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Visual Guide to Understanding Algorithms

This book provides a visual guide to understanding fundamental algorithms and data structures, focusing on common techniques for problem-solving. Learn how to implement core algorithms yourself.

• Implement efficient algorithms to solve everyday problems.
• Grasp complex algorithm concepts that are applicable across various programming languages.
• Gain a deeper understanding of computer science fundamentals.
• Improve your problem-solving skills.

Core Content:

1. Divide and Conquer (D&C)

• D&C is a powerful strategy for problem-solving that involves breaking a problem down into smaller, more manageable subproblems.

• Explanation:

  • Recursively reduce the problem until it reaches a base case that can be directly solved.
  • Combine the solutions of the subproblems to solve the original problem.

2. Quick Sort

• One of the essential sorting algorithm
• Explanation:
  • Quicksort uses D&C strategy
  • Pick an element, called pivot, from the list.
  • Reorder the list so that all elements with values less than the pivot come before the pivot.
  • Recursively sort the sub-list of lesser elements and the sub-list of greater elements.

3. Key Steps for D&C:

• Identify the Base Case: Determine the simplest form of the problem that can be directly solved.

  • Explanation: *For example, if the area is divided into two, you can get two squares.

• Reduce the Problem: Define how to break down the original problem into smaller subproblems that are easier to manage.

  • Explanation: *For example, if the area is not a correct square, we can eliminate most of its part and leave the last part as a new calculating target.

4. Euclid's Algorithm*

• Explanation:
  • Khan Academy's Euclidean Algorithm Tutorial
  • Link: https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm

Q&A:

Q: What is Divide and Conquer (D&C)?

A: D&C is a strategy that breaks a problem into subproblems, solves them recursively, and then combines the solutions to solve the original problem.

Q: Why use D&C for problem-solving?

A: D&C turns an unsolvable situation into sub-solvable questions. It is very helpful for problem thinking.

Q: Should I Know Euclidean Algorithm well?

A: If you want to know why the cutting strategy is the best, please study the Euclidean Algorithm.