Answer the following in context of graph algorithms:

$($a$)$ Write the Dijkstra's Greedy Criterion for calculating single$-$source shortest paths.

$($b$)$ What is the running time of the straightforward implementation of Dijkstra's algorithm w

structure? Give a step$-$wise implementation of the Dijkstra's algorithm using appropriat

runs in $O((m+n)logn)$ running time. Here, $m$ is the number of edges and $n$ the number $c$

Also analyze and show how your implementation features this running time.

$($c$)$ Apply the Bellman$-$Ford Algorithm to find shortest paths from source vertex S to eve

following weighted directed graph: