Dijkstra Algorithm Example
Pseudocode for Djikstra's algorithm
Every vertex's route distance must be preserved. That can be kept in a v-dimensional array, where v is the total number of vertices.
Not only do we want to know how long the shortest path is, but we also want to be able to find it. Each vertex is mapped to the vertex that most recently changed its route length for this purpose.
When the process is finished, we may move backwards to discover the path by going from the source vertex to the destination vertex.
The vertex with the shortest route distance can be efficiently received using a minimal priority queue.
Dijkstra's algorithm source code
Below is a C++ implementation of Dijkstra's algorithm. Although the abstractions make it easier to connect the code to the algorithm, the complexity of the code can still be increased.
Distance from start: 4 f g d a .................................... Process executed in 1.11 second Press any key to continue.
Dijkstra's Algorithm Complexity
Time Complexity: O(E Log V) Where, E is the number of edges and V is the number of vertices.
Space Complexity: O(V)
Examples of Dijkstra's Algorithms
Heap-based Dijkstra's shortest route algorithm in O(E logV)
It is generally advised to use a heap (or priority queue) for Dijkstra's algorithm since the necessary operations (extract minimum and reduce key) correspond with the specialty of the heap (or priority queue). The decrease key is not supported by priority_queue, which is a concern. Instead of updating a key to fix this issue, insert an additional duplicate of it. Therefore, we let the priority queue to include several instances of the same vertex. This method contains the following crucial characteristics and doesn't call for diminishing vital procedures.
Vertex Distance from Source 0 0 1 4 2 12 3 19 4 21 5 11 6 9 7 8 8 14 ............................... Process executed in 0.11 second Press any key to continue.
Time Complexity: O(E * logV), Where E is the number of edges and V is the number of vertices.
Auxiliary Space: O(V)