$8.$

Apply Dijkstra's algorithm for the following graph. Show the values for p and IN and the d values and s values for each pass. Write out the nodes in the shortest path from $\backslash ($ A $\backslash )$ to $\backslash ($ D $\backslash )$ and the distances of the path. $(20$ points$)$

Hint:

$(1)$ p is the current node that has the shortest d that you will include in your current IN set.

$(2)$ Node $\backslash ($ A $\backslash )$ is the starting node.

$(3)$ Node $\backslash ($ D $\backslash )$ is the ending node.

$(4)$ Please show all steps like we did during the class: draw the table for each step, calculate the new distance for each step, update the table, repeat until the ending node is included in the IN set, find the shortest path and the shortest length.