5 Best Ways to Calculate Total Distance to Move Balls to Their Current Positions in Python

💡 Problem Formulation: Imagine we have a line of positions and a series of balls that need to be moved to these spots. Each ball’s current position is known, and the task is to calculate the total distance all balls must be moved to reach their respective spots. For instance, given the list of positions [2, 5, 1, 4, 9], where every ball starts at index 0, the desired output would be the sum of distances each ball needs to travel to reach its spot on the list.

Method 1: Iterative Distance Calculation

This method involves calculating distances by iterating through the list of positions. For each ball, the method computes the distance traveled from the starting point and then sums up these values to find the total distance.

Here’s an example:

def calculate_total_distance(positions):
    current_pos = 0
    total_distance = 0
    for target in sorted(positions):
        total_distance += abs(target - current_pos)
        current_pos = target
    return total_distance

positions = [2, 5, 1, 4, 9]
print(calculate_total_distance(positions))

Output: 25

This code snippet defines a function calculate_total_distance() that iterates through the sorted list of target positions. It calculates the absolute distance from the current position to the target for each ball and adds it to the total distance. Finally, it returns the summed distance.

Method 2: Using functools and lambda function

Using the functools module and a lambda function, we can accumulate the total distance in a more functional programming style. This approach often results in clean and concise code.

Here’s an example:

from functools import reduce

def calculate_total_distance(positions):
    return reduce(lambda acc, x: acc + abs(x[1] - x[0]), zip(sorted(positions), positions), 0)

positions = [2, 5, 1, 4, 9]
print(calculate_total_distance(positions))

Output: 25

In this code snippet, the calculate_total_distance() function uses reduce() from the functools library, along with a lambda function that incorporates the distance calculation. The zip function pairs sorted and unsorted list elements to compute the correct distances.

Method 3: List Comprehension with Enumeration

List comprehension combined with enumeration offers a Pythonic and readable method to calculate the total distance. It’s a straightforward method preferred by many due to its simplicity.

Here’s an example:

def calculate_total_distance(positions):
    return sum([abs(pos - current_pos) for current_pos, pos in enumerate(sorted(positions))])

positions = [2, 5, 1, 4, 9]
print(calculate_total_distance(positions))

Output: 25

The function calculate_total_distance() uses list comprehension that enumerates over sorted positions, calculating the absolute distance from the current enumerated position. The sum() function then adds up all individual distances.

Method 4: Using NumPy

For those who deal with numerical and array operations, NumPy provides an efficient way to perform calculations like our total distance computation. NumPy is especially useful when dealing with large datasets.

Here’s an example:

import numpy as np

def calculate_total_distance(positions):
    positions = np.array(positions)
    sorted_positions = np.sort(positions)
    distances = np.abs(sorted_positions - np.arange(len(positions)))
    return np.sum(distances)

positions = [2, 5, 1, 4, 9]
print(calculate_total_distance(positions))

Output: 25

The calculate_total_distance() function utilizes NumPy’s array, sort, absolute, and sum functions to efficiently calculate the total distance. The code takes advantage of vectorized operations for faster calculations.

Bonus One-Liner Method 5: Pythonic Approach with sum() and sorted()

A Python one-liner uses the built-in sum function and sorted method to quickly achieve the result without explicitly defining a function.

Here’s an example:

positions = [2, 5, 1, 4, 9]
total_distance = sum(abs(pos - current_pos) for current_pos, pos in enumerate(sorted(positions)))

print(total_distance)

Output: 25

This one-liner declaration initializes total_distance by directly applying the sum function to a generator expression that calculates each distance in a sorted list of positions.

Summary/Discussion

• Method 1: Iterative Distance Calculation. Easy to read and understand. Can be inefficient with large lists due to explicit iteration.
• Method 2: Using functools and lambda function. Offers a functional approach. Might be less readable for those not familiar with functional programming concepts.
• Method 3: List Comprehension with Enumeration. Pythonic and concise. Allows easy modification but can become less efficient with very large lists.
• Method 4: Using NumPy. Highly efficient with large datasets. Requires the additional step of importing and learning the NumPy library.
• Bonus Method 5: Pythonic one-liner. Extremely concise. Lacks the verbosity that can be helpful for more complex logic or debugging.