Max list

Your task is to implement a class that maintains a list of numbers and has a method for efficiently finding the largest number on the list.

In a file maxlist.py, implement the class MaxList with the following methods:

• append(number): add a number to the end of the list
• max(): return the largest number

You may assume that the list has at least one number when the method max is called. Both methods should work efficiently in $O(1)$ time.

class MaxList:
    def __init__(self):
        # TODO

    def append(self, number):
        # TODO

    def max(self):
        # TODO

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

    numbers.append(1)
    numbers.append(2)
    numbers.append(3)
    print(numbers.max()) # 3

    numbers.append(8)
    numbers.append(5)
    print(numbers.max()) # 8

Here the elements $1$, $2$ and $3$ are first added to the list so that the list content is $[1,2,3]$ and the largest number is $3$. Then the numbers $8$ and $5$ are added to the list resulting in the content $[1,2,3,8,5]$ and the largest number $8$.

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

    numbers = MaxList()
    total = 0
    for i in range(10**5):
        numbers.append(i * 999983 % 10**9)
        total += numbers.max()
    print(total) # 99498381797517