$($b$)$ Given a path graph $G=(V,E)$ such that $V=\{v_1,v_2,...,v_n\}$

and an edge exists between $v_i$ and $v_j$ if and only if th

numbers i and $j$ differ by exactly $1.$ Each node has

positive integer weight $w_i.$ Give an algorithm to find a

independent set in $G$ whose total weight is as large a

possible.