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<div class="section" id="bidirectional-dijkstra">
<h1>bidirectional_dijkstra<a class="headerlink" href="#bidirectional-dijkstra" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="networkx.algorithms.shortest_paths.weighted.bidirectional_dijkstra">
<tt class="descname">bidirectional_dijkstra</tt><big>(</big><em>G</em>, <em>source</em>, <em>target</em>, <em>weight='weight'</em><big>)</big><a class="reference internal" href="../../_modules/networkx/algorithms/shortest_paths/weighted.html#bidirectional_dijkstra"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#networkx.algorithms.shortest_paths.weighted.bidirectional_dijkstra" title="Permalink to this definition">¶</a></dt>
<dd><p>Dijkstra’s algorithm for shortest paths using bidirectional search.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters :</th><td class="field-body"><p class="first"><strong>G</strong> : NetworkX graph</p>
<p><strong>source</strong> : node</p>
<blockquote>
<div><p>Starting node.</p>
</div></blockquote>
<p><strong>target</strong> : node</p>
<blockquote>
<div><p>Ending node.</p>
</div></blockquote>
<p><strong>weight: string, optional (default=’weight’)</strong> :</p>
<blockquote>
<div><p>Edge data key corresponding to the edge weight</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>length</strong> : number</p>
<blockquote>
<div><p>Shortest path length.</p>
</div></blockquote>
<p><strong>Returns a tuple of two dictionaries keyed by node.</strong> :</p>
<p><strong>The first dictionary stores distance from the source.</strong> :</p>
<p><strong>The second stores the path from the source to that node.</strong> :</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Raises :</th><td class="field-body"><p class="first"><strong>NetworkXNoPath</strong> :</p>
<blockquote class="last">
<div><p>If no path exists between source and target.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition-see-also admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><tt class="xref py py-obj docutils literal"><span class="pre">shortest_path</span></tt>, <tt class="xref py py-obj docutils literal"><span class="pre">shortest_path_length</span></tt></p>
</div>
<p class="rubric">Notes</p>
<p>Edge weight attributes must be numerical.
Distances are calculated as sums of weighted edges traversed.</p>
<p>In practice bidirectional Dijkstra is much more than twice as fast as
ordinary Dijkstra.</p>
<p>Ordinary Dijkstra expands nodes in a sphere-like manner from the
source. The radius of this sphere will eventually be the length
of the shortest path. Bidirectional Dijkstra will expand nodes
from both the source and the target, making two spheres of half
this radius. Volume of the first sphere is pi*r*r while the
others are 2*pi*r/2*r/2, making up half the volume.</p>
<p>This algorithm is not guaranteed to work if edge weights
are negative or are floating point numbers
(overflows and roundoff errors can cause problems).</p>
<p class="rubric">Examples</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">G</span><span class="o">=</span><span class="n">nx</span><span class="o">.</span><span class="n">path_graph</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">length</span><span class="p">,</span><span class="n">path</span><span class="o">=</span><span class="n">nx</span><span class="o">.</span><span class="n">bidirectional_dijkstra</span><span class="p">(</span><span class="n">G</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span>
<span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="n">length</span><span class="p">)</span>
<span class="go">4</span>
<span class="gp">>>> </span><span class="k">print</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
<span class="go">[0, 1, 2, 3, 4]</span>
</pre></div>
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