module challenge.city_tour#
Short summary#
module ensae_projects.challenge.city_tour
Function to solve the problem of the Route Inspection Problem.
Classes#
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wrong solution |
Functions#
function |
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Removes an edge from the graph. |
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Computes an Eulerian path. |
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Explores an Eulerian path, remove used edges from edges_from. |
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Computes shortest distances between all vertices. It assumes edges are symmetric. |
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Computes the final solution for the Eulerian path. |
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Compute the degree of vertices. |
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Returns the best path between two vertices. Uses Dikjstra … |
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Checks if a solution is really a solution and returns the distance of it, None if it is not a solution. The function … |
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Computes the length of edges if distances is None. |
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Computes an Eulerian path. |
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Computes Haversine formula. |
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Finds the best match between vertices. |
Documentation#
Function to solve the problem of the Route Inspection Problem.
- ensae_projects.challenge.city_tour._delete_edge(edges_from, n, to)#
Removes an edge from the graph.
- Parameters:
edges_from – structure which contains the edges (will be modified)
n – first vertex
to – second vertex
- Returns:
the edge
- ensae_projects.challenge.city_tour._euler_path(edges)#
Computes an Eulerian path.
- Parameters:
edges – edges
- Returns:
path, list of (vertex,edge)
The function assumes every vertex in the graph defined by edges has an even degree.
- ensae_projects.challenge.city_tour._explore_path(edges_from, begin)#
Explores an Eulerian path, remove used edges from edges_from.
- Parameters:
edges_from – structure which contains the edges (will be modified)
begin – first vertex to use
- Returns:
path
- ensae_projects.challenge.city_tour.bellman_distances(edges, distances, fLOG=None)#
Computes shortest distances between all vertices. It assumes edges are symmetric.
- Parameters:
edges – list of tuple (vertex A, vertex B)
distances – distances (list of floats)
fLOG – logging function
- Returns:
dictionary of distances
This function could be implemented based on shortest_path.
- ensae_projects.challenge.city_tour.best_euler_path(edges, vertices, distances, edges_index=None, algo='blossom', fLOG=None)#
Computes the final solution for the Eulerian path.
- Parameters:
edges – edges (list of tuple)
vertices – location of the vertices (not needed if distances are filled)
distances – distances for each edge (list of distance)
edges_index – list of indices of edges (if None –> range(len(edges))
algo – algorithm to use to computes the matching (see
matching_vertices)fLOG – logging function
- Returns:
list of edges as tuple, list of edges as indices, distance
- ensae_projects.challenge.city_tour.compute_degrees(edges)#
Compute the degree of vertices.
- Parameters:
edges – list of tuple
- Returns:
dictionary {key: degree}
- ensae_projects.challenge.city_tour.dijkstra_path(edges, distances, va, vb)#
Returns the best path between two vertices. Uses Dikjstra algorithm.
- Parameters:
edges – list of edges.
distances – list of distances
va – first vertex
vb – last vertex
- Returns:
list of edges
This function could be implemented based on shortest_path.
- ensae_projects.challenge.city_tour.distance_solution(edges_index, edges, distances, solution, exc=True)#
Checks if a solution is really a solution and returns the distance of it, None if it is not a solution. The function does not case about the order.
- Parameters:
edges_index – list of indices of edges (if None –> range(len(edges))
edges – list of tuple (vertex A, vertex B)
distances – list of distances of each edge
solution – proposed solutions (list of edge indices)
exc – raises an exception in case of error
- ensae_projects.challenge.city_tour.distance_vertices(edges, vertices, distances)#
Computes the length of edges if distances is None.
- Parameters:
edges – list of tuple (vertex A, vertex B)
vertices – locations of the vertices
distances – distances (None or list of floats)
- Returns:
distances (list of float)
- ensae_projects.challenge.city_tour.euler_path(edges_index, edges, solution)#
Computes an Eulerian path.
- Parameters:
edges_index – list of indices of edges (if None –> range(len(edges))
edges – list of tuple (vertex A, vertex B)
solution – proposed solutions (list of edge indices)
- Returns:
path, list of edges indices
The function assumes every vertex in the graph defined by edges has an even degree.
- ensae_projects.challenge.city_tour.haversine_distance(lat1, lng1, lat2, lng2)#
Computes Haversine formula.
- Parameters:
lat1 – lattitude
lng1 – longitude
lat2 – lattitude
lng2 – longitude
- Returns:
distance
- ensae_projects.challenge.city_tour.matching_vertices(distances, algo='blossom')#
Finds the best match between vertices.
- Parameters:
distances – result of function @bellman_distances but only for odd vertices (odd = odd degree), dictionary { (vi,vj) : distance}
algo – algorithm (see below)
- Returns:
sequences of best matches.
If
algo=='hungarian', the function relies on linear_sum_assignment from scipy which uses the Hungarian Algorithm. Vertex index do not have to start from zero and be continuous. The function will handle that particular case. However, the method works for a bi-partite matching and is not suitable here unless the algorithm is modified. Not done (yet?).If
algo=='blossom', it uses the Blossom algorithm which is known to be in
and finds the optimal matching.If
algo=='basic', the function sorts the distances by increasing order and builds new edges as they come in this list. It does not return an optimal solution but is much faster when the graph is big.