Write a program to form a cumulative sum list in Python

The cumulative sum till i^th element refers to the total sum from 0^th to i^th element. We need to form a new list where each element represents the running total up to that position.

For example, if we have [10, 20, 30, 40, 50], the cumulative sum list would be [10, 30, 60, 100, 150].

Example Input and Output

Example 1

Input: [10, 20, 30, 40, 50]

Output: [10, 30, 60, 100, 150]

Example 2

Input: [1, 2, 3, 4, 5]

Output: [1, 3, 6, 10, 15]

Using a Custom Function

We can create a function that iterates through the list and maintains a running sum ?

def cumSum(numbers):
    sm = 0
    cum_list = []
    for i in numbers:
        sm = sm + i
        cum_list.append(sm)
    return cum_list

a = [10, 20, 30, 40, 50]
print("Original list:", a)
print("Cumulative sum:", cumSum(a))

b = [1, 2, 3, 4, 5]
print("Original list:", b)
print("Cumulative sum:", cumSum(b))

Original list: [10, 20, 30, 40, 50]
Cumulative sum: [10, 30, 60, 100, 150]
Original list: [1, 2, 3, 4, 5]
Cumulative sum: [1, 3, 6, 10, 15]

Using List Comprehension

A more compact approach using list comprehension with sum() and slicing ?

numbers = [10, 20, 30, 40, 50]
cumulative = [sum(numbers[:i+1]) for i in range(len(numbers))]
print("Original list:", numbers)
print("Cumulative sum:", cumulative)

Original list: [10, 20, 30, 40, 50]
Cumulative sum: [10, 30, 60, 100, 150]

Using itertools.accumulate()

Python's itertools.accumulate() function provides a built-in solution ?

import itertools

numbers = [10, 20, 30, 40, 50]
cumulative = list(itertools.accumulate(numbers))
print("Original list:", numbers)
print("Cumulative sum:", cumulative)

Original list: [10, 20, 30, 40, 50]
Cumulative sum: [10, 30, 60, 100, 150]

How It Works

The algorithm maintains a running sum:

• Initialize an empty result list and sum variable to 0

• Iterate through each element in the input list

• Add the current element to the running sum

• Append the running sum to the result list

• Return the cumulative sum list

Comparison

Conclusion

Use itertools.accumulate() for the most efficient and readable solution. The custom function approach is best for learning the underlying logic, while list comprehension offers a compact but less efficient alternative.