### view env/lib/python3.9/site-packages/networkx/algorithms/shortest_paths/dense.py @ 0:4f3585e2f14bdraftdefaulttip

author shellac Mon, 22 Mar 2021 18:12:50 +0000
line wrap: on
line source
```
"""Floyd-Warshall algorithm for shortest paths.
"""
import networkx as nx

__all__ = [
"floyd_warshall",
"floyd_warshall_predecessor_and_distance",
"reconstruct_path",
"floyd_warshall_numpy",
]

def floyd_warshall_numpy(G, nodelist=None, weight="weight"):
"""Find all-pairs shortest path lengths using Floyd's algorithm.

Parameters
----------
G : NetworkX graph

nodelist : list, optional
The rows and columns are ordered by the nodes in nodelist.
If nodelist is None then the ordering is produced by G.nodes().

weight: string, optional (default= 'weight')
Edge data key corresponding to the edge weight.

Returns
-------
distance : NumPy matrix
A matrix of shortest path distances between nodes.
If there is no path between to nodes the corresponding matrix entry
will be Inf.

Notes
------
Floyd's algorithm is appropriate for finding shortest paths in
dense graphs or graphs with negative weights when Dijkstra's
algorithm fails. This algorithm can still fail if there are negative
cycles.  It has running time \$O(n^3)\$ with running space of \$O(n^2)\$.
"""
try:
import numpy as np
except ImportError as e:
raise ImportError("to_numpy_array() requires numpy: http://numpy.org/ ") from e

# To handle cases when an edge has weight=0, we must make sure that
# nonedges are not given the value 0 as well.
A = nx.to_numpy_array(
G, nodelist=nodelist, multigraph_weight=min, weight=weight, nonedge=np.inf
)
n, m = A.shape
np.fill_diagonal(A, 0)  # diagonal elements should be zero
for i in range(n):
# The second term has the same shape as A due to broadcasting
A = np.minimum(A, A[i, :][np.newaxis, :] + A[:, i][:, np.newaxis])
return A

def floyd_warshall_predecessor_and_distance(G, weight="weight"):
"""Find all-pairs shortest path lengths using Floyd's algorithm.

Parameters
----------
G : NetworkX graph

weight: string, optional (default= 'weight')
Edge data key corresponding to the edge weight.

Returns
-------
predecessor,distance : dictionaries
Dictionaries, keyed by source and target, of predecessors and distances
in the shortest path.

Examples
--------
>>> G = nx.DiGraph()
...     [
...         ("s", "u", 10),
...         ("s", "x", 5),
...         ("u", "v", 1),
...         ("u", "x", 2),
...         ("v", "y", 1),
...         ("x", "u", 3),
...         ("x", "v", 5),
...         ("x", "y", 2),
...         ("y", "s", 7),
...         ("y", "v", 6),
...     ]
... )
>>> predecessors, _ = nx.floyd_warshall_predecessor_and_distance(G)
>>> print(nx.reconstruct_path("s", "v", predecessors))
['s', 'x', 'u', 'v']

Notes
------
Floyd's algorithm is appropriate for finding shortest paths
in dense graphs or graphs with negative weights when Dijkstra's algorithm
fails.  This algorithm can still fail if there are negative cycles.
It has running time \$O(n^3)\$ with running space of \$O(n^2)\$.

--------
floyd_warshall
floyd_warshall_numpy
all_pairs_shortest_path
all_pairs_shortest_path_length
"""
from collections import defaultdict

# dictionary-of-dictionaries representation for dist and pred
# use some defaultdict magick here
# for dist the default is the floating point inf value
dist = defaultdict(lambda: defaultdict(lambda: float("inf")))
for u in G:
dist[u][u] = 0
pred = defaultdict(dict)
# initialize path distance dictionary to be the adjacency matrix
# also set the distance to self to 0 (zero diagonal)
undirected = not G.is_directed()
for u, v, d in G.edges(data=True):
e_weight = d.get(weight, 1.0)
dist[u][v] = min(e_weight, dist[u][v])
pred[u][v] = u
if undirected:
dist[v][u] = min(e_weight, dist[v][u])
pred[v][u] = v
for w in G:
dist_w = dist[w]  # save recomputation
for u in G:
dist_u = dist[u]  # save recomputation
for v in G:
d = dist_u[w] + dist_w[v]
if dist_u[v] > d:
dist_u[v] = d
pred[u][v] = pred[w][v]
return dict(pred), dict(dist)

def reconstruct_path(source, target, predecessors):
"""Reconstruct a path from source to target using the predecessors
dict as returned by floyd_warshall_predecessor_and_distance

Parameters
----------
source : node
Starting node for path

target : node
Ending node for path

predecessors: dictionary
Dictionary, keyed by source and target, of predecessors in the
shortest path, as returned by floyd_warshall_predecessor_and_distance

Returns
-------
path : list
A list of nodes containing the shortest path from source to target

If source and target are the same, an empty list is returned

Notes
------
This function is meant to give more applicability to the
floyd_warshall_predecessor_and_distance function

--------
floyd_warshall_predecessor_and_distance
"""
if source == target:
return []
prev = predecessors[source]
curr = prev[target]
path = [target, curr]
while curr != source:
curr = prev[curr]
path.append(curr)
return list(reversed(path))

def floyd_warshall(G, weight="weight"):
"""Find all-pairs shortest path lengths using Floyd's algorithm.

Parameters
----------
G : NetworkX graph

weight: string, optional (default= 'weight')
Edge data key corresponding to the edge weight.

Returns
-------
distance : dict
A dictionary,  keyed by source and target, of shortest paths distances
between nodes.

Notes
------
Floyd's algorithm is appropriate for finding shortest paths
in dense graphs or graphs with negative weights when Dijkstra's algorithm
fails.  This algorithm can still fail if there are negative cycles.
It has running time \$O(n^3)\$ with running space of \$O(n^2)\$.