Given a Graph $$$D$$$ of $$$N$$$ nodes, where each node $$$i$$$ has $$$C_i$$$ coins attached with it. You have to choose a subset of nodes such that no two adjacent nodes(i.e. nodes connected directly by an edge) are chosen and sum of coins attached with nodes in chosen subset is maximum.
For a tree this is a famous DP on Tree problem ( solution for Tree version here: https://mirror.codeforces.com/blog/entry/20935 -> Problem 1 ). Can we extend the DP on trees logic to solve it for a general graph. If not how can should I approach it?
It's NP. Since we have an equivalence with maximum independent set.
Is it NP even for a DAG?
Yes, because the edge directions are completely irrelevant here. Given any graph, you can direct its edges so that it becomes a DAG.