I'm Walking Around Manhattan, How Far Am I From My Hotel?

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The Unnecessary and Convoluted Story

As I walked around Manhattan, block by block, my feet had gotten tired and I yearned to return home. The traffic was pretty bad, but fortunately, I was very rich and had a personal helicopter at my disposal. However, I was in a philosophical mood and decided to take a stroll around the city instead. I had a peculiar question in mind - how far was I from my hotel? I had no idea, but I was determined to find out.

The Problem

Given my current location in Manhattan, I wanted to calculate the distance from my current position to my hotel. I knew that Manhattan is a grid-like city, with streets and avenues intersecting at right angles. I also knew that the distance between two points in a grid can be calculated using the Manhattan distance formula, also known as the L1 distance or the taxicab distance.

The Manhattan Distance Formula

The Manhattan distance formula is given by:

d = |x2 - x1| + |y2 - y1|

where (x1, y1) is my current location and (x2, y2) is the location of my hotel.

The Code

Here is a simple Python function that calculates the Manhattan distance between two points in Manhattan:

def manhattan_distance(x1, y1, x2, y2):
    """
    Calculate the Manhattan distance between two points in Manhattan.

Parameters:
x1 (int): The x-coordinate of the first point.
y1 (int): The y-coordinate of the first point.
x2 (int): The x-coordinate of the second point.
y2 (int): The y-coordinate of the second point.

Returns:
int: The Manhattan distance between the two points.
"""
return abs(x2 - x1) + abs(y2 - y1)

The Challenge

The challenge is to write a function that takes my current location and the location of my hotel as input, and returns the Manhattan distance between the two points. However, there's a catch - I'm a code golfer, and I want to write the shortest possible code that solves the problem.

The Solution

Here is a solution in Python that uses the abs function to calculate the Manhattan distance:

f=lambda x1,y1,x2,y2:abs(x2-x1)+abs(y2-y1)

This solution is much shorter than the previous one, but it's still readable and easy to understand.

The Explanation

The f function takes four arguments: x1, y1, x2, and y2. It uses the abs function to calculate the absolute difference between x2 and x1, and between y2 and y1. The two results are then added together to give the Manhattan distance.

The Example Use Case

Here is an example use case for the f function:

print(f(1, 1, 3, 4))  # Output: 6

In this example, the f function is called with the arguments 1, 1, 3, and 4. The function returns the Manhattan distance between the points (1, 1) and (3, 4), which is 6.

The Conclusion

In conclusion, the Manhattan distance formula is a simple and efficient way to calculate the distance between two points in a grid-like city like Manhattan. The f function is a concise and readable solution to the problem, and it can be used to calculate the Manhattan distance between any two points in Manhattan.

The Future Work

In the future, I plan to explore other ways to calculate the Manhattan distance, such as using a more efficient algorithm or a different programming language. I also plan to apply the Manhattan distance formula to other problems, such as calculating the distance between two points in a 3D space or a non-grid-like city.

The Final Thoughts

Q: What is the Manhattan distance formula?

A: The Manhattan distance formula is a simple and efficient way to calculate the distance between two points in a grid-like city like Manhattan. It is given by:

d = |x2 - x1| + |y2 - y1|

where (x1, y1) is the current location and (x2, y2) is the location of the hotel.

Q: How do I use the Manhattan distance formula?

A: To use the Manhattan distance formula, you need to know the coordinates of your current location and the location of your hotel. You can then plug these values into the formula to calculate the distance between the two points.

Q: What is the difference between the Manhattan distance and the Euclidean distance?

A: The Manhattan distance and the Euclidean distance are two different ways to calculate the distance between two points. The Manhattan distance is the sum of the absolute differences in the x and y coordinates, while the Euclidean distance is the square root of the sum of the squares of the differences in the x and y coordinates.

Q: When should I use the Manhattan distance formula?

A: You should use the Manhattan distance formula when you are working with grid-like cities or when you need to calculate the distance between two points in a city with a grid-like layout.

Q: Can I use the Manhattan distance formula in other cities?

A: Yes, you can use the Manhattan distance formula in other cities, but you need to make sure that the city has a grid-like layout. If the city does not have a grid-like layout, you may need to use a different formula to calculate the distance between two points.

Q: How do I calculate the Manhattan distance in a 3D space?

A: To calculate the Manhattan distance in a 3D space, you need to use the following formula:

d = |x2 - x1| + |y2 - y1| + |z2 - z1|

where (x1, y1, z1) is the current location and (x2, y2, z2) is the location of the hotel.

Q: Can I use the Manhattan distance formula in a non-grid-like city?

A: No, you cannot use the Manhattan distance formula in a non-grid-like city. The Manhattan distance formula is designed to work with grid-like cities, and it will not give accurate results in a non-grid-like city.

Q: What are some real-world applications of the Manhattan distance formula?

A: The Manhattan distance formula has many real-world applications, including:

  • Calculating the distance between two points in a city with a grid-like layout
  • Determining the shortest path between two points in a grid-like city
  • Calculating the distance between two points in a 3D space
  • Determining the shortest path between two points in a 3D space

Q: Can I use the Manhattan distance formula in a programming language?

A: Yes, you can use the Manhattan distance formula in a programming language. Here is an example of how to calculate the Manhattan distance in Python:

def manhattan_distance(x1, y1, x2, y2):
    return abs(x2 - x1) + abs(y2 - y1)

Q: What are some common mistakes to avoid when using the Manhattan distance formula?

A: Some common mistakes to avoid when using the Manhattan distance formula include:

  • Using the formula in a non-grid-like city
  • Not taking into account the absolute differences in the x and y coordinates
  • Not using the correct formula for calculating the distance in a 3D space

Q: Can I use the Manhattan distance formula in a real-world scenario?

A: Yes, you can use the Manhattan distance formula in a real-world scenario. For example, you can use it to calculate the distance between two points in a city with a grid-like layout, or to determine the shortest path between two points in a grid-like city.