Dijkstra Shortest Path

Dijkstra’s algorithm computes shortest paths between nodes in weighted and unweighted graphs. In weighted graphs, edge weights should be non-negative. Dijkstra’s algorithm is implemented with a priority queue and runs in O(|E|log|V|) for connected graphs, where |E| is the number of edges and |V| the number of vertices in the graph.

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Syntax

calculates the shortest path between on start_vertex and one end_vertex using Dijkstra’s algorithm. Works on both weighted as well as unweighted graphs. For unweighted graphs, a unit weight is used for each edge.

template <typename V, typename E, graph_type T, typename WEIGHT_T = decltype(get_weight(std::declval<E>()))>
std::optional<graph_path<WEIGHT_T>> 
dijkstra_shortest_path(const graph<V, E, T>& graph, vertex_id_t start_vertex, vertex_id_t end_vertex);

• graph The graph to extract shortest path from.
• start_vertex Vertex id where the shortest path should start.
• end_vertex Vertex id where the shortest path should end.
• return An optional with the shortest path (list of vertices) if found.

Find the shortest paths from a source vertex to all other vertices in the graph using Dijkstra’s algorithm.

template <typename V, typename E, graph_type T, typename WEIGHT_T = decltype(get_weight(std::declval<E>()))>
[[nodiscard]] std::unordered_map<vertex_id_t, graph_path<WEIGHT_T>>
dijkstra_shortest_paths(const graph<V, E, T>& graph, vertex_id_t source_vertex);

• graph The graph we want to search.
• source_vertex The source vertex from which to compute shortest paths.
• return A map containing the shortest paths from the source vertex to all other vertices. The map keys are target vertex IDs, and the values are instances of graph_path, representing the shortest distance and the path (list of vertex IDs) from the source to the target. If a vertex is not reachable from the source, its entry will be absent from the map.