CXC CSEC Problem Solving

INTRODUCTION How are instructions given to the computer? Computer programs finite set of precise instructions

written in a computer language Before program is written we must find a way to solve the

problem After figuring out how to solve the problem we then

translate the solution into a language meaningful to the computer

INTRODUCTION

Giving precise, unambiguous instructions is not

inherent in human nature Consider the following: Proceed a mile or so down the

road until you reach the roundabout. Turn left at the roundabout and follow the road until you reach a green house on the right hand side. The Post office is about the 3rd or 4th building on the right after the green house. You cant miss it!

INTRODUCTION Problem-solving statements/ instructions should be: Precise Unambiguous Must be in a logical sequence Finite, i.e. terminate after a definite number of steps

Teachers must ensure that students have a good grasp of

what these attributes mean Students should engage students in problem-solving exercises involving everyday problems they can relate to.

PROBLEM-SOLVING ON THE COMPUTER

Examples of everyday problems: Write a recipe for making a cheese sandwich Write instructions to teach your mom how to retrieve voice

message from a generic cell phone Write instructions to give directions to a visitor to get to the

nearest hospital, starting from the school premises Write instructions to tell a novice how to download music

from the Internet.

PROBLEM-SOLVING ON THE COMPUTER The design of any computer program involves two phases: The Problem-solving Phase The Implementation Phase Problem-Solving Phase comprises the following steps: 1. Define the problem 2. Find a solution to the problem 3. Evaluate alternative solutions 4. Represent the most efficient solution as an algorithm 5. Test the algorithm for correctness

DEFINING THE PROBLEM The problem must first be defined: Ensure that students

understand the Problem Defining the problem is the first step towards finding a

solution It helps the programmer to understand what is given and

what is required If the programmer does not fully understand what is

required, he/she cannot produce the desired solution to the problem

DEFINING THE PROBLEM One of the biggest challenges faced in problem-solving is

understanding the problem to be solved. Defining the program can be accomplished by

decomposing the problem into three key components:1. 2.

What is given (the inputs) The tasks that must be performed (processing)

3.

The expected results (the output)

THE DEFINING DIAGRAM Define the problem by constructing a defining diagram A table with three columns which represents the three

components: input, processing and output. E.g. A program is required to read three numbers and

calculate and print the total.INPUT 3 numbers e.g. Num1, num2, num3 PROCESSING 1. Get 3 numbers 2. Ad numbers together 3. Print total OUTPUT Total

THE DEFINING DIAGRAM Input refers to the source data provided - easily identified

by the keywords given, read or accept, input Output refers to the end result required - keywords are

print, display, produce, output Processing are the actions must be performed to achieve

the required output - it answers the question: What must I do with the inputs in order to produce the desired result?

THE DEFINING DIAGRAM In the defining diagram, the actions must be listed in a

logical sequential manner All necessary actions must be explicitly stated

The processing section is NOT the solution to the problem.

Its simply the actions that must be done in order to solve the problem Note that in some cases the input, processing and output

statements might not be as explicitly stated.

PROBLEM 2 E.g. of problem not clearly stated to facilitate student

identification of the problem: Given three integers representing the age of three boys respectively, write a solution to find their average age and also determine the age of the oldest boy. This problem statement could have been stated more

precisely to read: Given three integers A, B, C, representing the age of three boys respectively, write a solution to find and display their average age as well as the age of the eldest boy.

DEFINING DIAGRAM

Two major tasks to be performed, each consisting of

multiple actions:INPUT 3 integers Say age1, age2, age3 PROCESSING 1. Read/accept/get 3 integers 2. Find the average of the three integers 3. Find the highest age 4. Print the average, highest age OUTPUT Average-age Highest-age

PROBLEM 3

The cost of a new car is the sum of the wholesale cost,the local sales tax and the dealers percentage mark-up. Assuming that the dealers mark-up is 10 percent of the wholesale cost and the sales tax is 6 percent, design an algorithm to read a car ID (an integer value) and the

wholesale cost of the car (a real value) and print the carID and the cost to the consumer.

