8.2 approach in problem solving (9 hour)

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Programming

8.2 Approach in Problem Solving

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• 8.2.1 Input Process Output (IPO) Analysis

Approach in Problem Solving

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Learning Outcome

• Identify input, process and output from a given problem

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Input Process Output (IPO) Analysis

• The IPO is used to analyze problems and develop algorithms

• Used to organize and summarize the results of a problem analysis

• It shows where in the solution the processing takes place

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Input Processing OutputProcessing items:

Algorithm

• It can also be represent using IPO chart

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To do the IPO Analysis, start with:1- Output (Display the results)2- Input (Read the data)3- Process (Perform the computation)

Input :Process :Output :

Identify

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• Output should answer the following question: What does the user want to see

printed on the printer, displayed on the

screen, or stored in a file?


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• Input should answer the following question: What information will the computer

need to know to print, display, or store the output items?


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• Processing item: An intermediate value that the

algorithm uses when processing the input into the output


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Analyze the Problem

• What is it you are trying to accomplish?

• What outcome are you trying to arrive at?

• List the Inputs and Outputs

• Often you work backwards from the Output

• List the Outputs, and then figure out what Inputs you need in order to arrive at the Outputs

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Example 1Problem statement:

Calculate the area of a rectangleWe can summarize the information contained in the problem statement as follows

width

height

Analyze the Problem

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Problem Analysis:

To do the IPO Analysis, start with:1 – Output2 – Input3 – Process

INPUT :PROCESS :OUTPUT :

Identify :

Analyze the Problem

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Problem Analysis:

Input: width, height

Process: area = width x height

Output: area of rectangle

Analyze the Problem

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Input Processing Output

widthheight

Processing items:area = width x height

Algorithm :

area of rectangle

Analyze the Problem

The Problem Analysis, can also be represent using IPO (Input, Processing, Output) Chart

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Find the average of three numbers input by userWe can summarize the information contained in the problem statement as follows

Analyze the Problem

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Problem Analysis:



Identify :

Analyze the Problem

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Problem Analysis:

Input: number1, number2, number3

Process: average = (number1 + number2 + number3) / 3

Output: average

Analyze the Problem

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number1number2number3

Processing items:average = (number1 + number2 + number3) / 3

Algorithm :

average

Analyze the Problem


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Determine the total cost of apples, given the number of kilos of apples purchased and the cost of apples per kilo We can summarize the information contained in the problem statement as follows

Analyze the Problem

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Problem Analysis:



Identify :

Analyze the Problem

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Problem Analysis:

Input: Number of kilos of applesCost of apples per kiloProcess: Total cost = Number of kilos of apples × Cost of apples per kiloOutput: Total cost of apples

Analyze the Problem

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Analyze the Problem



Number of kilos of applesCost of apples per kilo

Processing items:Total cost = Number of kilos of apples × Cost of apples per kilo

Algorithm :

Total cost of apples

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Summary

• Approaches in problem solving• Identify Input Process Output (IPO) from a

problem statement

What have you learned ?

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• 8.2.2 Algorithm• 8.2.3 Pseudocode


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Learning Outcome

• Define algorithm

• Solve problem using pseudocode

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ALGORITHM

• The algorithm is the abstract idea of solving a problem.

• An algorithm is a step-by-step instructions that will transform the input into the output

• It can be represent using pseudocode or flow chart

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From Algorithms to Programs

Problem

C++ Program

1. Problem Analysis2. Algorithm

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Algorithm in everyday’s life

• How to make a mug of hot coffee:1.Start• Boil water• Prepare a mug• Put a tea spoon of coffee & sugar• Pour hot water• Stir• End

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ALGORITHM

can be described using three control structures(Bohm and Jacopini-1966);

• A Sequence o is a series of statements that execute one after

another

• A Selection – (branch) o statement is used to determine which of two different

statements to execute depending on certain conditions

• A Looping – (repetition) o statement is used to repeat statements while certain

conditions are met

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PLANNING THE ALGORITHM

Identify:INPUT :PROCESS :OUTPUT :

2. Transfer to pseudo code or flow chart

3. a. Must start with a start b. Must close with an end

1. Do Problem Analysis

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TECHNIQUES TO REPRESENT THE ALGORITHM

Pseudocode Flow chart

• Artificial, informal language used to develop algorithms

• Similar to everyday English

• Graphical representation of an algorithm

• Special-purpose symbols connected by arrows (flow lines)

