How do you find the ancestors of a node in a tree?

To find the ancestors of a node in a tree, you traverse from the node up to the root of the tree.

In more detail, an ancestor of a node in a tree is any node that is located on the path from the node to the root. This includes the node's parent, the parent's parent, and so on, up to the root of the tree. The root is considered an ancestor of all nodes in the tree.

To find the ancestors of a node, you start at the node and follow the links to its parent, then the parent's parent, and so on, until you reach the root. This process is known as traversal. In a binary tree, each node has at most one parent, so the path from any node to the root is unique. In trees where nodes can have more than two children (known as n-ary trees), the same principle applies: each node has exactly one parent, so the path from any node to the root is unique.

The process of finding the ancestors of a node can be implemented using a simple loop or recursive function. If you're using a loop, you start at the node and repeatedly move to the parent until you reach the root. If you're using recursion, you define a function that takes a node as input, adds the node to a list of ancestors, and then calls itself with the node's parent as input. The base case for the recursion is when the input node is the root of the tree.

In terms of time complexity, finding the ancestors of a node takes O(h) time, where h is the height of the tree (i.e., the maximum number of links from the root to any leaf). This is because in the worst case, you have to traverse from a leaf node to the root. The space complexity is also O(h), because in the worst case, you have to store h nodes in the list of ancestors.