Identifying Computing Problems

Definition

  • In computer science, a computing problem is a challenge or situation that needs to be overcome using computation.
  • It is solved step-by-step using computation.
  • Can include any type of calculation such as arithmetical or logical.
  • Usually has a well-defined input and some desired properties that output must satisfy.

Types of Computing Problems

1. Decision Problems

  • Requires a binary response (Yes/No, True/False)
  • Can be simple or complex, involving multiple decision factors and criteria
  • Examples:
    • Determining if a given number is odd or even
    • Checking if a given number is prime
    • Finding if there's any occurrence of "aa" in a sequence of English alphabets

2. Search Problems

  • Common in science and engineering
  • Involves searching for a solution among a set of objects
  • Often represented using graphs with nodes and links
  • Key components:
    • Initial State: Starting point of the search
    • Operations: Moves to transition between nodes
    • Goal: Target or end condition
  • Example: Route Finding Problem
    • Finding a path between two cities in a graph representing a map
    • Nodes represent cities, links represent routes between cities

3. Counting Problems

  • Based on the principle of combinations
  • If event A has X choices and event B has Y choices, total possible combinations = X * Y
  • Example:
    • Calculating possible outfit combinations from a set of shirts and pants
    • Solution: Total combinations = (number of shirts) * (number of pants)

Real-world Applications

  • Google Maps
    • An example of a search problem application
    • Finds optimal routes between locations
  • Computer System Configuration
    • A more complex counting problem
    • Example: Choosing components for a computer system
      • 4 monitors, 2 keyboards, 4 computers, 3 printers
      • Total possible combinations = 4 * 2 * 4 * 3 = 96

Problem-Solving Approach

  • Identify the type of problem (Decision, Search, or Counting)
  • Define the inputs and desired outputs
  • Break down the problem into smaller steps or components
  • Apply appropriate algorithms or methods based on the problem type
  • Verify the solution against the desired properties or constraints