PROBLEM 3 Here, input and output data are clearly stated. To

determine the processing steps we may ask What should I do with wholesale cost in order to find the cost to the consumer?INPUT PROCESSING OUTPUT Car-ID Consumer-Cost

Car-ID, Wholesale-cost 1. Read/get wholesale-cost 2. Calculate dealers markup 3. Calculate the sales tax 4. Find the sum of the wholesale-cost, the dealers mark-up and the sales tax 5. Print the results

THE PROBLEM WITH PROBLEM SPECIFICATION Many real-world programming problems are not always

precise Initial descriptions are often vague, and ambiguous

Students should be encouraged to evaluate problem

statements and ask questions if they are perceived as ambiguous Also, some information may be implicit in the problem

statement and therefore should be taken into account when defining the problem

THE PROBLEM WITH PROBLEM SPECIFICATION

Have students evaluate several problem statements, ranging from simple to complex, some precise, some ambiguous, lacking pertinent information.Here are some examples of imprecise problem statements: #4: Write a program to print a list of all the employees

who have been in the company for over five years #5: Write a program that reads a file that contains

information on the height, weight and age of 100 children. The program should print the names of all the children who are overweight.

FINDING A SOLUTION TO THE PROBLEM

Introduction The Concept of Variables Choosing Variable Names Initialization of Variables

FINDING A SOLUTION TO THE PROBLEM INTRODUCTION

Now that we have defined the problem, we know what we need to do. We must now figure out how to do it. A problem can have many different solutions

Let students arrive at one that works, however long-winded Once a solution is found, it can then be reviewed to see

how it can be optimized, or made more efficient The first approach in deriving a solution to a problem is to

do the problem by hand, noting each step as you proceed.

FINDING A SOLUTION TO THE PROBLEM INTRODUCTION

Problem #6: Find and print the average of three numbers Define the problemINPUT PROCESSING OUTPUT

3 Numbers Say num1, num2, num3

Read/get 3 numbers Find the average Print average

average

Create sample data: sample input data 5, 3, 25

Execute each processing step in the defining diagram

manually

FINDING A SOLUTION TO THE PROBLEM INTRODUCTION Having completed a manual solution to the problem, the

next step is to write your solution as a sequence of instructions Initial solution Get the first number, call it num1 Get the second number, call it num2 Get the third number, call it num3 Add num1 + num2 + num3 Divide result by 3 Print result Stop


THE CONCEPT OF VARIABLES

In our solution to problem #6, we did not tell the computer where to put the result of the add operation. The result must be stored somewhere so it can be accessed later.Grandmas fluffy pancakes: Method: Sift flour in mixing bowl ... Melt the butter in a frying pan ... Pour batter into a bowl ... Just as we need containers to hold or store ingredients, likewise, in computation, we need something to store or hold the values we manipulate



In the computer, values are stored in memory locations. There are many memory locations, so in order to keep

track of where our values are stored we need to place a label or identifier on a particular memory location. The label or identifier is called a variable. A variable is a symbolic name assigned to a memory

location that stores a particular value



When we say num1, num2, etc we are actually defining a

variable or an identifier for each number, so that we can refer to (access) it later. We need to tell the computer where to put the result of the

addition of num1, num2, num3 Add num1 + num2 + num3 storing in Sum

This would tell the computer that the result of the

computation should be stored in a memory location called Sum.



Likewise, we must address a similar issue in the last two statements where we stated, Divide result by 3 Print result Computations are performed by the ALU, part of the CPU

and results are temporarily stored in registers within the cpu These values must be stored in memory locations if they are to be accessed later

THE CONCEPT OF VARIABLES The word variable is derived from the verb to vary. This

means that the value stored in a particular location can change from time to time, although the label remains the same. When new values are placed into previously assigned

memory locations, the old values are replaced by the new .



It is always useful to illustrate the concept of a variable

by using diagrams to show the memory locations:Memory locationsNum 1 Variables Num 2 Num 3 5 3 25



We can now revise the initial solution to include the new variables called sum and averageGet three numbers, say num1, num2, num3 Add num1, num2, num3, storing in sum Divide sum by 3, storing in average Print average

CHOOSING VARIABLE NAMES Its good practice to choose variable names that reflect the


kind of data that is being stored It helps the programmer as well as the reader to understand

the solution better Its important that students grasp the concept of variables

very early in the problem-solving phase.

EVALUATE ALTERNATIVE SOLUTIONS

Having found a solution to a problem the programmer

should proceed to explore alternative solutions The aim is to arrive at the most efficient solution

The initial solution is usually the first that comes to

mind, but is not always the best solution The programmer must evaluate all feasible alternatives

and choose the optimal solution

EVALUATE ALTERNATIVE SOLUTIONS

Points to consider when developing alternative solutions. Can the result be derived differently? Can the solution be made more general? Would it work if

there were 100 integers, instead of 3? Can the solution be used for another problem? E.g. Average

temperature or average grade? Can the number of steps be reduced and still maintain the

logic? Can it be made more robust? What would happen if incorrect data is entered?

REDUCING THE NUMBER OF STATEMENTS We can reduce the number of statements by combining two arithmetic statements into one: 1. Add num1, num2, num3 can be written as

Sum = num1 + num2 + num3(the variable sum is assigned the value of num1 plus num2 plus num3)

2.

