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Diffstat (limited to '.venv/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/dense.py')
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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/dense.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/dense.py new file mode 100644 index 00000000..107b9208 --- /dev/null +++ b/.venv/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/dense.py @@ -0,0 +1,260 @@ +"""Floyd-Warshall algorithm for shortest paths.""" + +import networkx as nx + +__all__ = [ + "floyd_warshall", + "floyd_warshall_predecessor_and_distance", + "reconstruct_path", + "floyd_warshall_numpy", +] + + +@nx._dispatchable(edge_attrs="weight") +def floyd_warshall_numpy(G, nodelist=None, weight="weight"): + """Find all-pairs shortest path lengths using Floyd's algorithm. + + This algorithm for finding shortest paths takes advantage of + matrix representations of a graph and works well for dense + graphs where all-pairs shortest path lengths are desired. + The results are returned as a NumPy array, distance[i, j], + where i and j are the indexes of two nodes in nodelist. + The entry distance[i, j] is the distance along a shortest + path from i to j. If no path exists the distance is Inf. + + Parameters + ---------- + G : NetworkX graph + + nodelist : list, optional (default=G.nodes) + The rows and columns are ordered by the nodes in nodelist. + If nodelist is None then the ordering is produced by G.nodes. + Nodelist should include all nodes in G. + + weight: string, optional (default='weight') + Edge data key corresponding to the edge weight. + + Returns + ------- + distance : 2D numpy.ndarray + A numpy array of shortest path distances between nodes. + If there is no path between two nodes the value is Inf. + + Examples + -------- + >>> G = nx.DiGraph() + >>> G.add_weighted_edges_from( + ... [(0, 1, 5), (1, 2, 2), (2, 3, -3), (1, 3, 10), (3, 2, 8)] + ... ) + >>> nx.floyd_warshall_numpy(G) + array([[ 0., 5., 7., 4.], + [inf, 0., 2., -1.], + [inf, inf, 0., -3.], + [inf, inf, 8., 0.]]) + + 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 $O(n^2)$. + + Raises + ------ + NetworkXError + If nodelist is not a list of the nodes in G. + """ + import numpy as np + + if nodelist is not None: + if not (len(nodelist) == len(G) == len(set(nodelist))): + raise nx.NetworkXError( + "nodelist must contain every node in G with no repeats." + "If you wanted a subgraph of G use G.subgraph(nodelist)" + ) + + # 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, 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 + + +@nx._dispatchable(edge_attrs="weight") +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() + >>> G.add_weighted_edges_from( + ... [ + ... ("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 $O(n^2)$. + + See Also + -------- + 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) + + +@nx._dispatchable(graphs=None) +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 + + See Also + -------- + 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)) + + +@nx._dispatchable(edge_attrs="weight") +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. + + Examples + -------- + >>> G = nx.DiGraph() + >>> G.add_weighted_edges_from( + ... [(0, 1, 5), (1, 2, 2), (2, 3, -3), (1, 3, 10), (3, 2, 8)] + ... ) + >>> fw = nx.floyd_warshall(G, weight="weight") + >>> results = {a: dict(b) for a, b in fw.items()} + >>> print(results) + {0: {0: 0, 1: 5, 2: 7, 3: 4}, 1: {1: 0, 2: 2, 3: -1, 0: inf}, 2: {2: 0, 3: -3, 0: inf, 1: inf}, 3: {3: 0, 2: 8, 0: inf, 1: 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 $O(n^2)$. + + See Also + -------- + floyd_warshall_predecessor_and_distance + floyd_warshall_numpy + all_pairs_shortest_path + all_pairs_shortest_path_length + """ + # could make this its own function to reduce memory costs + return floyd_warshall_predecessor_and_distance(G, weight=weight)[1] |