For Tree dp , I used the same trick every-time .
Never do that recursion/backtracking stuff for tree dp , its just not very intuitive .
Make node "1" as the root of the tree .
Always, do the reverse bfs technique on tree and solve tree dp problems iteratively . Iterative things are usually very intuitive and the best for the mind to grasp . Traverse nodes at last level , then nodes at level : last - 1 , till you reach the root .
dp[i] should always store the best answer of node 'i' , which means if tree started from node 'i' and only the nodes below it (children , grandchildren existed) , then what would be the answer for our tree ? It would be dp[i] . After computing dp[i] for each node, dp is the final answer :)
dp[i] is , in most cases a function of its children , and as we travelled from bottom , dp values for children of any node have already been calculated!
dp[i] = f(dp[child1],dp[child2],.....) , where child1,child2,child3,....childn are the direct children on node 'i' . (Tree is rooted at node '1')
Hope it helps!