Consider a directed graph G = (V, E).

Problem    Determine the length of the shortest path from the source to each of the other nodes of the graph. This problem can be solved by a greedy algorithm often called Dijkstra's algorithm.

The algorithm maintains two sets of vertices, S and C. At every stage the set S contains those vertices that have already been selected and set C contains all the other vertices. Hence we have the invariant property V=S U C. When algorithm starts Delta contains only the source vertex and when the algorithm halts, Delta contains all the vertices of the graph and problem is solved. At each step algorithm choose the vertex in C whose distance to the source is least and add it to S.