Algorithms & Problem Solving Grade 10

Before writing a single line of code, good programmers plan their solution. This page covers algorithms, pseudocode, flowcharts, IPO tables and trace tables — the thinking tools of programming.

What is an Algorithm?

Imagine you want to make a cup of tea. You don't just randomly pour hot water and hope for the best — you follow steps: boil water, put teabag in cup, pour water, wait, add milk. That ordered list of steps is an algorithm.

In computing, an algorithm is a precise, step-by-step set of instructions used to solve a problem or complete a task. Every program you write starts as an algorithm in your head (or on paper) before it becomes code.

Key Characteristics of a Good Algorithm

Why Do Algorithms Matter?

Before writing code, planning with an algorithm helps you:

• Spot logical errors before they become code bugs
• Save time — plan once, code faster
• Communicate your solution to others
• Prove your solution is correct

The Problem-Solving Cycle

1. Understand the problem — State it in your own words. What is given? What must be produced?
2. Plan the solution — Write pseudocode or draw a flowchart. Use an IPO table.
3. Implement — Convert your plan into Delphi code.
4. Test — Run the program and check output against expected results using a trace table.
5. Fix errors — Debug and correct any mistakes, then retest.

IPO Tables (Input – Process – Output)

An IPO table is the first planning tool you use. It forces you to identify three things before writing any code: what data goes in, what happens to it (process), and what comes out.

TOE Charts (Task – Object – Event)

Once a program has several buttons and several jobs to do, an IPO table stops being enough on its own — it never says which component is responsible for a job, or what has to happen before that component springs into action. A TOE chart closes that gap: for every task the program must carry out, it records the object (component) that will handle it and the event that sets that component's code running.

Worked Example: Tuck Shop Cooldrink Stand

A cooldrink at the school tuck shop costs R12. A learner types in how many cooldrinks they want, clicks a button to see the total, types in the money they handed over, then clicks a second button to see their change. Breaking that down task by task produces the following TOE chart:

Once the chart is finished, coding becomes close to mechanical: open one event handler for every distinct event you listed, and turn that row's task into a line or two of Delphi inside it.

Flowcharts

A flowchart shows the steps of an algorithm as a picture using standard symbols connected by arrows. It is easier to spot errors in a diagram than in written text, which is why flowcharts are so useful.

Flowchart Symbol Reference

Flowchart example: checking if a colour is blue

Worked Example: Is a Number Even or Odd?

This flowchart takes a number as input, checks if it divides evenly by 2, and displays "Even" or "Odd" before ending.

Worked Example: Nested Decisions

Here one decision sits inside another. First we check the age; only if that is True do we ask the second question about the licence.

Flowchart: nested decisions — check age first; only if True check the licence.

Pseudocode

Pseudocode is fake code written in plain English that describes the logic of a program. It is not real Delphi code — it is for planning only. Anyone who understands programming should be able to read your pseudocode, even if they don't know Delphi.

Pseudocode Rules

• Use CAPITALS for keywords: IF, THEN, ELSE, ENDIF, WHILE, FOR, INPUT, OUTPUT
• Indent inside structures to show what is inside a block
• Use := or = for assignment (both are accepted)
• Keep it short and clear — no Delphi syntax needed
• Start with START and end with END

SET total TO 10          // assignment
INPUT age                // get data from user
OUTPUT total             // show result
SET area TO length * width   // calculation

IF age >= 18 THEN
    OUTPUT "May vote"
ELSE
    OUTPUT "Too young to vote"
ENDIF

Example: Find the Average of Three Marks

START
    INPUT mark1
    INPUT mark2
    INPUT mark3
    SET total TO mark1 + mark2 + mark3
    SET average TO total / 3
    OUTPUT "Total: ", total
    OUTPUT "Average: ", average
END

Example: Even or Odd

START
    INPUT num
    IF num MOD 2 = 0 THEN
        OUTPUT num, " is Even"
    ELSE
        OUTPUT num, " is Odd"
    ENDIF
END

Trace Tables

A trace table is used to test an algorithm by hand. You pick a test value, then track every variable as you step through the algorithm line by line. This helps you check whether the algorithm produces the correct output.

Trace Table Example: Even or Odd (num = 7)

Trace Table Example: Average of Three Marks (90, 70, 80)

Comparing Algorithms

When two algorithms solve the same problem, we compare them. Three key criteria matter in CAPS exams:

Common Algorithm Patterns in Delphi

Finding Smallest and Largest Values

The trick: assume the first value is both smallest and largest, then compare the rest one by one.

var
  iNum1, iNum2, iNum3: Integer;
  iSmallest, iLargest: Integer;
begin
  iNum1 := StrToInt(edtNum1.Text);
  iNum2 := StrToInt(edtNum2.Text);
  iNum3 := StrToInt(edtNum3.Text);

  iSmallest := iNum1;   // assume first is smallest
  iLargest  := iNum1;   // assume first is largest

  if iNum2 < iSmallest then iSmallest := iNum2;
  if iNum3 < iSmallest then iSmallest := iNum3;
  if iNum2 > iLargest  then iLargest  := iNum2;
  if iNum3 > iLargest  then iLargest  := iNum3;

  lblResult.Caption := 'Smallest: ' + IntToStr(iSmallest)
                     + ' Largest: ' + IntToStr(iLargest);
end;

Swapping Two Values

var
  iA, iB, iTemp: Integer;
begin
  iA := StrToInt(edtA.Text);
  iB := StrToInt(edtB.Text);

  iTemp := iA;    // step 1: save A into temp
  iA    := iB;    // step 2: overwrite A with B
  iB    := iTemp; // step 3: put saved A into B

  edtA.Text := IntToStr(iA);
  edtB.Text := IntToStr(iB);
end;

Even or Odd

var
  iNum: Integer;
begin
  iNum := StrToInt(edtNum.Text);
  if iNum MOD 2 = 0 then
    lblResult.Caption := 'Even number'
  else
    lblResult.Caption := 'Odd number';
end;

Factor Check

A number is a factor if it divides another with no remainder (MOD = 0). For example, 3 is a factor of 12 because 12 ÷ 3 = 4 with remainder 0.

if iNum2 MOD iNum1 = 0 then
  lblResult.Caption := IntToStr(iNum1) + ' is a factor of ' + IntToStr(iNum2)
else
  lblResult.Caption := IntToStr(iNum1) + ' is NOT a factor of ' + IntToStr(iNum2);