Exploring 5 Best Ways to Calculate the Cumulative Sum in Python

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πŸ’‘ Problem Formulation: We often require to process lists in a way to obtain progressive totals. Imagine having a list of numbers, and you want to find a new list where each element is the sum of all previous elements in the original list, including itself. For example, given [1, 2, 3, 4], the cumulative sum would yield [1, 3, 6, 10].

Method 1: Using the accumulate() Function from the itertools Module

The accumulate() function from the itertools module continuously applies a function (by default, addition) and yields accumulated results. This method is straightforward and efficient, especially suitable for large lists.

Here’s an example:

from itertools import accumulate

original_list = [1, 2, 3, 4]
cumulative_sum = list(accumulate(original_list))

print(cumulative_sum)

The output of this code is: [1, 3, 6, 10]

This method takes the original list and calculates the cumulative sum using the accumulate() function which makes the code clean and expressive. It handles the iteration and summation internally and produces the result in a single line of readable code.

Method 2: Using a Loop to Manually Accumulate Sums

Manually iterating through the list and summing elements is a simple technique that doesn’t require importing any additional libraries. This is a basic approach that demonstrates the underlying mechanism of cumulative summing.

Here’s an example:

original_list = [1, 2, 3, 4]
cumulative_sum = []
current_sum = 0

for number in original_list:
    current_sum += number
    cumulative_sum.append(current_sum)

print(cumulative_sum)

The output of this code is: [1, 3, 6, 10]

In this snippet, we initialize a variable to keep track of the ongoing sum and a new list to store the results. As we iterate through each number in the original list, we update the sum and append it to the cumulative sum list.

Method 3: Using List Comprehension with the sum() Function

Python’s list comprehension combined with the sum() function can be used to produce the cumulative sum in a more Pythonic way. This method is compact and can be written in a single line.

Here’s an example:

original_list = [1, 2, 3, 4]
cumulative_sum = [sum(original_list[:i+1]) for i in range(len(original_list))]

print(cumulative_sum)

The output of this code is: [1, 3, 6, 10]

This one-liner uses a list comprehension to iterate through the indices of the original list and applies the sum() function to slices of the list up to the current index, inclusively.

Method 4: Using a Loop with enumerate()

In this approach, we use the built-in enumerate() function to keep track of both index and the elements of the list. This technique is preferable when you want to avoid manual index management.

Here’s an example:

original_list = [1, 2, 3, 4]
cumulative_sum = []
current_sum = 0

for index, number in enumerate(original_list):
    current_sum += number
    cumulative_sum.append(current_sum)

print(cumulative_sum)

The output of this code snippet is: [1, 3, 6, 10]

The enumerate() function simplifies tracking the current number and its index, aiding clarity when accessing elements during iteration.

Bonus One-Liner Method 5: Using NumPy’s cumsum() Function

If you are working within a scientific computing context or handling numerical data, utilizing NumPy’s cumsum() function can be exceptionally efficient. This is particularly beneficial when dealing with large datasets.

Here’s an example:

import numpy as np

original_list = [1, 2, 3, 4]
cumulative_sum = np.cumsum(original_list)

print(cumulative_sum)

The output of this code snippet is: [1 3 6 10]

NumPy’s cumsum() function is optimized for performance and is the go-to method for numerical calculations in Python. This is the most concise and performant method for those who already use NumPy for data processing.

Summary/Discussion

  • Method 1: itertools.accumulate(). Strengths: Simple, concise, part of the standard library. Weaknesses: May be less intuitive for beginners.
  • Method 2: Loop with Manual Sum. Strengths: Easy to understand, no external dependencies. Weaknesses: Verbose, potentially slow for large lists.
  • Method 3: List Comprehension with sum(). Strengths: Pythonic, one-liner. Weaknesses: Inefficient due to repeated summation.
  • Method 4: Loop with enumerate(). Strengths: Clear index and element tracking. Weaknesses: Similar to Method 2 with a slight improvement in readability.
  • Method 5: NumPy’s cumsum(). Strengths: Highly efficient for numerical and large data sets. Weaknesses: Requires NumPy, which is an external library.