision Trees

Drawn horizontally

Root of tree is to the left side

Square Nodes indicate actions

Circle Nodes represent possible conditions

Circle is analogous to the condition part of an IF statement

Square is analogous to the consequent of an IF statement (the ‘THEN’ part)

“IF Circle THEN Square”

Decision Trees Decision Trees

Assume the following discount policy: “ Bookstores get a trade discount of

25%; for orders from libraries and individuals, 5% allowed on orders of 6-19 copies per book title; 10% on orders for 20-49 copies per book title;15% on orders for 50 copies or more per book title.”

Using the Decision Table describe the above mentioned discount policy.

Decision Tree ExampleDecision Tree Example

1

booksto

re 2

3

libraries & individuals

4Osize>=50 25% Discount

5

Osize<50 Nil Discount

Osize

:6-1

9 6 5% Discount

Osize:20-49 710% Discount

Osize>50

8 15 % Discount