Change list

Your task is to implement a class that maintains a list of numbers and has a method for efficiently incrementing all elements of the list by a given amount.

In a file changelist.py, implement the class ChangeList with the following methods:

• append(number): add number to the end of the list
• get(index): access a number on the list
• change_all(amount): increment all list numbers by amount

In the method change_all, the parameter amount can be negative too, in which case all numbers are decremented. All methods should work in $O(1)$ time.

class ChangeList:
    def __init__(self):
        # TODO

    def append(self, number):
        # TODO

    def get(self, index):
        # TODO

    def change_all(self, amount):
        # TODO

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

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

    print(numbers.get(0)) # 1
    print(numbers.get(1)) # 2
    print(numbers.get(2)) # 3

    numbers.change_all(2)
    print(numbers.get(0)) # 3
    print(numbers.get(1)) # 4
    print(numbers.get(2)) # 5

    numbers.append(8)
    numbers.change_all(-1)
    print(numbers.get(0)) # 2
    print(numbers.get(1)) # 3
    print(numbers.get(2)) # 4
    print(numbers.get(3)) # 7

Here the numbers $1$, $2$ and $3$ are first added to the list, after which the list contents are $[1,2,3]$. Then all numbers are incremented by $2$, after which the list contents are $[3,4,5]$. Finally, the number $8$ is added to the list and all numbers are changed by $-1$, after which the list contents are $[2,3,4,7]$.

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

    numbers = ChangeList()
    total = 0
    for i in range(10**5):
        numbers.append(i + 1)
        numbers.change_all(i % 11 - 5)
        total += numbers.get(i // 2)
    print(total) # 2500049970