from _DoublyLinkedBase import _DoublyLinkedBase
class PositionalList(_DoublyLinkedBase):
    """A sequential container of elements allowing positional access."""

    class Position:
        """An abstraction representing the location of a single element."""

        def __init__(self, container, node):
            """Constructor should not be invoked by user."""
            self._container = container
            self._node = node

        def element(self):
            """Return the element stored at this Position."""
            return self._node._element

        def __eq__(self, other):
            """Return True if other is a Position representing the same location."""
            return type(other) is type(self) and other._node is self._node

        def __ne__(self, other):
            """Return True if other does not represent the same location."""
            return not (self == other)

    def _validate(self, p):
        """Return position's node, or raise appropiate error if invalid."""
        if not isinstance(p, self.Position):
            raise TypeError('p must be proper Position type')
        if p._container is not self:
            raise ValueError('p does not belong to this container')
        if p._node._next is None:
            raise ValueError('p is no longer valid')
        return p._node

    def _make_position(self, node):
        """Return Position instance for given node (or None if sentinel)."""
        if node is self._header or node is self._trailer:
            return None
        else:
            return self.Position(self, node)

    def first(self):
        """Return the first Position in the list (or None if list is empty)."""
        return self._make_position(self._header._next)

    def last(self):
        """Return the last Position in the list (or None if list is empty)."""
        return self._make_position(self._trailer._prev)

    def before(self, p):
        """Return the Position just before Position p (or None if p is first)."""
        node = self._validate(p)
        return self._make_position(node._prev)

    def after(self, p):
        """Return the Position just after Position p (or None if p is last)."""
        node = self._validate(p)
        return self._make_position(node._next)

    def __iter__(self):
        """Generate a forward iteration of the elements of the list."""
        cursor = self.first()
        while cursor is not None:
            yield cursor.element()
            cursor = self.after(cursor)

    def _insert_between(self, e, predecessor, sucessor):
        """Add element between existing nodes and return new Position."""
        node = super()._insert_between(e, predecessor, sucessor)
        return self._make_position(node)

    def add_first(self, e):
        """Insert element e at the front of the list and return new Position."""
        return self._insert_between(e, self._header, self._header._next)

    def add_last(self, e):
        """Insert element e at the back of the list and return new Position."""
        return self._insert_between(e, self._trailer._prev, self._trailer)

    def add_before(self, e):
        """Insert element e into list before Position p and return new Position."""
        original = self._validate(p)
        return self._insert_between(e, original._prev, original)

    def add_after(self, p, e):
        """Insert element e into list after Position p and return new Position."""
        original = self._validate(p)
        return self._insert_between(e, original, original._next)

    def delete(self, p):
        """Remove and return the element at Position p."""
        original = self._validate(p)
        return self._delete_node(original)

    def replace(self, p, e):
        """Replace the element at Position p with e.
        Return element formerly at Position p."""
        original = self._validate(p)
        old_value = original._element
        original._element = e
        return old_value
     
    def insertion_sort(L):
        """Sort PositionalList of comparable elements into nondecreasing order."""
        if len(L) > 1:
            marker = L.first()
            while marker != L.last():
                pivot = L.after(marker)
                value = pivot.element()
                if value > marker.element():
                    marker = pivot
                else:
                    walk = marker
                    while walk != L.first() and L.before(walk).element() > value:
                        walk = L.before(walk)
                    L.delete(pivot)
                    L.add_before(walk, value)
    
    def max(self):
        """Return max element"""
        if self.__len__() > 2:
            marker = self.first()
            while marker != self.before(self.last()):
                pivot = self.after(marker)
                value = pivot.element()
                if value > self.after(pivot).element():
                    value = self.after(pivot).element()
                marker = pivot
            return value
        elif len(self) == 1:
            return self.first().element()
        else:
            return None

if __name__ == '__main__':
    from PositionalList import PositionalList
    r = PositionalList()
    r.add_last(4)
    r.add_first(5)
    r._insert_between(10,r.first(),r.last())
    print(r.max())