Divide sum by 3 storing in average can be written Average = sum/3 We can combine the two statements to produce: Average = sum/3

REVISED SOLUTION Option 2Get num1, num2, num3 Average = (num1 + num2 num3)/3 Print Average Stop Option 1 Get num1, num2, num3 Sum = num1 + num2 + num3 Average = sum/3 Print Average Stop

The most efficient solution should have the following attributes: Should be maintainable Should be memory efficient Should be robust

INITIALIZATION OF VARIABLES

Variables that are used as counters or used to store totals

should always be assigned an initial value of 0 before they are incremented. This is called initialization E.g. Count = 0

This ensures that the variable is cleared of any values that

may have been assigned in a previous execution of the program.

WHAT IS AN ALGORITHM?At this time, we can now introduce the term algorithm. An algorithm is a sequence of precise instructions for solving a problem in a finite number of steps. Properties: Algorithms must: be precise,

be unambiguous, be logically sequenced, give the correct solution an all cases, and eventually end.

WHAT IS AN ALGORITHM?Algorithmic structureHeader : Algorithms name or title

Declaration : Brief description of algorithm and variables used. i.e. A statement of purpose as well as the initialization of variables Body : Sequence of steps

Terminator : An end statement

ALGORITHMIC STRUCTUREProblem: Write an algorithm that prompts a student to enter his/her name and age, accepts the name and age and then display a welcoming message on the screen such as hello Michael! You are 16 years old!Write the algorithm identifying the header, declaration, body and terminator.

ALGORITHMIC STRUCTUREAlgorithm Student data This algorithm displays a students name and age on the screen. Start Display Enter your name: Accept Name Display Enter your age: Accept Age Display Hello, Name Display You are, Age, years old Stop {Header} {declaration}

{Body}

{Terminator}

FLOWCHARTS VERSUS PSEUDOCODE Pseudocode is more concise, closely resembles

programming language Flowchart gives good view of the structure and flow of

the logic Beginners tend to follow the logic easier when using

flowcharts rather than pseudocode Longer, more complex solutions are better represented

using pseudocode.

FLOWCHARTS VERSUS PSEUDOCODE Usage is a matter of preference for experienced

programmers Students should be asked to use both flowcharts as well as

pseudocode to represent algorithms Flowcharts must use special geometrical objects that

designate the basic steps of a program:

Input/Output

Processing/ Assignment

Decision

Start/ Stop

PSEUDOCODE AND FLOWCHART Start Get num1, num2, num3 Average StopAverage (num1+num2+num3)/3 Start

(num1 + num2 + num3)/3

Print Average

Read num1, num2, num3

Print Average

Stop

CONDITIONAL/SELECTION STRUCTURESSelection (decision) The IFTHEN selection statement Syntax: IF (expression) THEN {Statement (s)}

Execute this statement if logical expression is TRUE

This construct is used when no action needs to be performed if the expression returns false.

SELECTION STRUCTURES

Get Mark IF Mark >= 50 THEN Print Well done Stop

This requires only that the expression Well done be printed should the student score 50 marks or more. No action is intended should the mark be less than 50

SELECTION STRUCTURES IF THEN ELSE construct syntax: IF (expression) THEN

{Statements} executed only if condition is TRUE ELSE {Statements} executed only if condition is FALSE ENDIF Only one group of statements could be executed each time

the program is executed.

SELECTION STRUCTURESGet Mark IF Mark >= 50 THEN PRINT Well done ELSE PRINT Must do better ENDIF Stop Well done will be

printed should the students mark be 50 or greater. If the mark is less than 50

then the statement Must do better would be printed.


A worker in a clothing factory is paid an additional incentive according to the amount of shirts she folds. The basic salary is $300.00 per week. Should the worker fold 500 or more shirts per week, an additional 15%, is added to her basic salary. If the worker folds less than 500 shirts however, she is paid just the

basic salary.Write an algorithm to determine and print the salary of the worker.


Write an algorithm to accept any two numbers, the first anumerator and the second the denominator. If the second is equal to zero print Cannot divide by 0. Otherwise

divide the first number by the second and print the answer.

SELECTION STRUCTURESA teacher has realized an error in his marking of studentsscripts. He has therefore decided to credit all students who got 55 marks and under with an additional 10 marks. Those

who got more than 55 would be credited with an additional15 marks. Write an algorithm to accept the mark from a student in a class. Calculate and print the students adjusted mark.

