**π‘ Problem Formulation:** Python developers often need to calculate the product of the index and its value in a list and then find the sum of all these products. For instance, given `[2, 3, 4, 5]`

, the desired output is `2*0 + 3*1 + 4*2 + 5*3 = 26`

. This article elucidates various methods to achieve this calculation.

## Method 1: Using a for-loop

This method involves iterating over the list with a standard for-loop while keeping track of both the index and the value. It is simple and easy to understand, which makes it suitable for those new to Python programming.

Here’s an example:

nums = [2, 3, 4, 5] total = 0 for idx, val in enumerate(nums): total += idx * val print(total)

Output: 26

This code snippet uses the built-in `enumerate`

function to get both the index and value. The index is then multiplied with its corresponding value and added to the total sum.

## Method 2: Using list comprehension and sum()

List comprehensions provide a concise way to create lists and perform operations in Python. This method leverages list comprehension to calculate the product of the index and its value, combined with `sum()`

to get the total summation.

Here’s an example:

nums = [2, 3, 4, 5] total = sum(idx * val for idx, val in enumerate(nums)) print(total)

Output: 26

In this snippet, a list comprehension generates the list of products, and then `sum()`

function is used to sum them up, producing a clean one-liner solution.

## Method 3: Using NumPy library

For those working with numerical data in Python, using NumPy can significantly speed up calculations. The method uses NumPy arrays and vectorized operations to calculate the product of index and value and their summation efficiently.

Here’s an example:

import numpy as np nums = np.array([2, 3, 4, 5]) total = np.sum(np.arange(len(nums)) * nums) print(total)

Output: 26

This example creates a NumPy array and uses vectorized operations to multiply the indices (generated by `np.arange`

) with their corresponding values and sum them with `np.sum`

.

## Method 4: Using functools and operator modules

The `functools`

and `operator`

modules contain higher-order functions and operators as functions, respectively. Here we employ them in combination to calculate the required summation in a functional programming style.

Here’s an example:

import functools import operator nums = [2, 3, 4, 5] total = functools.reduce(operator.add, (idx * val for idx, val in enumerate(nums))) print(total)

Output: 26

The `functools.reduce()`

function is used to apply the `operator.add`

function cumulatively to the items of the iterator, which in this case is generated by a generator expression that calculates the products.

## Bonus One-Liner Method 5: Using a generator expression with sum()

For maximum conciseness, this method employs a generator expression directly inside the `sum()`

function. It’s a compact, readable one-liner perfect for simple scripts or inline calculations.

Here’s an example:

total = sum(idx * val for idx, val in enumerate([2, 3, 4, 5])) print(total)

Output: 26

This concise code snippet directly places the generator expression inside the `sum()`

function call, resulting in a succinct and efficient way to calculate the summation.

## Summary/Discussion

**Method 1:**For-loop with enumerate. Strengths: Simple and transparent. Weaknesses: Potentially less performant with large data sets.**Method 2:**List comprehension and sum(). Strengths: More Pythonic and concise. Weaknesses: Less readable for Python beginners.**Method 3:**NumPy library. Strengths: Highly efficient for large arrays. Weaknesses: Requires external library.**Method 4:**functools and operator modules. Strengths: Functional programming style, more abstract. Weaknesses: Less intuitive for those not familiar with functional programming.**Method 5:**Generator expression with sum(). Strengths: Extremely concise. Weaknesses: May be less efficient than list comprehensions for large lists due to the overhead of the generator.