# networkx.algorithms.shortest_paths.weighted.bidirectional_dijkstra¶

bidirectional_dijkstra(G, source, target, weight='weight')[source]

Dijkstra’s algorithm for shortest paths using bidirectional search.

Parameters
GNetworkX graph
sourcenode

Starting node.

targetnode

Ending node.

weightstring or function

If this is a string, then edge weights will be accessed via the edge attribute with this key (that is, the weight of the edge joining `u` to `v` will be `G.edges[u, v][weight]`). If no such edge attribute exists, the weight of the edge is assumed to be one.

If this is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number.

Returns
length, pathnumber and list

length is the distance from source to target. path is a list of nodes on a path from source to target.

Raises
NodeNotFound

If either `source` or `target` is not in `G`.

NetworkXNoPath

If no path exists between source and target.

`shortest_path`
`shortest_path_length`

Notes

Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

In practice bidirectional Dijkstra is much more than twice as fast as ordinary Dijkstra.

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.

This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems).

Examples

```>>> G = nx.path_graph(5)
>>> length, path = nx.bidirectional_dijkstra(G, 0, 4)
>>> print(length)
4
>>> print(path)
[0, 1, 2, 3, 4]
```