Think First

Before reading the solution, think:

$1.$ What states do you need? For each node u, what decisions affect the answer? (Hint: Does u use an edge to its parent?)

$2.$ How do you combine child states? If u does not use edge to parent, what can children do? If u does use it, what happens to one child?

$3.$ what is the recurrence? Write dp[u][0] and dp[u][1] in terms of children.

Try to define the states clearly: 'dp[u][$0$] means.' and 'dp[u][$1$] means.'. Then write the transitions. Spend $1$ minute thinking. Then continue.