How is a binary tree traversed using in-order traversal?

In-order traversal of a binary tree visits nodes in the order of left subtree, root, then right subtree.

In-order traversal is a depth-first algorithm used in binary trees. It's called 'in-order' because it visits the nodes in a specific order: first the left subtree, then the root node, and finally the right subtree. This order of traversal is particularly useful when you want to retrieve the data in the tree in sorted order, as it's the case with binary search trees.

To perform an in-order traversal, you start from the root node and move to the leftmost node. You then visit the left subtree of the root node. After the left subtree has been completely visited, you visit the root node. Finally, you visit the right subtree. This process is repeated recursively for each subtree until all nodes have been visited.

Here's a step-by-step guide on how to perform an in-order traversal:

1. Start from the root node.
2. Move to the leftmost node of the tree (or subtree).
3. Visit the left subtree by recursively calling the in-order function.
4. Visit the root node and process the data.
5. Visit the right subtree by recursively calling the in-order function.

It's important to note that in-order traversal is a depth-first algorithm, meaning it explores as far as possible along each branch before backtracking. This is in contrast to breadth-first algorithms, which explore all the nodes at one level before moving on to the next level.

In terms of complexity, in-order traversal has a time complexity of O(n), where n is the number of nodes in the tree. This is because each node is visited exactly once. The space complexity is O(h), where h is the height of the tree, as it requires stack space for recursive calls.

In conclusion, in-order traversal is a fundamental algorithm in binary tree operations, providing an efficient way to visit all nodes in a sorted order. It's a depth-first algorithm with linear time complexity and logarithmic space complexity.