1.Pseudocode

2.Flow Chart

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Calculate the area of a circle

Pseudocode Flow chartStart:Input radiusCalculate circle areacircle area = 3.142 * radius * radiusPrint the circle areaEnd:

1. Example of Pseudocode & Flow chart

radius

circle area = 3.142 * radius * radius

circle area

start

end

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1. Pseudocode- Pseudocode Format

start statement 1

statement 2end

1

3

2


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Algorithm Design : Pseudocode

Example 1

Problem statement:Calculate the area of a rectangle

Remember!1. Do Problem Analysis2. Transfer to pseudo code or flow chart

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1. Problem Analysis:





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startread width and heightcalculate area area of rectangle = width * heightprint area of rectangleend

2. Pseudocode

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IPO Chart with PseudocodeInput Processing Output

widthheight


Algorithm - Pseudocode:

Start

Read width and height

Calculate area area of rectangle = width * height

Print area

End

area of rectangle

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Example 2

Problem statement:Find the average of three numbers input by userRemember!1. Do Problem Analysis2. Transfer to pseudo code or flow chart

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Output: average


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startinput number1, number2, number3calculate average average = (number1 + number2 + number3) / 3 print averageend

2. Pseudocode

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IPO Chart with PseudocodeInput Processing Output


Processing items:average = (number1 + number2 + number3) / 3


Start

Input number1, number2, number3

Calculate average average = (number1 + number2 + number3) / 3

Print average

End

average

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Example 3

Problem statement:Determine the total cost of apples, given the number of kilos of apples purchased and the cost of apples per kiloRemember!1. Do Problem Analysis2. Transfer to pseudo code or flow chart

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startRead Number of kilos of apples and Cost of apples per kiloCalculate Total cost Total cost = Number of kilos of apples x Cost of apples per kilo

Print Total cost of applesend

2. Pseudocode

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Total cost = Number of kilos of apples × Cost of apples per kilo


Start

Read Number of kilos of apples andCost of apples per kilo

Calculate Total CostTotal cost = Number of kilos of apples × Cost of apples per kilo

Print Total cost of apples

End


IPO Chart with Pseudocode

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Summary

• Approaches in problem solving• Planning the algorithm• Steps in building pseudocode• Problem solving using pseudocode


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• 8.2.4 Flow Chart


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Learning Outcome

• Solve problem using flow chart

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2. Flow Chart- Flow Chart Format


Statement 1

Statement 2

The statement refers to any input, output & process involved

start

end

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FLOW CHART - SYMBOLS

Graphic Symbol

Name Meaning

Terminal Symbol (oval)

indicates the beginning and end points of an algorithm

Process Symbol

(rectangle)

shows an instruction other than input, output or selection

Input-Output Symbol

(parallelogram)

shows an input or output operation

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Graphic Symbol

Name Meaning

Disk Storage Input-Output

Symbol (cylinder)

indicates input from or output to disk storage

Printer Output Symbol

shows hardcopy printer output

Selection Symbol (diamond)

shows a selection process for two-way selection

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Graphic Symbol

Name Meaning

Flow Lines (arrow)

indicates the logical sequence of execution steps in the algorithm

Off-Page Connector

provides continuation of a logical path on another page

On-Page Connector

(circle)

provides continuation of a logical path at another point in the same page

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Algorithm Design : Flow Chart

Example 1

Problem statement:Calculate the area of a rectangle

Remember!1. Do Problem Analysis2. Transfer to pseudo code or flow chart

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2. Flow Chart

area = width * height

width, height

area

start

end

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IPO Chart with Flow ChartInput Processing Output

widthheight


Algorithm – Flow Chart:

area of rectangle


width, height

area

start

end

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Example 2

Problem statement:Find the average of three numbers input by userRemember!1. Do Problem Analysis2. Transfer to pseudo code or flow chart

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Output: average


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2. Flow Chart

average = (number1 + number2 + number3) / 3

number1, number2, number3

average

start

end

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Processing items:average = (num1 + num2 + num3) / 3

Algorithm – Flow Chart:

average

average = (number1 + number2 + number3) / 3

number1, number2, number3

average

start

end

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Example 3

Problem statement:Determine the total cost of apples, given the number of kilos of apples purchased and the cost of apples per kiloRemember!1. Do Problem Analysis2. Transfer to pseudo code or flow chart

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2. Flow Chart

Number of kilos of apples,

Cost of apples per kilo

Total cost = Number of kilos of apples x

Cost of apples per kilo


end

start

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Total cost = Number of kilos of apples × Cost of apples per kiloAlgorithm – Flow Chart:


Number of kilos of apples, Cost of apples

per kilo

Total cost = Number of kilos of apples x Cost of apples per kilo


end

start

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Summary

• Approaches in problem solving• Steps in building flow chart• Problem solving using flow chart


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Revision

• What is IPO analysis?• What is algorithm?• What are the steps in planning your

algorithm?• Differentiate between pseudocode and

flowchart.


