min_stack.py

from Stack import MyStack

class MinStack(MyStack):
    def __init__(self):
        super().__init__()
        self.__min = None
        self.__last_min_stack = MyStack()

    def push(self, value):
        if self.__last_min_stack.is_empty():
            self.__min = min(
                value, self.__min or float('inf'))
        elif value < self.__last_min_stack.top():
            self.__min = value
        if self.__min != self.__last_min_stack.top():
            self.__last_min_stack.push(self.__min)
        return super().push(value)
    
    def pop(self):
        val = super().pop()
        if not self.__last_min_stack.is_empty() and (
            val == self.__last_min_stack.top()):
            self.__last_min_stack.pop()
            self.__min = self.__last_min_stack.top()
        return val

    # Returns minimum value from newStack in O(1) Time
    def min(self):
        return self.__min