Consider the same problem of finding a minimum$-$weight $-$node simple path from node $1$ in an input weighted graph, but this time give a greedy method to find a solution.

b$)$ Analyze the time complexity of your algorithm.

c$)$Does your method guarantee optimality? Prove your answer. Problem $6$: $(10$ points$)$

a$)$ Consider the same problem of finding a minimum$-$weight $\backslash ($ k $\backslash )-$node simple path from node $1$ in an input weighted graph, but this time give a greedy method to find a solution.

b$)$ Analyze the time complexity of your algorithm.

c$)$ Does your method guarantee optimality? Prove your answer.