5 Best Ways to Calculate Total Distance to Visit City Blocks in Python

💡 Problem Formulation: Suppose we want a program that can calculate the total walking distance required to visit a sequence of city blocks laid out in a grid. Given a list of (x, y) tuples representing the coordinates of each block, the program should return the total Manhattan distance needed to travel between the blocks sequentially. For example, inputting [(0, 0), (1, 3), (2, 2)] should output 4, which is the distance from (0, 0) to (1, 3) plus the distance from (1, 3) to (2, 2).

Method 1: Iterative Pairwise Distance Calculation

A straightforward approach to calculate the total distance is by iterating through pairs of consecutive blocks and summing up the differences in their x and y coordinates, which represent the distances on a city grid. This method directly implements the Manhattan distance computation in a sum that loops over the list of coordinates.

Here’s an example:

def calculate_total_distance(blocks):
    total_distance = 0
    for i in range(len(blocks) - 1):
        total_distance += abs(blocks[i+1][0] - blocks[i][0]) + abs(blocks[i+1][1] - blocks[i][1])
    return total_distance

blocks = [(0, 0), (1, 3), (2, 2)]
print(calculate_total_distance(blocks))

Output:

This code snippet defines a function calculate_total_distance that takes a list of coordinate tuples. It uses a for loop to iterate through the list and calculate the horizontal and vertical distances between each pair of consecutive blocks,summing them up to calculate the total distance.

Method 2: Using a Zip and List Comprehension

Python’s zip function can be used in combination with a list comprehension to calculate the distance in a more concise and Pythonic way. This method improves readability by eliminating the need for explicitly indexing the list of coordinates.

Here’s an example:

def calculate_total_distance(blocks):
    return sum(abs(x1 - x0) + abs(y1 - y0) for (x0, y0), (x1, y1) in zip(blocks, blocks[1:]))

blocks = [(0, 0), (1, 3), (2, 2)]
print(calculate_total_distance(blocks))

Output:

In this snippet, the calculate_total_distance function uses a list comprehension that pairs each block with its successor using zip. The Manhattan distances are computed within the comprehension and then summed up, resulting in a clean and efficient one-liner computation of the total distance.

Method 3: Using the itertools.starmap Function

The itertools library in Python provides a function starmap that, together with a lambda function, can map the Manhattan distance calculation over each tuple of consecutive blocks. This method is useful for those familiar with functional programming concepts.

Here’s an example:

import itertools

def calculate_total_distance(blocks):
    return sum(itertools.starmap(lambda x0, y0, x1, y1: abs(x1 - x0) + abs(y1 - y0), zip(blocks, blocks[1:])))

blocks = [(0, 0), (1, 3), (2, 2)]
print(calculate_total_distance(blocks))

Output:

This code uses itertools.starmap to apply a lambda function that calculates the distance between two points, to each pair of consecutive blocks. These distances are then summed to obtain the total distance.

Method 4: Using NumPy Arrays

For those dealing with a large set of coordinates or looking for performance optimization, NumPy arrays facilitate vectorized operations. This method takes advantage of NumPy’s efficient array computation capabilities.

Here’s an example:

import numpy as np

def calculate_total_distance(blocks):
    points = np.array(blocks)
    return np.sum(np.abs(np.diff(points, axis=0)))

blocks = [(0, 0), (1, 3), (2, 2)]
print(calculate_total_distance(blocks))

Output:

The function calculate_total_distance converts the list of tuples into a NumPy array. It then uses np.diff to compute the difference between successive points, applying the Manhattan distance principle. The total distance is obtained by summing the absolute values of these differences using np.sum.

Bonus One-Liner Method 5: Functional One-Liner with map and lambda

For a functional programming flair, one can combine the built-in map and lambda to calculate the total distance. This one-liner is succinct but requires understanding of lambda functions and the map operation.

Here’s an example:

blocks = [(0, 0), (1, 3), (2, 2)]
total_distance = sum(map(lambda b1, b2: abs(b2[0] - b1[0]) + abs(b2[1] - b1[1]), blocks[:-1], blocks[1:]))
print(total_distance)

Output:

The one-liner uses map to apply a lambda function that calculates the Manhattan distance to the pairs of blocks obtained by slicing the list. The sum function captures the total distance as the final output.

Summary/Discussion

• Method 1: Iterative Pairwise. Straightforward and easy to understand. Not the most pythonic or concise.
• Method 2: Zip with List Comprehension. More concise and pythonic. Requires familiarity with zip and list comprehensions.
• Method 3: itertools.starmap. Functional approach that is clean but may be less intuitive for those not comfortable with functional programming.
• Method 4: Using NumPy Arrays. Best for performance and large datasets. Requires NumPy installation and familiarity with its operations.
• Method 5: Functional One-Liner. Extremely concise. Potentially tricky for those not well-versed in lambda and map functions.