3.2 How would you design a stack which, in addition to push and pop, also has a function min which returns the minimum element? Push, pop and min should all operate in O(1) time.

minStack.py

# idea: use another stack to store current minimum value each time a new element is pushed in. 
#       pop top values from both 2 stacks when doing pop operation
# time complexity: O(1)
# space complexity: O(n)

class myStack:
    def __init__(self):
        self.__array = []
        self.__min = []
        self.__topIndex = -1
        

    def pop(self):
        if self.__topIndex == -1:
            print 'no element to pop'
            return

        self.__array.pop(self.__topIndex)
        self.__min.pop(self.__topIndex)
        self.__topIndex -= 1

    def push(self, element):
        if self.__topIndex == -1 or element <= self.__min[self.__topIndex]:
            self.__min.append(element)
        else:
            self.__min.append(self.__min[self.__topIndex])
            
        self.__array.append(element)
        self.__topIndex += 1

    def min(self, order):
        if self.__topIndex == -1:
            print 'no element exists'
            return -1

        return self.__min[self.__topIndex]