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8.2 Approach in Problem Solving8.2.5 Control Structure8.2.5.2 Sequence

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8.2.5.1 Sequence

Learning Outcome

At the end of the lesson, students should be ableto :1. Understand basic problem solving techniques.• Use the sequence structured in problem solving.• Develop flowchart through the process of top-down.

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8.2.5.1 Sequence

• The simplest programs consist just sequence of statements :

• no loops, no selections amongst alternative actions, no use of subroutines.

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8.2.5.1 Sequence

• Instruction in sequence programming are executed sequentially one by one

• The sequence structure directs the computer to process the instructions, one after another, in the order listed in the program.

first instruction last instruction.

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8.2.5.1 Sequence

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8.2.5.1 Sequence• Planning the Algorithm

• Record the algorithm using IPO analysis / IPO chart.

Problem Analysis:

Input: sales

Process: bonus = sales * (0.05)

Output: bonus

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startinput salesbonus = sales * (0.05) print bonusend

Pseudocode-tool programmers use to help them plan an algorithm-consist of short, English-like statements

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Algorithm Design : Flow ChartFlow Chart- Use standardized symbols to show the steps the computer need to take to accomplish the program’s goal

start

bonus = sales * (0.05)

end

sales

bonus

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8.2.5.1 Sequence

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8.2.5.1 Sequence

Problem Analysis:

Input: width, length, price of tile

Process: area = width * lengthtotal of price = area * price of tile

Output: total of price

• Planning the Algorithm• Record the algorithm using IPO analysis / IPO

chart.

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startinput width, length, price of tile area = width * lengthtotal price of tile = area * price of tile print total price of tileend


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start

area = width * lengthtotal price of tile = area * price of

tile

end

widthlength

price of tile

Total price of tile

Flow Chart- Use standardized symbols to show the steps the computer need to take to accomplish the program’s goal

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8.2.5.1 Sequence

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8.2.5.1 Sequence

Problem Analysis:

Input: hour

Process: Total overtime payment = hour * 5.00

Output: total overtime payment

• Planning the Algorithm• Record the algorithm using IPO analysis / IPO

chart.

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startinput hourtotal overtime payment = hour * 5.00print total overtime paymentend


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start

Total overtime payment = hour * 5.00

end

hour

Total overtime payment

Flow Chart- Use standardized symbols to show the steps the computer need to take to accomplish the program’s goal

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Summary

• Instruction in sequence programming are executed sequentially one by one

• First step in the problem-solving process it to analyze the problem

• Planning the algorithm is using IPO analysis / IPO chart

• Programmer uses the pseudocode as a guide when coding the algorithm

• Flow chart uses standardized symbols to show the steps the computer needs to take to accomplish the program’s goal

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8.0PROGRAMMING

8.2: Approach in Problem Solving8.2.5: Control Structure8.2.5.2 Selection

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• At the end of this topic, students should be able to:

a) explain the purpose of selection control structure.b) apply selection control structure in problem solving.

Learning Outcome

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Control Structure : Selection

SELECTION AnalogyYou need to choose to make “Coffee O” or

“Milk Coffee”

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SEQUENCE

Control Structures

SELECTION LOOPING

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What is Selection Structure?• The selection structure allows instructions

to be executed non-sequentially.• It allows the comparison of two

expressions, and based on the comparison, to select certain course of action.


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if-else

Types of selection structure

nested if-else switch

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• If-else structure’s form

if (expression)statement_1elsestatement_2

Selection (1) if-else

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• In this form, the expression is first evaluated.

• If it evaluates to non-zero (TRUE), statement_1 is executed.

• Otherwise, statement_2 is executed.• Either statement_1 or statement_2 is

executed but not BOTH.


