Chapter 1

Algorithms

Objectives

• Understanding the concept of an algorithm.

• Exploring various examples of algorithms.

• Distinguishing between actions and control statements in algorithms.

• Examining the differences between algorithms designed for human understanding versus those for computer execution.

• Understanding the process by which an algorithm transforms into a computer program.

• Clarifying the distinction between problems and algorithms.

What is an Algorithm?

• Definition: An algorithm is defined as an ordered list of actions designed to solve a specific problem or perform a particular task.

Example 1: Making Ramen

1. Boil water.

2. Add noodles to the boiling water.

3. Wait 6-8 minutes.

4. Drain the noodles.

5. Stir in contents of flavor packet.

6. Place cooked noodles in a bowl.

Actions in Algorithms

• An algorithm is characterized by a sequence of actions that must be adhered to for it to function correctly.

Requirements for Actions:

1. Imperative: Each action must be phrased as a clear command instructing what to do.

2. Feasible: The action must be executable by the intended recipient (e.g., a child, adult, or computer).

3. Self-explanatory: Each action must be easily understandable without requiring additional explanation to execute.

Recipient Considerations:

• The effectiveness of an action in an algorithm is contingent upon the capabilities of the recipient (e.g., whether it’s a human or a computer).

  • Example: The action "Sort the list of numbers in ascending order"

  • Feasible for a computer or trained programmer.

  • Not feasible for a child who may not have the ability to compare numbers or understand the sorting process.

Control Flow of Algorithms

• Example Algorithm: PlayJenga

  1. Stack the blocks to form a tower.

  2. Choose a current player.

  3. While the tower of blocks is still standing:

  • Current player takes a block from the middle.

  • Current player puts the block on top of the tower.

  • If the tower is still standing:

    • Make the other player the current player.

  1. The current player loses if the tower falls.

Methods of Writing Algorithms

• Natural Language: Allows for a more conversational style but may lack precision.

• Pseudocode: A structured format that combines natural language and programming concepts, providing a clear outline.

• Programming Language: Utilized for implementation in computer programs; follows specific syntax and rules.

• Images and Visual Instructions: Utilizes diagrams or visuals to convey the steps involved in an algorithm.

Algorithms for Humans vs Algorithms for Computers

Problems vs. Algorithms

• Problems:

  • Definition: Represents a task that requires execution.

  • Description: There may be multiple algorithms available to address a specific problem.

• Algorithms:

  • Definition: A specific and structured set of steps designed to carry out a task.

  • Description: Each algorithm provides a solution to only one defined problem.