SELECTION STRUCTURESA store offers customers a discount of 15% if the cost ofany item purchased is equal to or exceeds $200.00. Should the cost be less than $200.00 however, then a 5% discount is applied. Write an algorithm to accept the cost of an item. Apply the relevant discount and

calculate and print the net cost (cost discount).

REPETITION STRUCTURES Repetition or Loop or Iteration structures allow statements

to be repeated a fixed number of times or until some condition evaluates to false. There are three repetition constructs:1.

FOR Loop

- counted loop

2.3.

REPEAT Loop - conditional loopWHILE Loop - conditional loop

REPETITION STRUCTURESThe FOR loop construct syntax: FOR = TO DO {Statements} ENDFOR e.g. FOR X = 1 to 10 DO {Statements to be executed} ENDFOR

REPETITION STRUCTURES The FOR loop is used when the required number of

iterations (loops) is known beforehand The statements are repeated as long as the value of the

identifier specified by the element does not exceed the value specified by . A comparison is made each time the loop iterates to check whether the is exceeded. If it is not then the counter value is incremented by one (the default step value)

REPETITION STRUCTURES The 12 workers employed in the folding section of a

clothing factory are each paid a basic salary of $500.00 per week. An incentive is offered according to the amount of shirts folded. Should a worker fold 600 or more shirts per week a bonus of 20%, is added to his/her basic salary. If a worker does not fold as much as 600 shirts however, he/she is paid just the basic salary. Write an algorithm to determine and print the salary of each worker.

REPETITION STRUCTURESA teacher has realized an error in his marking after having marked all his students scripts. He has therefore decided to credit all students

who got less than 60 with an additional 5 marks. Those who got 60 andover would be credited with an additional 15 marks. Write an algorithm to accept the initial marks obtained by the 20 students in the class. Calculate and print each students adjusted mark. The teacher would like to determine the class average after the marks are credited. Should the class average exceed 60, Instructions well received should be printed. Otherwise, Reconsider Teaching Methods should be printed.

REPETITION STRUCTURESA store offers customers a discount of 15% if the total cost of items purchased is equals or exceeds $400.00. Should the total be less than $400.00 then 5% discount

is given. Write an algorithm to accept the costs of fiveitems. Calculate and print the total cost. Apply the relevant discount and calculate and print the net cost (total cost discount).

REPETITION STRUCTURES WHILE LoopThe WHILE Loop construct syntax: INPUT Value WHILE (expression) Do {statements} executed if Boolean argument in logical expression is true INPUT value to be tested ENDWHILE

REPETITION STRUCTURES

WHILE Loop

In processing, the argument (condition) between WHILE

and DO is tested to see if it is true. If the condition returns true, the statement(s) that follow

DO will be executed. If the condition returns false, execution of the WHILE

statement is stopped. It is possible for the loop never to be executed if the initial input renders the condition is to be proven false.

REPETITION STRUCTURES

WHILE Loop

The while loop can iterate indefinitely, as long as the

condition in the argument expression remains true. It is terminated only when the condition returns false.

Write an algorithm that reads a number of arbitrary

integers and find the average of all numbers read. The program should be terminated if the sentinel value 999 is entered.

REPETITION STRUCTURES WHILE Loop Write an algorithm to accept an unspecified amount of

integers. Calculate and print the sum of the numbers entered. The algorithm should also determine and print the highest number entered. The process should be terminated if the number entered exceeds 1000. Write an algorithm to accept the price of items purchased

at a supermarket. The entry of prices should continue as long as the price entered is not $101.00. Calculate and print the total cost of items purchased.

REPETITION STRUCTURES REPEAT LoopRepeat Loop construct syntax: REPEAT {statements to be executed} UNTIL (Boolean expression) The repeat loop is used to iterate a sequence of events until

a specific condition becomes true. The statements in the body of a Repeat loop are executed at least once, because the test of the condition takes place at the end of the loop.

TRACE TABLESState what is printed when the following algorithm is executed.FOR X = 1 to 3 DO FOR Y = 1 to 3 DO Product = Y * X Print Product ENDFOR ENDFOR

TRACE TABLESWhats printed by the following Algorithm? AMOUNT = 2 G=4 WHILE AMOUNT < 50 Do G = G*2 AMOUNT = AMOUNT + G Print AMOUNT, G ENDWHILE

TRACE TABLESINPUT A,B,C A=B+C B=AC C= A+B IF A > B THEN C=AB ELSE C=BA ENDIF Print A,B,C

State what is printed by the algorithm above when the following data is input:(i) (ii) 5, 7, 9 9, -7, 5

TRACE TABLESComplete the trace table based on the following algorithm.B=2 C=4 Total = 3 WHILE B

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CXC CSEC Problem Solving