$(10$ pts$)$ Consider the single source shortest path problem on a directed graph $G=(V,E)$ and a source vertex $sinV$ where each einE has a weight, $w(e).$ There are no cycles in the graph containing a negative weighted edge, and the only negative weighted edges are those leaving $s($i$.$e$.,)(s.$ Given these assumptions, will Dijkstra's algorithm fail when run on this graph? Prove your conclusion.

$(10$ pts$)$ Design an algorithm which accepts a directed graph as input, and determines if there is a vertex within the graph from which all other vertices are reachable. The algorithm should run in $(|V|+|E|)$ time, and you must demonstrate this fact.