Notes on Algorithms and Flowcharts

Phases of Programming

  • Problem solving phase
    • Produce an ordered sequence of steps that describe the solution of a problem.
    • This sequence of steps is called an algorithm.
  • Implementation phase
    • Implement the program in some programming language.

Steps in Problem Solving

  • First produce a general algorithm (one can use pseudocode).
  • Refine the algorithm successively to obtain a step‑by‑step detailed algorithm that is very close to a computer language.
  • Pseudocode is an artificial and informal language that helps programmers develop algorithms.
  • Pseudocode is very similar to everyday English.

Pseudocode & Algorithm: Example 1

  • Task: Write an algorithm to determine a student’s final grade and indicate whether it is passing or failing. The final grade is calculated as the average of four marks.

Pseudocode

  • Input a set of 4 marks
  • Calculate their average by summing and dividing by 4
  • if average is below 50 Print “FAIL” else Print “PASS”

Pseudocode & Algorithm: Detailed Algorithm (Example 1)

  • Step 1: Input M1, M2, M3, M4
  • Step 2: GRADE = (\frac{M1 + M2 + M3 + M4}{4})
  • Step 3: if (GRADE < 50) then Print “FAIL” else Print “PASS” endif

The Flowchart

  • (Dictionary) A schematic representation of a sequence of operations, as in a manufacturing process or computer program.
  • (Technical) A graphical representation of the sequence of operations in an information system or program.
    • Information system flowcharts show how data flows from source documents through the computer to final distribution to users.
    • Program flowcharts show the sequence of instructions in a single program or subroutine.
    • Different symbols are used to draw each type of flowchart.

The Flowchart: A Flowchart

  • Flowcharts show the logic of an algorithm.
  • Emphasize individual steps and their interconnections.
  • Example: control flow from one action to the next.

Flowchart Symbols

  • Basic Symbols
    • Oval: Denotes the beginning or end of the program.
    • Parallelogram: Denotes an input operation.
    • Rectangle: Denotes a process to be carried out (e.g. addition, subtraction, division, etc.).
    • Diamond: Denotes a decision (or branch) to be made; program continues along one of two routes (e.g. IF/THEN/ELSE).
    • Hybrid: Denotes an output operation.
    • Flow line: Denotes the direction of logic flow in the program.

Example 1: Flowchart for PASS/FAIL (Algorithm and Flowchart)

  • Step 1: Input M1, M2, M3, M4
  • Step 2: GRADE = (\frac{M1 + M2 + M3 + M4}{4})
  • Step 3: if (GRADE < 50) then Print “FAIL” else Print “PASS” endif
  • START → Input → Compute GRADE → Decision (GRADE < 50?) → [Yes: PRINT “FAIL”] → End; [No: PRINT “PASS”] → End
  • Note: The flow includes START and STOP, a decision node, and two possible branches (Yes/No).

Example 2: Feet to Centimeters (Pseudocode & Algorithm)

  • Task: Convert length in feet to centimeters.
  • Pseudocode:
    • Input the length in feet (Lft)
    • Calculate the length in cm (Lcm) by multiplying Lft with 30
    • Print length in cm (LCM)

Example 2: Algorithm

  • Step 1: Input Lft
  • Step 2: Lcm = Lft × 30
  • Step 3: Print Lcm
  • START → Input Lft → Lcm = Lft × 30 → Print Lcm → STOP

Example 3: Area of a Rectangle

  • Task: Read the two sides of a rectangle and calculate its area.
  • Pseudocode:
    • Input the width (W) and length (L) of a rectangle
    • Calculate the area (A) by multiplying L with W
    • Print A
  • Algorithm:
    • Step 1: Input W, L
    • Step 2: A = L × W
    • Step 3: Print A
    • START → Input W, L → A = L × W → Print A → STOP

Principles of Programming - Flowcharts

  • Flowcharts are graphs used to depict or show a step-by-step solution using symbols which represent a task.
  • Symbols are geometrical shapes connected by flow lines.
  • It is an alternative to pseudocoding; pseudocode is verbal, while a flowchart is graphical.

Flowchart Symbols (Continued)

  • Terminal symbol: beginning and end points of an algorithm.
  • Process symbol: an instruction other than input, output or selection.
  • Input-output symbol: an input or an output operation.
  • Disk storage I/O symbol: input from or output to disk storage.
  • Printer output symbol: hardcopy printer output.

Flowchart Symbols (Cont.)

  • Selection symbol: a selection process for two-way selection.
  • Off-page connector: continuation of a logical path on another page.
  • On-page connector: continuation of a logical path at another point on the same page.
  • Flow lines: indicate the logical sequence of execution steps in the algorithm.

Flowchart – Sequence Control Structure

  • Sequence: Statement 1 → Statement 2 → Statement 3

Flowchart – Selection Control Structure

  • Condition → then statements; else statements; with Yes/No branches.

Flowchart – Repetition (Loop) Control Structure

  • Condition → Yes → Loop back to previous steps; No → Continue forward

Flowchart – Example 1

  • Begin → Read birth date → Calculate Age = current year − birth date → Display age → End

Flowchart – Example 2

  • Begin → Read age → [YES age > 55?] → print “Pencen” → End / [NO] → print “Kerja lagi” → End

Flowchart – Example 5

  • Begin → currentnumber ≤ 10? → Yes: sum = sum + currentnumber; currentnumber = currentnumber + 1 → Go back to condition
  • → No: print sum → End

Flowchart – Example 4 (Quadratic Roots)

  • Task: Calculate the roots of a quadratic equation ax^2 + bx + c = 0.
  • Hint: d = \sqrt{b^{2} - 4ac}, and the roots are:
  • x1=−b+d2ax_1 = \frac{-b + d}{2a}
  • x2=−b−d2ax_2 = \frac{-b - d}{2a}

Exercises: Algorithm & Flowchart

1) Create an algorithm and a flowchart that will accept/read two numbers and then display the bigger number.
2) Create an algorithm and a flowchart that will compute the area of a circle.
3) Create an algorithm and a flowchart that will compute the sum of two numbers. If the sum is below or equal to twenty, two numbers will be entered again. If the sum is above 20, it will display the sum.

Lab Activity: Algorithm & Flowchart

4) Create an algorithm and a flowchart that will output the largest number among the three numbers.

Assignment 1

  1. Create an algorithm and a flowchart that will output for g.c.d. (greatest common divisor).
  2. Create an algorithm and a flowchart that will output the factorial of a given number.
  3. Create an algorithm and a flowchart that will output the Fibonacci series up to a given number.
  4. Create an algorithm and a flowchart that will output all the prime numbers between 2 numbers.