Expressions
===========

Save all functions into the same file named ``expressions.py``.

#. Write function :py:func:`items_count_1` that takes a string
   (:class:`str`) which represents a Python expression and returns two
   integers (:class:`int`) corresponding respectively to the number of
   alphabetical characters and digits. Examples:

   .. literalinclude:: items_1.txt
      :language: python3
      :lines: 3-
             
   .. note::

       More tests are provided in the :download:`items_1.txt<items_1.txt>` file.

#. Write function :py:func:`items_count_2` that takes a string which
   represents a Python expression and returns two integers
   corresponding to the number of items of the following types found
   in this expression. The first type are the following characters
   corresponding to some operators, ``'+'``, ``'-'``, ``'*'``,
   ``'/'``, ``'%'``, ``'='``, ``'!'``, ``'>'`` and ``'<'``. The second
   type are the following bracket type characters: ``'('``, ``')'``,
   ``'['``, ``']'``, ``'{'`` and ``'}'``. Examples:

   .. literalinclude:: items_2.txt
      :language: python3
      :lines: 3-
             
   .. note::

       More tests are provided in the :download:`items_2.txt<items_2.txt>` file.

#. Write the function :py:func:`well_parenthesized_1` that takes a
   string (:class:`str`) which represents a Python expression and
   returns ``True`` if it is well-parenthesized or ``False`` otherwise.

   A well-parenthesized expression must fulfil the following rules:

   1. while traversing it left to right, the number of open parenthesis
      must be always greater than or equal to the number of closed parenthesis.

   2. at the end of the traversal, the number of open parenthesis must be
      equal to the number of closed parenthesis.
      
   See the following examples:
   
   .. literalinclude:: parenthesis_1.txt
      :language: python3
      :lines: 3-
             
   .. note::

       More tests are provided in the :download:`parenthesis_1.txt<parenthesis_1.txt>` file.

#. Write the function :py:func:`well_parenthesized_2` that takes a
   string (:class:`str`) which represents a Python expression and
   returns the string ``'correct'`` if it is a well-parenthesized
   expression. If not, the function returns the string ``'incorrect
   closed parenthesis'`` together with the first position (string
   index) (:class:`int`) in which rule 1 fails. If rule 2 fails, the
   function returns the string ``'more open than closed
   parenthesis'``. Examples:

   .. literalinclude:: parenthesis_2.txt
      :language: python3
      :lines: 3-
             
   .. note::

       More tests are provided in the :download:`parenthesis_2.txt<parenthesis_2.txt>` file.

.. rubric:: Solution
      
A solution of these functions is provided in the
:download:`expressions.py<solutions/expressions.py>` file.