$**$Problem Statement:$**$

Write a Python program that implements Dijkstra's Algorithm to find the shortest path in a weighted, directed graph. The program should take as input the following:

$1.$ The number of vertices in the graph.

$2.$ A list of edges in the format $($source$,$ destination, weight$).$

$3.$ The starting vertex from which the shortest path should be calculated.

The program should output:

$-$ The shortest path from the starting vertex to all other vertices.

$-$ The corresponding distance for each path.

Constraints:

$-$ The graph is represented using an adjacency matrix.

$-$ The graph does not contain negative weight edges.

$-$ Assume the graph is connected, i$.$e$.,$ every vertex is reachable from the start vertex.

Input Example:

$```$

Number of vertices: $5$

Edges: $[(0,1,10),(0,3,5),(1,2,1),(3,1,3),(3,2,9),(3,4,2),(4,2,6)]$

Starting vertex: $0$

$```$

Expected Output:

$```$

Vertex Distance from Source

$00$

$18$

$29$

$35$

$47$

$```$