How can the traversal of a binary tree be implemented using a stack?

Traversal of a binary tree can be implemented using a stack by using depth-first search (DFS) algorithms.

In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child. Traversal of a binary tree means visiting each node of the tree exactly once in a specific order. This can be achieved using a stack, which is a linear data structure that follows the Last In First Out (LIFO) principle.

There are three types of depth-first search (DFS) algorithms that can be used to traverse a binary tree using a stack: pre-order, in-order, and post-order.

In a pre-order traversal (root, left, right), the process is as follows: start from the root node, visit the node, then recursively do a pre-order traversal of the left subtree, followed by a pre-order traversal of the right subtree. To implement this using a stack, push the root node to the stack. Then, as long as the stack is not empty, pop a node from the stack, visit it, and push its right child (if any) and then its left child (if any) to the stack.

In an in-order traversal (left, root, right), start from the root node, recursively do an in-order traversal of the left subtree, visit the node, then do an in-order traversal of the right subtree. To implement this using a stack, start from the root node, push it and all its left descendants to the stack. Then, as long as the stack is not empty, pop a node from the stack, visit it, and if it has a right child, push it and all its left descendants to the stack.

In a post-order traversal (left, right, root), start from the root node, recursively do a post-order traversal of the left subtree, then do a post-order traversal of the right subtree, and finally visit the node. Implementing post-order traversal using a stack is more complex than pre-order and in-order traversals. It requires two stacks. Push the root to the first stack. Then, as long as the first stack is not empty, pop a node from the first stack, push it to the second stack, and push its left and right children (if any) to the first stack. Finally, pop and visit the nodes from the second stack.

In all these methods, the stack helps keep track of the