.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/graph_theory/search/plot_01_astar_search.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_graph_theory_search_plot_01_astar_search.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_graph_theory_search_plot_01_astar_search.py:


A* search on a grid with obstacles
========================================

Finds a shortest path across a grid with a wall. With the Manhattan
distance as its heuristic, A* reaches the same distance as Dijkstra's
algorithm while expanding far fewer vertices.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.graph_theory import astar_shortest_path, grid_graph








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Build the grid and search it twice
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-43

.. code-block:: Python


    rows = cols = 30
    blocked = [(r, 15) for r in range(0, 24)] + [(8, c) for c in range(3, 15)]
    g, pos = grid_graph(rows, cols, blocked=blocked)
    source, target = 2 * cols + 2, (rows - 3) * cols + (cols - 3)


    def manhattan(v):
        return float(np.abs(pos[v] - pos[target]).sum())


    guided = astar_shortest_path(g, source, target, manhattan)
    blind = astar_shortest_path(g, source, target)
    print(f"A* (Manhattan): distance {guided.distance:.0f}, expanded {guided.n_expanded} vertices")
    print(f"Dijkstra (h = 0): distance {blind.distance:.0f}, expanded {blind.n_expanded} vertices")

    fig, ax = plt.subplots(figsize=(6, 6))
    wall = np.array([(c, r) for r, c in blocked])
    ax.plot(*wall.T, "ks", ms=6)
    ax.plot(*pos[guided.path].T, "-", color="tab:red", lw=2.5, label="A* path")
    ax.plot(*pos[[source, target]].T, "o", color="tab:green", ms=10)
    ax.set_aspect("equal")
    ax.invert_yaxis()
    ax.legend()



.. image-sg:: /api/gallery/graph_theory/search/images/sphx_glr_plot_01_astar_search_001.png
   :alt: plot 01 astar search
   :srcset: /api/gallery/graph_theory/search/images/sphx_glr_plot_01_astar_search_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    A* (Manhattan): distance 50, expanded 378 vertices
    Dijkstra (h = 0): distance 50, expanded 621 vertices

    <matplotlib.legend.Legend object at 0x11a2a2cf0>




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.017 seconds)


.. _sphx_glr_download_api_gallery_graph_theory_search_plot_01_astar_search.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_astar_search.ipynb <plot_01_astar_search.ipynb>`

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

      :download:`Download Python source code: plot_01_astar_search.py <plot_01_astar_search.py>`

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

      :download:`Download zipped: plot_01_astar_search.zip <plot_01_astar_search.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_