$(15\%)$ For the graph in Question $2,$ apply Dijkstra's algorithm to find the shortest path from the source $a$ to each other vertex. Illustrate each algorithm step of relaxation by updating the shortest path of each vertex from the source $a($label aside of the vertex as in Figure $($a$),$ or use a table to show steps$)$

$($a$)$

$($b$)$

$($c$)$

$($d$)($cont$)$