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• Pseudocode format:


start if (expression)

statement_1 else statement_2

end

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• Flow chart format:


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• Example 1:Print “Excellent!” when user enter marks greater than and equal to 80, else print “Sorry, try again”.


Remember to plan your algorithm!1.Do IPO Analysis• Transfer to Pseudocode or Flow

Chart

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• Example 1:Print “Excellent!” when user enter marks greater than and equal to 80, else print “Sorry, try again”.


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IPO Analysis:

Input: marks

Process: if (marks >= 80)print “Excellent” elseprint “Sorry, try again”

Output: “Excellent!” or “Sorry, try again”


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• Pseudocode


startread marksif (marks >= 80)print “Excellent!”elseprint “Sorry, try again”end

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• Flow chartstart

end

marks

“Excellent!”

marks >= 80

true “Sorry, try again”

false


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• Example 2:A high school poetry competition is open only for students above 15 years old. Display “Eligible” if the students meet the requirement, else display “Not eligible” if otherwise.


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IPO Analysis:

Input: age

Process: if (age > 15)print “Eligible” elseprint “Not eligible”

Output: “Eligible” or “Not eligible”


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• Pseudocode


startread ageif (age > 15)print “Eligible”elseprint “Not eligible”end

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• Flow chartstart

end

age

“Eligible”

age > 15

true “Not eligible”

false


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• Example 3:If x is greater than y, display “x is bigger than y” else display “x is smaller than y”.


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IPO Analysis:

Input: x,y

Process: if (x > y)print “x is bigger than y” elseprint “x is smaller than y”

Output: “x is bigger than y” OR “x is smaller than y”


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• Pseudocode


startread x,yif (x > y)print “x is bigger than y”elseprint “x is smaller than y”end

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• Flow chartstart

end

x,y

“x is bigger than y”

x > y

true “x is smaller than y”

false


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Selection (2) nested if-else

if-else


nested if-else

switch

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• The if-else structure can also be nested to any depth.


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• The nested if-else if structured takes the general form:

if (expression_1) statement_1; else if (expression_2) statement_2; else if (expression_3) statement_3; else statement_4;


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• In this nested form, expression_1 is evaluated. If it evaluates to non-zero (TRUE), statement_1 is executed.

• If not, control goes to the second if, where expression_2 is evaluated. If it evaluates to non-zero (TRUE), statement_2 is executed.

• If not, control goes to the third if, where expression_3 is evaluated. If it evaluates to non-zero (TRUE), statement_3 is executed.


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• If not, statement_4 is executed.• Rules Only ONE of the statements is

executed.


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• Example 1:

if student’s grade is greater than or equal to 80Print “A”

else if student’s grade is greater than or equal to 60Print “B”else if student’s grade is greater than or equal to 50 Print “C”else Print “Failed”


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IPO Analysis:

Input: grade

Process: if (grade >= 80)print “A” else if (grade >= 60)print “B”else if (grade >= 50)print “C”elseprint “Failed”

Output: “A” or “B” or “C” or “Failed”


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• Pseudocode


startread gradeif (grade >= 80)print “A” else if (grade >= 60)print “B”else if (grade >= 50)print “C”elseprint “Failed”end

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• Flow chart


start

end

grade

grade >= 80true

“A”

falsegrade >= 60

grade >= 50

“B”

“C”false

false“Failed”

true

true

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• Example 2:

if (x > 0) display "x is positive" else if (x < 0)

display "x is negative" else display "x is 0"

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IPO Analysis:

Input: x

Process: if (x > 0) display "x is positive" else if (x < 0)

display "x is negative" else display "x is 0“

Output: “x is positive“ or "x is negative“ or “x is 0”

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• Pseudo code

startread xif (x > 0) display "x is positive" else if (x < 0) display "x is negative" else display "x is 0"

end

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Selection (2) nested if-else• Flow chart

start

end

x

(x > 0)true

"x is positive”

false(x < 0) “x is

negative”false

“x is 0”

true

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Selection (3) Switch

if-else


nested if-else switch

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• Switch case statements are to check several possible constant values for an expression.

• Switch form:switch (expression) { case constant1: group of statements1 break case constant2: group of statements2 break . . . default: default group of statements }


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• switch evaluates expression and checks if it is equivalent to constant1, if it is, it executes group of statements1 until it finds the break statement.


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• If expression was not equal to constant1 it will be checked against constant2. If it is equal to this, it will execute statements2.


