How do you implement tree traversal non-recursively?

You can implement tree traversal non-recursively by using a stack or queue data structure to keep track of nodes.

Tree traversal is a fundamental operation in tree data structures where each node of the tree is visited in a specific order. The most common types of tree traversal are pre-order, in-order, and post-order. These can be implemented recursively, but it's also possible to do it non-recursively, which can be more efficient in terms of memory usage.

To implement tree traversal non-recursively, you can use a stack or queue data structure. A stack is a Last-In-First-Out (LIFO) data structure, while a queue is a First-In-First-Out (FIFO) data structure. The choice between a stack and a queue depends on the type of traversal you want to implement.

For pre-order traversal (visit the root, traverse the left subtree, traverse the right subtree), you can use a stack. Start by pushing the root node onto the stack. Then, while the stack is not empty, pop a node from the stack, visit it, and push its right child and then its left child onto the stack (if they exist).

For in-order traversal (traverse the left subtree, visit the root, traverse the right subtree), you can also use a stack. Start by pushing the root node and all its left descendants onto the stack. Then, while the stack is not empty, pop a node from the stack, visit it, and push its right child and all its left descendants onto the stack (if they exist).

For post-order traversal (traverse the left subtree, traverse the right subtree, visit the root), it's a bit more complicated, but you can still use a stack. You need two stacks: push the root onto the first stack, and then while this stack is not empty, pop a node from it, push it onto the second stack, and push its left and then its right child onto the first stack (if they exist). Finally, pop and visit the nodes from the second stack.

For level-order traversal (visit the nodes level by level from left to right), you can use a queue. Start by enqueuing the root node. Then, while the queue is not empty, dequeue a node, visit it, and enqueue its left child and then its right child (if they exist).