Question

Use Dijkstra's single-source shortest path algorithm to calculate the shortest path from vertex 1 (or Root Vertex) to each vertex of the graph. The Example you are going to implement should have minimum 10- Vertices.

Submit the following:

1.      Source Code (C++, Python, Java etc.)

2.      Output of the Code

3.      Trace diagrams (hand written) of the implemented Example

Answer 1

Dijkstra’s shortest path algorithm:-

Algorithm
1) Create a set sptSet (shortest path tree set) that keeps track of vertices included in shortest path tree, i.e., whose minimum distance from source is calculated and finalized. Initially, this set is empty.
2) Assign a distance value to all vertices in the input graph. Initialize all distance values as INFINITE. Assign distance value as 0 for the source vertex so that it is picked first.
3) While sptSet doesn’t include all vertices
….a) Pick a vertex u which is not there in sptSet and has minimum distance value.
….b) Include u to sptSet.
….c) Update distance value of all adjacent vertices of u. To update the distance values, iterate through all adjacent vertices. For every adjacent vertex v, if sum of distance value of u (from source) and weight of edge u-v, is less than the distance value of v, then update the distance value of v.