• Company hierarchy is a tree: nodes = employees, edges = direct boss–subordinate.
• Constraint: No employee attends with their direct upper hand (boss).
  Equivalently: In the tree, no two adjacent nodes can both attend.
• Goal: Maximize total number of attendees.

For each node u, define two states:

• dp[u][0] = max attendees in u's subtree when u does NOT attend.
• dp[u][1] = max attendees in u's subtree when u attends.

Let children(u) be the set of u's direct subordinates.

• If u attends → none of its children can attend (otherwise they'd be with their boss).
  So we add 1 for u plus the best of each child's not‑attending state:

  $$dp[u][1] = 1 + \sum_{v \in children(u)} dp[v][0]$$

• If u does NOT attend → each child is free to attend or not, independently.
  We take the maximum of the two options for each child:

  $$dp[u][0] = \sum_{v \in children(u)} \max(dp[v][0],\ dp[v][1])$$

$$ dp[leaf][1] = 1 \qquad dp[leaf][0] = 0 $$

Let root be the CEO (root of the tree).
Maximum attendees = $$\max(dp[root][0],\ dp[root][1])$$

• Time: O(N) – visit each node once.
• Space: O(N) for storing DP values + recursion stack.

Tree:

    A
   / \
  B   C
  |
  D

Compute bottom‑up:

• Leaves C, D:
  dp[C][1]=1, dp[C][0]=0
dp[D][1]=1, dp[D][0]=0

• Node B:
  dp[B][1] = 1 + dp[D][0] = 1
dp[B][0] = max(dp[D][0], dp[D][1]) = 1

• Node A:
  dp[A][1] = 1 + dp[B][0] + dp[C][0] = 1+1+0 = 2
dp[A][0] = max(dp[B][0], dp[B][1]) + max(dp[C][0], dp[C][1]) = 1+1 = 2

Answer: max(2,2) = 2 (e.g., invite {A, D} or {B, C}).

To recover which employees are invited, store a choice for each dp[u][state] and backtrack.