In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

Solving the stated problem using:

• Dijkstra's algorithm (Using Min-heap)
• Dijkstra's algorithm (Using Unsorted array)
• Bellman–Ford algorithm

Comparing all three methods using

• Adjacency List
• Adjacency Matrix

The Timing results will be written to the

Adjacency Dijkstra heap  0.000033 sec
Adjacency Dijkstra array 0.000024600 sec
Adjacency Bellman Ford   0.000087600 sec
Matrix Dijkstra heap     0.000044100 sec
Matrix Dijkstra array    0.000025400 sec
Matrix Bellman Ford      0.000048300 sec

main.cpp <Source File> <Output File>

• Vertex Amount
• Main Source Vertex
• Main Destination Vertex

For each Edge (u,v):

• <u><v> <Weight>

6
1
6
1 2 16
1 3 13
2 3 10

For the Example given, the result printed will be the minimum weight between 1 to 6.