.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "tutorials/08_minimum_cost.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_tutorials_08_minimum_cost.py>`
        to download the full example code.

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

.. _sphx_glr_tutorials_08_minimum_cost.py:


A custom minimum-cost calculation
=====================================
The same Boolean circuit can answer more than counting questions. Here we
find the cheapest valid backup configuration: local storage costs 5, remote
storage 2, and encryption 1. Notifications are free.

.. GENERATED FROM PYTHON SOURCE LINES 10-19

.. code-block:: Python

    from math import inf
    from tididi import Vtree, literal

    vtree = Vtree.balanced(4)
    local = literal(vtree, 1)
    remote = literal(vtree, 2)
    encrypted = literal(vtree, 3)
    configurations = (local | remote.copy()) & (~remote.copy() | encrypted.copy())








.. GENERATED FROM PYTHON SOURCE LINES 20-26

Supply the algebra
----------------------
A false function has infinite cost. A positive literal pays its variable's
cost; a negative literal costs zero. For a free variable, either value is
possible, so choose the cheaper one. Disjunction chooses the minimum;
conjunction adds costs over disjoint variable groups.

.. GENERATED FROM PYTHON SOURCE LINES 26-51

.. code-block:: Python

    class Costs:
        def __init__(self, prices):
            self.prices = prices

        def zero(self):
            return inf

        def leaf(self, variable, sign):
            price = self.prices[variable]
            if sign is None:
                return min(0, price)
            return price if sign else 0

        def add(self, a, b):
            return min(a, b)

        def mul(self, a, b):
            return a + b


    costs = Costs({1: 5, 2: 2, 3: 1, 4: 0})
    print("Minimum configuration cost:", configurations.evaluate(costs))
    discount = Costs({1: 1, 2: 2, 3: 1, 4: 0})
    print("Minimum with discount:", configurations.evaluate(discount))





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

 .. code-block:: none

    Minimum configuration cost: 3
    Minimum with discount: 1




.. GENERATED FROM PYTHON SOURCE LINES 52-54

Reuse the circuit with new costs, or constrain it with another Boolean
condition. Evaluation borrows; Boolean operations consume their operands.

.. GENERATED FROM PYTHON SOURCE LINES 54-59

.. code-block:: Python

    with_remote = configurations.copy() & remote
    print("Minimum with remote backups:", with_remote.evaluate(discount))
    without_encryption = with_remote & ~encrypted
    print("Minimum without encryption:", without_encryption.evaluate(costs))





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

 .. code-block:: none

    Minimum with remote backups: 3
    Minimum without encryption: inf




.. GENERATED FROM PYTHON SOURCE LINES 60-64

Algebra values must be immutable, and ``add`` and ``mul`` must return values
without mutating their arguments. Python callbacks make this flexible but
add interpreter overhead per evaluation step. For exact weighted sums,
``weighted_count()`` runs the arithmetic directly in Rust.


.. _sphx_glr_download_tutorials_08_minimum_cost.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 08_minimum_cost.ipynb <08_minimum_cost.ipynb>`

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

      :download:`Download Python source code: 08_minimum_cost.py <08_minimum_cost.py>`

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

      :download:`Download zipped: 08_minimum_cost.zip <08_minimum_cost.zip>`