Create an N array tree and add values and traversal

Model each node with a value and a list of child references; this is an N-ary tree, not a binary tree with implicit left/right positions. Clarify how an add operation identifies the parent, whether duplicate values are allowed, and whether child order matters. For preorder DFS, visit the node then recursively visit children in stored order; for postorder, visit children first; for level order, use a queue and process its current size per level. If insertion searches by value and values are unique, a map from value to node gives expected O(1) parent lookup after initialization; otherwise a traversal costs O(n). Ensure the tree has a single root and reject or handle attempts to add a node twice. Traversing all nodes is O(n) time and O(height) DFS stack or O(width) BFS space.