Definition and Purpose 🎯

An algorithm is a well-defined, step-by-step procedure or formula for solving a specific problem or achieving a particular outcome. In computer science, an algorithm is the foundational logic that is translated into a program. It acts as a blueprint for the code, ensuring that the problem is solved correctly and efficiently.

Before writing a single line of code, a programmer must first design a clear and correct algorithm.

Characteristics of a Valid Algorithm ✅

To be considered a valid algorithm, a set of instructions must have the following five properties:

·         Input: An algorithm must have zero or more well-defined inputs—the data it works with.

·         Output: It must produce at least one well-defined output—the result of the computation.

·         Finiteness: It must terminate after a finite number of steps. An algorithm that never ends is not useful.

·         Definiteness (Unambiguous): Every step of the algorithm must be precisely defined and have only one interpretation. There should be no ambiguity.

·         Effectiveness: Each step must be basic enough that it can be carried out by a person in a finite amount of time with just a pen and paper.

Examples of Algorithms 📚

Algorithms can vary greatly in complexity. They are often expressed in pseudocode, which is a simplified, language-agnostic way of writing out the steps.

1. Basic Example: Area of a Circle

·         Problem: Calculate the area of a circle given its radius.

·         Logic: The solution uses the mathematical formula Area=π×r2, where r is the radius and π (pi) is a constant value (approx. 3.14159).

·         Pseudocode:

START

  // Define constants and variables

  SET PI = 3.14159

  DECLARE Radius, Area

  // Input

  READ Radius

  // Process

  Area = PI * Radius * Radius

  // Output

  PRINT "The area is", Area

END

2. Moderate Example: Leap Year Check

·         Problem: Determine if a given year is a leap year.

·         Logic: A year is a leap year if it meets one of two conditions:

1.   It is divisible by 4 but not by 100.

2.   It is divisible by 400. The order of these checks is important for the logic to be correct.

·         Pseudocode:

START

  // Input

  READ Year

  // Process and Decision

  IF (Year % 400 == 0) OR ((Year % 4 == 0) AND (Year % 100 != 0)) THEN

    PRINT Year, "is a Leap Year."

  ELSE

    PRINT Year, "is not a Leap Year."

  ENDIF

END

3. Advanced Example: Prime Factorization of a Number

·         Problem: Find and print all the prime factors of a given integer. For example, the prime factors of 12 are 2, 2, 3.

·         Logic: The algorithm iteratively finds the smallest prime that divides the number.

1.   Start by repeatedly dividing the number by 2 until it's no longer even. Print '2' for each successful division.

2.   The number must now be odd. Loop from 3 up to the square root of the remaining number, incrementing by 2 (to check only odd divisors).

3.   For each odd divisor i, repeatedly divide the number by i until it's no longer divisible, printing i each time.

4.   If the number that remains after the loop is greater than 2, it must be a prime factor itself.

·         Pseudocode:

START

  // Input

  READ Number

  PRINT "Prime factors are:"

  // Process 1: Check for divisibility by 2

  WHILE Number % 2 == 0 DO

    PRINT 2

    Number = Number / 2

  ENDWHILE

  // Process 2: Check for odd factors from 3 upwards

  FOR i from 3 to SQRT(Number) step 2 DO

    WHILE Number % i == 0 DO

      PRINT i

      Number = Number / i

    ENDWHILE

  ENDFOR

  // Process 3: Handle the case where Number is a prime > 2

  IF Number > 2 THEN

    PRINT Number

  ENDIF

END