Exercise: Cumulative Sums

Background/Motivation

A cumulative sum (also known as a prefix sum) is a sequence of partial sums of a given sequence. For example, the cumulative sums of the sequence ${a, b, c, \dots}$ are ${a, a+b, a+b+c, \dots}$. This is a fundamental technique used in competitive programming and data analysis to quickly calculate the sum of any sub-range of a list in $O(1)$ time after a one-time $O(n)$ preprocessing step.

The Task

Implement a function prefix_sums(numbers: list[int]) -> list[int] that takes a list of integers and returns a new list where each element at index $i$ is the sum of all elements from the original list from index $0$ to $i$.

Specifications

Function Name: prefix_sums
Arguments: numbers (list of integers)
Return Type: list[int]
Expected Output: A list of the same length containing the cumulative sums.

Constraints

$0 \le \text{len(numbers)} \le 10^5$
Elements are integers within the range $[-10^9, 10^9]$.

Example

>>> prefix_sums([1, 2, 3])
[1, 3, 6]
>>> prefix_sums([10, -10, 5])
[10, 0, 5]

Instructions

Open exercises/prefix_sums/solution.py.
Implement the prefix_sums function.
Change SUBMIT = False to SUBMIT = True at the top of the file when you are ready to be graded.
Run python solution.py locally to verify your solution with the built-in self-tests.