.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "tutorials/06_vtrees.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_tutorials_06_vtrees.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_tutorials_06_vtrees.py:


Choosing a variable grouping
================================
A vtree groups variables into subproblems. Consider the function
``(x₁ ↔ x₃) ∧ (x₂ ↔ x₄)``.
One vtree puts each equality together; another splits them across the root.

.. image:: /_static/vtree-grouping.svg
   :alt: Grouped vtree pairs x1 with x3 and x2 with x4. Split vtree pairs x1 with x2 and x3 with x4.
   :width: 780

.. GENERATED FROM PYTHON SOURCE LINES 14-28

.. code-block:: Python

    from tididi import Vtree, literal


    def equalities(vtree):
        x1, x2, x3, x4 = [literal(vtree, variable) for variable in range(1, 5)]
        return (~(x1 ^ x3) & ~(x2 ^ x4)).minimize()


    grouped = equalities(Vtree.balanced_over([1, 3, 2, 4]))
    split = equalities(Vtree.balanced_over([1, 2, 3, 4]))
    print("Models:", grouped.model_count(), split.model_count())
    print("Pairs with grouped equalities:", grouped.pair_count())
    print("Pairs with split equalities:", split.pair_count())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Models: 4 4
    Pairs with grouped equalities: 5
    Pairs with split equalities: 12




.. GENERATED FROM PYTHON SOURCE LINES 29-36

The function has four models in either case, but the circuit size changes.
A useful grouping keeps strongly related variables together.

Use ``Vtree.join(left, right)`` to assemble a particular grouping or
``Vtree.linear(variable_order)`` for a right-linear vtree. These constructors
create new domains. Construct or reload all operands on the resulting
shared vtree before combining them.


.. _sphx_glr_download_tutorials_06_vtrees.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 06_vtrees.ipynb <06_vtrees.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 06_vtrees.py <06_vtrees.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 06_vtrees.zip <06_vtrees.zip>`