Sum list

Your task is to implement a class that maintains a list of numbers and has a method that efficiently computes the sum of the numbers in a given sublist.

In a file sumlist.py, implement the class SumList with the following methods:

• append(number): add number to the end of the list
• sum(a, b): return the sum of the numbers from the position a to the position b

Both methods should work in $O(1)$ time.

class SumList:
    def __init__(self):
        # TODO

    def append(self, number):
        # TODO

    def sum(self, a, b):
        # TODO

if __name__ == "__main__":
    numbers = SumList()

    numbers.append(1)
    numbers.append(2)
    numbers.append(3)
    numbers.append(4)
    numbers.append(5)

    print(numbers.sum(0, 4)) # 15
    print(numbers.sum(1, 1)) # 2
    print(numbers.sum(1, 3)) # 9
    print(numbers.sum(2, 3)) # 7
    print(numbers.sum(0, 3)) # 10

    numbers.append(1)
    print(numbers.sum(0, 5)) # 16
    print(numbers.sum(5, 5)) # 1

Here the list content is first set to $[1,2,3,4,5]$ and then the following sublist sums are computed:

• $[1,2,3,4,5]$: sum $15$
• $[2]$: sum $2$
• $[2,3,4]$: sum $9$
• $[3,4]$: sum $7$
• $[1,2,3,4]$: sum $10$

Then the number $1$ is added to the end of the list and the following sublist sums are computed:

• $[1,2,3,4,5,1]$: sum $16$
• $[1]$: sum $1$

You can test the efficiency of your solution with the following code. In this case too the code should finish almost immediately.

    numbers = SumList()
    total = 0
    for i in range(10**5):
        numbers.append(i + 1)
        total += numbers.sum(i // 2, i)
    print(total) # 125005000050000