Electronique industrielle

chessboard distance

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Test Your Knowledge

Chessboard Distance Quiz

Instructions: Choose the best answer for each question.

1. What is the chessboard distance between the points (2, 3) and (5, 1) on a 2-dimensional integer lattice?

a) 2

Answer

Incorrect

b) 3

Answer

Correct

c) 4

Answer

Incorrect

d) 5

Answer

Incorrect

2. In which of the following electrical engineering applications is chessboard distance NOT directly relevant?

a) Detecting edges in an image.

Answer

Incorrect

b) Analyzing the frequency spectrum of a signal.

Answer

Correct

c) Finding the shortest path for a robot in a grid-based environment.

Answer

Incorrect

d) Identifying potential faults in a power grid.

Answer

Incorrect

3. What is the key difference between the chessboard distance and the Euclidean distance?

a) Chessboard distance is always greater than Euclidean distance.

Answer

Incorrect

b) Chessboard distance considers only the maximum difference between coordinates, while Euclidean distance considers the sum of squared differences.

Answer

Correct

c) Chessboard distance is used for continuous spaces, while Euclidean distance is used for discrete spaces.

Answer

Incorrect

d) Chessboard distance is more computationally intensive than Euclidean distance.

Answer

Incorrect

4. What is the chessboard distance between the points (1, 2, 3) and (4, 1, 5) in a 3-dimensional integer lattice?

a) 3

Answer

Correct

b) 4

Answer

Incorrect

c) 5

Answer

Incorrect

d) 6

Answer

Incorrect

5. Which of the following best describes the significance of the chessboard distance in electrical engineering?

a) It provides a complex measure of distance between points in multi-dimensional spaces.

Answer

Incorrect

b) It offers a simple and efficient way to measure distance between discrete points in various applications.

Answer

Correct

c) It is essential for understanding continuous signals and their transformations.

Answer

Incorrect

d) It is primarily used for theoretical analysis and has limited practical applications.

Answer

Incorrect

Chessboard Distance Exercise

Task: Imagine a simple 2D grid representing a robotic arm's workspace. The arm's current position is (2, 3), and it needs to reach a target point at (5, 1).

1. Calculate the chessboard distance between the current position and the target position.

2. Using the chessboard distance, outline a possible shortest path the robot arm could take to reach the target.

3. Explain how this path would be different from the shortest path calculated using Euclidean distance.

Exercice Correction

**1. Chessboard distance:** * The difference in x-coordinates is |2 - 5| = 3 * The difference in y-coordinates is |3 - 1| = 2 * The maximum difference is 3. Therefore, the chessboard distance is 3. **2. Shortest path using chessboard distance:** * The robot arm can move three steps horizontally to the right (from (2, 3) to (5, 3)) and then two steps vertically downwards (from (5, 3) to (5, 1)). **3. Difference from Euclidean distance:** * The Euclidean distance between the points would be calculated using the formula: √((5-2)² + (1-3)²) = √(9 + 4) = √13 ≈ 3.61. * The shortest path using Euclidean distance would involve diagonal movements, resulting in a more curved path. The chessboard distance focuses on moving along grid lines, leading to a "blocky" path that may not be the most visually direct but is optimal in terms of the number of steps required.


Books

  • "Concrete Mathematics: A Foundation for Computer Science" by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik: This book covers a wide range of mathematical topics, including combinatorial analysis, where the chessboard distance is discussed in relation to the Manhattan distance.
  • "Introduction to Algorithms" by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein: This classic algorithms textbook presents various distance metrics, including the chessboard distance, in the context of graph theory and pathfinding algorithms.

Articles

  • "Chessboard Distance and Its Applications" by [Author Name] (if available): This could be a relevant article specifically discussing the concept and applications of chessboard distance.
  • "Efficient Algorithms for Computing the Chessboard Distance" by [Author Name] (if available): This article could explore different algorithms and data structures for calculating chessboard distance effectively.

Online Resources

  • Wikipedia Page on Manhattan Distance: While not specifically about chessboard distance, the Manhattan distance is closely related and provides a good overview of similar concepts. Link to Wikipedia Page
  • Stack Overflow Discussions: Search for terms like "chessboard distance," "king's movement," or "distance metrics" on Stack Overflow to find related discussions and code examples.
  • MathWorld: Chessboard Distance: Search for "chessboard distance" on MathWorld to potentially find relevant definitions and explanations.
  • Blog Posts and Tutorials: Search for "chessboard distance" or "king's movement" on popular coding blogs and educational websites to find explanations and practical implementations.

Search Tips

  • Specific Terms: Use precise keywords like "chessboard distance," "king's move distance," "maximum difference distance," or "city block distance" to narrow down your search.
  • "Intitle:" Operator: Use "intitle:chessboard distance" to find articles where "chessboard distance" appears in the title.
  • "Site:" Operator: Use "site:wikipedia.org chessboard distance" to search for related content on Wikipedia.
  • Combine Keywords: Use phrases like "chessboard distance applications" or "chessboard distance algorithm" to find relevant resources.

Techniques

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