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