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• If the value of expression DID NOT match any of the previously specified constants (you can include as many case labels as values you want to check), the program will execute the statements included after the default.


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iv) Selection - switch

switch Flow chart

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• Example 1:


x Print1 X is 1

2 X is 2

Other value Value of x unknown

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Selection (3) SwitchIPO Analysis:

Input: x

Process: switch (x) { case 1: print "x is 1“breakcase 2: print "x is 2“break default: Print "value of x unknown” }

Output: "x is 1" or "x is 2" or "value of x unknown”

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Selection (3) Switch• Pseudocode

startread xswitch (x) { case 1: print "x is 1“breakcase 2: print "x is 2" breakdefault: print "value of x unknown” }end

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b) Flow chart

iv) Selection - switch

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SUMMARY

if-else


nested if-else

switch

* Use an appropriate selection control structure in problem solving

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Topic: 8.2Approach in Problem Solving

8.2.5: Control Structure8.2.5.3: Looping

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Learning OutcomeAt the end of this topic, students should be able to:

• explain the purpose of looping control structure.

• apply looping control structure in problem solving.

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What is looping control structure?

• The looping (or repetition) structure allows a sequence of instructions to be executed repeatedly until a certain condition is reached.

• The looping structure has three forms:o whileo do..whileo for

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The essentials of looping (repetition)

• The loop counter (loop control variable ):o Counts the number of repetitions in the counter-

controlled loopo Controls the execution of loop

• The loop counter requires the following to be known in advance:1.Name of a loop counter• Initial value of the loop counter• Increment (or decrement) by which to modify the

loop counter in each traversal• Condition to test the final value of loop counter

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1. The while Construct

The looping control structure:

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The while Construct

• The while construct has the general form:

while (expression) statement;

• where the expression is first evaluated.• If it is true (not zero), the *statement(s) is

executed,• else if it false (zero), the statement is bypassed.

* note: statement(s); which can be a block of statements – more than 1 statement

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Applying Algorithm in while Construct

• Pseudocode

start initialize counter while (expression) statement(s) counter increment end

12

4

3

* note: please refer to slide #4 for numbering details

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Applying Algorithm in while Construct

• Flow Chart start

initialize counter

while (expression)

statement(s)

True

counter increment

False

end

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The Counter Table for while Construct

counter expression input process output counter increment

initial value of counter condition to

test

IPO analysisincrement to

modify the loop

i i <= 3 input process output i = i + 1

Example of while counter table:

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Example 1: while Construct

• Problem Statement:o Calculate the area of a rectangle for 3 times.

• Remember to plan your algorithm.o Do Problem Analysis.o Transfer to Pseudocode or Flow Chart.

width

height

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i i <= 3 width,height area = width * height area i = i + 1

while counter table


Problem Analysis:

Input: width, heightProcess: area = width * heightOutput: area

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1 T 2

2 T 3

3 T 4

4 F Loop terminate

while counter table


Problem Analysis:


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• Pseudocode


start 1. initialize counter i = 1 2. while (i <= 3) 3. input width, height 4. calculate area of rectangle area = width * height 5. print area 6. counter increment i = i + 1 7. repeat until i > 3 end

IPO analysis

initial value of counter

condition to test

increment to modify the loop

Repeat step 2 – 6 until expression is false

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• Flow Chart


start

i = 1

(i <= 3)

width, height

True

i = i + 1

False

end


area

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2. The do..while Construct


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The do..while Construct

• The do..while construct has the general form:

do statement while (expression);

• where the expression is last evaluated, after the statement(s) is executed.

• This means the statement(s) in the do..while will be executed at least once.

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Applying Algorithm in do..while Construct• Pseudocode

start initialize counter do statement(s) counter increment while (expression) end

12

4

3


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Applying Algorithm in do..while Construct• Flow Chart start

initialize counter

while (expression)

statement(s)

True

counter increment

False

end

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The Counter Table for do..while Construct

counter input process output counter increment

expression


condition to testIPO analysis


i input process output i = i + 1 i <= 3

Example of do..while counter table:

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Example 2: do..while Construct



width

height

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i width,height area = width * height area i = i + 1 i <= 3

do..while counter table


Problem Analysis:


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i width,height area = width * height area i = i + 1 i <= 3

1 2 T

2 3 T

3 4 F

Loop terminate

do..while counter table


Problem Analysis:


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• Pseudocode


start 1. initialize counter i = 1 2. do 3. input width, height 4. calculate area of rectangle area = width * height 5. print area 6. counter increment i = i + 1 7. repeat while (i <= 3) end

IPO analysis


condition to test


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• Flow Chart

Example 2: do..while Constructstart

i = 1

(i <= 3)

width, height

True

i = i + 1

Falseend


area

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3. The for Construct


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The for Construct• The for construct has the general form:

for (initialization; expression; incrementation) statement;

• where the initialization refers to the initial value of a loop counter.

