.. _sphx_glr_api_gallery_optimization_dynamic_programming:

Dynamic programming
-------------------

Bellman's principle of optimality applied to the 0/1 knapsack problem.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Fills a table of optimal values for every prefix of the items and every capacity, then traces back the chosen items. The table is the dynamic-programming &quot;value function&quot;.">

.. only:: html

  .. image:: /api/gallery/optimization/dynamic_programming/images/thumb/sphx_glr_plot_01_knapsack_thumb.png
    :alt:

  :doc:`/api/gallery/optimization/dynamic_programming/plot_01_knapsack`

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      <div class="sphx-glr-thumbnail-title">Bellman's principle of optimality: the 0/1 knapsack</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/optimization/dynamic_programming/plot_01_knapsack