inordertraversal

Inorder traversal is a depth-first traversal of a binary tree in which, for every node, the traversal visits the left subtree first, then the node itself, and finally the right subtree. This order means that, for binary search trees, an inorder traversal visits the nodes in nondecreasing order of their keys.

The simplest way to implement inorder traversal is recursively. A typical recursive definition is: inorder(node) if node is not null, then inorder(node.left); visit(node); inorder(node.right). An explicit iterative version commonly uses a stack: initialize current to the root; while the stack is not empty or current is not null, push all left ancestors of current, then pop a node, visit it, and move to its right child.

There are also space-optimized variants, such as Morris traversal, which uses temporary threading to enable traversal without a stack or recursion, achieving O(1) additional space on average while still visiting each node exactly once.

The time complexity of inorder traversal is O(n), where n is the number of nodes, since each node is visited once. The space complexity depends on the method: recursion or an explicit stack requires O(h) space, where h is the tree height (O(log n) for a balanced tree, O(n) in the worst case). Morris traversal reduces extra space to O(1) but involves modifying and restoring pointers during traversal.

Applications of inorder traversal include producing a sorted sequence from a binary search tree, validating BST properties, and performing operations that require ordered access to elements. It is one of the standard depth-first traversal orders, alongside preorder and postorder.