QUESTION $1(20$ pts$)$: $($Minimum Spanning Tree and Shortest Paths: Dijkstra's Algorithm$)$

Consider a connected graph G of $11$ nodes labeled $($named$)$ A to K$.$ Add $17$ undirected edges of your choice such that there are $4$ nodes fully connected. Assign the links integer weights of your choice from the range $[1,30]$ such that not more than two edges will get the same weight and no path of three consecutive edges have their weights in sorted order like $($A$,$B$)=5,($B$,$C$)=9,($C$,$D$)=12,$ instead these three edges may get weights like $($A$,$B$)=5,($B$,$C$)=12,($C$,$D$)=9$ which are not sorted.

a$)$ Find and draw minimum spanning tree $($MST$)$ of graph G$.$

b$)$ Apply Dijkstra's shortest path $($SP$)$ algorithm to graph G using vertex A as the root. Show all the steps of your work in a table with a row per iteration and column per node. Draw the final SP Tree and the content of d $($distance$)$ table for all vertices $($including the determined SP and estimated values$)$ at each iteration. Circle the entry corresponding to the selected node for each iteration.