In trees where each node can have more than two children, known as n-ary trees, traversal principles still apply but must be adapted to account for multiple branches. Instead of having strictly left and right children, each node may hold a list or array of child nodes. Traversal methods such as pre-order and post-order remain valid. In pre-order traversal, you visit the node first, then recursively traverse each of its children in order from left to right (or first to last). Post-order traversal works similarly, but you visit the node only after visiting all its children. There is no standard in-order traversal for n-ary trees because the concept of “middle” doesn’t make sense when a node has more than two children. Traversing such trees typically involves using recursive functions or a queue for level-order traversal. These structures are common in applications like organisational charts, file directories, and XML parsing.

Yes, tree traversal can be applied to trees stored in arrays, but the implementation differs from that used with pointer-based or linked structures. In a typical array-based binary tree, nodes are stored in a level-order manner where the root is at index 0. For any node at index i, its left child is at index (2i + 1) and its right child is at index (2i + 2). Traversal algorithms need to compute these indices rather than following node references. Recursive or iterative traversal is still possible, but it relies on calculating positions rather than accessing child pointers. This structure is efficient for complete binary trees and is often used in heaps or binary heaps. It is less suitable for sparse or unbalanced trees because array slots may go unused, leading to wasted memory. Nonetheless, traversal logic can be directly adapted by translating traditional tree navigation into index arithmetic.

In real-world implementations, trees often contain nodes with only one child or even none at all. When performing traversal, the algorithm must handle these cases gracefully to avoid errors such as null reference exceptions. In recursive traversal, the function typically begins by checking if the current node is null. If it is, the function returns immediately without attempting further access. This acts as the base case for recursion. In iterative implementations, a similar check is included before pushing or popping nodes from a stack or queue. For example, in a binary tree, a node may have a left child but no right child. In such cases, the traversal logic should only recurse or iterate into existing children. This pattern ensures traversal remains robust and avoids crashes. Handling null or missing children is especially important when parsing sparse trees, such as expression trees with incomplete subexpressions or dynamically modified structures in databases or game logic.

Recursive tree traversal is typically more intuitive and easier to write, as the structure of the algorithm closely mirrors the structure of the tree. It requires fewer lines of code and naturally handles depth-first traversal using the call stack. However, recursion comes with limitations. The most significant is the risk of stack overflow in the case of deep or unbalanced trees. Languages with limited recursion depth (such as Python) may encounter errors when traversing large trees. Iterative traversal avoids this issue by using an explicit stack or queue, offering more control over memory usage and avoiding system-imposed limits. Although iterative implementations are generally more complex and verbose, they can handle larger trees and allow for custom stack manipulation. For applications requiring fine-grained control or those operating in constrained environments, iteration may be preferred. Overall, the trade-off is between simplicity (recursion) and flexibility/performance (iteration), and the best choice depends on the context of the problem.

Yes, it is possible to traverse certain types of trees, especially binary trees, without using recursion or an explicit stack by employing Morris traversal or threaded binary trees. These techniques temporarily modify the structure of the tree to allow traversal using only constant space. Morris traversal, for example, creates temporary links between nodes to simulate the behaviour of a stack, enabling in-order traversal without using additional memory. Once the node has been visited, the structure is restored to its original form. This method is particularly efficient in memory-constrained environments, such as embedded systems or devices with limited stack space. However, it comes with added complexity and is not suitable for all tree types, especially if the tree structure must remain untouched. Morris traversal is mainly used for in-order traversal of binary search trees and is a demonstration of how traversal algorithms can be optimised when memory usage is a concern.