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

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π‘ 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])

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

Output:

`4`

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:

`4`

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:

`4`

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:

`4`

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:

`4`

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.