• the expression determines whether the loop should be continued; if it is true (not zero), the *statement(s) is executed, else if it false (zero), the for loop is terminated.

• The incrementation increments the loop counter.

* note: statement(s); which can be a block of statements – more than 1 statement

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Applying Algorithm in for Construct

• Pseudocode

start for (initialize counter; expression; counter

increment) statement(s); end

2


1 4 3

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The for loop is executed as follows:

start for (initialize counter; expression; counter

increment) statement(s); end

o After one-time initialization, the expression is first evaluated.

o If it is false, the for loop is terminated; if it is true the statement(s) in the loop is executed.

o And then the incrementation is performed.o The expression condition is again evaluated, until

the expression becomes false.

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Applying Algorithm in for Construct

• Flow Chart start

initialize counter

(expression)

statement(s)

True

counter increment

False

end

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The Counter Table for for Construct

counter expression input process output counter increment

initial value of counter condition to

test

IPO analysisincrement to

modify the loop

i i <= 3 input process output i = i + 1

Example of for counter table:

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Example 3: for Construct



width

height

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for counter table


Problem Analysis:


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1 T 2

2 T 3

3 T 4

4 F Loop terminate

for counter table


Problem Analysis:


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• PseudocodeExample 3: for Construct

start 1. initialize counter i = 1 2. for (i <= 3) 3. read width, height 4. calculate area of rectangle area = width * height 5. print area 6. counter increment i = i + 1 7. repeat until i > 3 end

IPO analysis


condition to test



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• Flow Chart


start

i = 1

(i <= 3)

width, height

True

i = i + 1

False

end


area

02/10/12

Accumulating in Problem Solving• Accumulating or summing is a task a program must

often perform.• Accumulating means summing a group of numbers:

1.where a variable is added to another variable,• which holds the value of the sum or total.

• The expression for accumulating is as follow:

sum = sum + num

total = total + marks

2 1

2 1

02/10/12

How to apply Accumulating in Problem Solving?Example 4: Accumulating in Sequence Structure• Problem Statement:

o Calculate the average of three numbers.

Problem Analysis:

Input: num1, num2, num3Process: total = num1 + num2 + num3average = total / 3

oraverage = (num1 + num2 + num3) / 3Output: average

Accumulating

02/10/12

How to apply Accumulating in Looping?Example 5: Accumulating in Looping Structure• Problem Statement:

o Calculate the average of three numbers.

Problem Analysis:

Input: numProcess: total = total + numaverage = total / 3Output: average

Accumulating

02/10/12

Example 5: Accumulating in Looping StructureProblem Analysis:

Input: numProcess: total = total + numaverage = total / 3Output: average

total i i <= 3

num total = total + num

i = i + 1 average = total / 3

average

0 1 T 70 70 2

2 T 80 150 3

3 T 90 240 4

4 F Loop terminate average = 240 / 3 80

Using accumulating in while construct (while counter table)

02/10/12

Pseudocode for Accumulating in while Construct:

start 1. initialize total total = 0 2. initialize counter i = 1 3. while (i <= 3) 4. input num 5. accumulate total total = total + num 6. counter increment i = i + 1 7. repeat until i > 3 8. calculate average average = total / 3 9. print average end

IPO analysis


condition to test



initial value of total

IPO analysis

02/10/12

Flow Chart for Accumulating in while Construct:

start

i = 1

(i <= 3)

num

True

False

end

total = total + num

i = i + 1

total = 0

average = total / 3

average

02/10/12

Summary• What have you learned?

o The three forms of looping control structure:whiledo..while for

o The loop counter requirement.o Apply looping control structure in problem

solving.Remember to plan your algorithm.

Do Problem Analysis.Transfer to Pseudocode or Flow Chart.

o Applying accumulating in looping.

8.2 approach in problem solving (9 hour)

Education

problem analysis

process input

ipo input

problem statement

given problem

output items

output list

computation input