# Exploring 5 Best Ways to Calculate the Cumulative Sum in Python

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π‘ 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.