5 Efficient Ways to Calculate Prefix Sums in a Python List

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💡 Problem Formulation: Calculating prefix sums involves creating a new list where the ith element is the sum of all elements up to the ith position in the input list. For instance, given the input list [3, 4, 2, 6], the desired output for the prefix sums would be [3, 7, 9, 15].

Method 1: Iterative Approach

Using an iterative approach to compute prefix sums involves initializing an empty list and appending the cumulative sum of elements up to the current index. This method is straightforward and easy to understand, making it great for beginners.

Here’s an example:

def prefix_sum_iterative(input_list):
    prefix_sums = []
    current_sum = 0
    for number in input_list:
        current_sum += number
        prefix_sums.append(current_sum)
    return prefix_sums

# Example usage:
print(prefix_sum_iterative([3, 4, 2, 6]))

Output: [3, 7, 9, 15]

This code snippet defines a function prefix_sum_iterative() which takes a list as input and returns a new list containing the prefix sums. Inside the function, we iterate over the input list, maintaining a running total which we append to our result list at each step.

Method 2: Using Python’s accumulate() Function

The accumulate() function in Python’s itertools module provides an elegant and concise way to compute prefix sums. Its primary strength lies in its simplicity and Python’s built-in efficiency.

Here’s an example:

from itertools import accumulate

# Example usage:
prefix_sums = list(accumulate([3, 4, 2, 6]))
print(prefix_sums)

Output: [3, 7, 9, 15]

The accumulate() function does all the heavy-lifting here. We simply pass our input list to it and convert the resulting iterator to a list before printing. This single line of code replaces the need for manual iteration and sum accumulation.

Method 3: List Comprehension with sum()

This method leverages list comprehension to create prefix sums. It’s a Pythonic way to do it in a single line, but it is less efficient for longer lists as it recalculates the sum every time.

Here’s an example:

input_list = [3, 4, 2, 6]
prefix_sums = [sum(input_list[:i+1]) for i in range(len(input_list))]
print(prefix_sums)

Output: [3, 7, 9, 15]

This one-liner uses list comprehension to iterate over indices in the input list and calculates the sum up to each index. This method is not recommended for larger lists as the computational complexity increases with the size of the list, since it does not utilize the previously computed sums.

Method 4: Using NumPy Library

If working within a numerical computing context, using the NumPy library can provide a very fast and efficient way to calculate prefix sums due to its optimized C backend.

Here’s an example:

import numpy as np

input_list = np.array([3, 4, 2, 6])
prefix_sums = np.cumsum(input_list)
print(prefix_sums)

Output: [ 3 7 9 15]

The np.cumsum() function is a part of the NumPy library and computes the cumulative sum of array elements. After converting the input list to a NumPy array, np.cumsum() can be used to get the prefix sums. This method is ideal for large datasets or when working within the NumPy ecosystem.

Bonus One-Liner Method 5: Reduce with Lambda Function

For fans of functional programming, Python’s reduce() function combined with a lambda can be used to compute prefix sums. It compactly captures the essence of prefix sum computation in one expressive line of code.

Here’s an example:

from functools import reduce

input_list = [3, 4, 2, 6]
prefix_sums = list(reduce(lambda acc, x: acc + [acc[-1] + x], input_list, [0])[1:])
print(prefix_sums)

Output: [3, 7, 9, 15]

The reduce() function applies a rolling computation (provided by the lambda) to the elements of the list. Starting with a list containing only the integer 0, the lambda adds the last element of the accumulated list to the current element. We slice the final result to remove the initial 0.

Summary/Discussion

  • Method 1: Iterative Approach. Easy to understand. Good for beginners. Not as elegant or as efficient as other methods.
  • Method 2: Using accumulate(). Very concise. Python’s built-in efficiency. Limited customization.
  • Method 3: List Comprehension with sum(). Pythonic. Not efficient for larger lists due to repeated sum calculations.
  • Method 4: Using NumPy Library. Highly efficient for large datasets. Requires NumPy, which is not included in Python’s standard library.
  • Method 5: Reduce with Lambda Function. Compact functional programming style. Can be less readable to those unfamiliar with reduce and lambda functions.