Problem #$2$:

Draw a directed graph as described below.

No$.$ of vertices: $7,$ No$.$ of edges: $9$

List of vertices, $V$:$\{1,2,3,4,5,6,7\}$

List of edges, in $(u,v,w)$ format which means there is an outgoing edge from $u$ to $v$ with

weight $w]$ :

$\{(1,2,8),(2,3,-8),(1,3,1)(3,4,4),(4,5,-4),(3,5,1),(5,6,2),(6,7,-2),(5,7,1)\}$

a$.$ Show a simulation of Dijkstra's algorithm to find the shortest path costs from vertex $1$ to

all others. You can use the following pseudocode as reference. it should be handwriten and drawn with proper steps