Question

The three common types of traversal with a binary tree are _________, __________, and __________.

Short answer

Answer: The three common types of traversal with a binary tree are "inorder", "preorder", and "postorder".

Step-by-step solution

Identify the first traversal method

The first common type of traversal with a binary tree is "inorder" traversal. In this method, first, we traverse the left subtree, then visit the root node, and finally traverse the right subtree.

Identify the second traversal method

The second common type of traversal with a binary tree is "preorder" traversal. In this method, we first visit the root node, then traverse the left subtree, and finally traverse the right subtree.

Identify the third traversal method

The third common type of traversal with a binary tree is "postorder" traversal. In this method, we first traverse the left subtree, then traverse the right subtree, and finally visit the root node. Now, we can fill in the blanks with the three traversal methods: The three common types of traversal with a binary tree are "inorder", "preorder", and "postorder".

Key concepts

Inorder Traversal

Inorder traversal is a method used to process binary trees in a very specific sequence. During this type of traversal, the algorithm first visits all the nodes in the left subtree, then processes the root node, and finally visits all the nodes in the right subtree. This sequence ensures that the nodes are visited in a linear order that corresponds to the natural way one might read the values if they were all laid out on a line. To put it simply, if one were to perform an inorder traversal on a binary search tree, the output would generate the stored numbers in ascending order.

Here's a quick way to remember inorder traversal: Left, Root, Right. That means you always start with the leftmost node and end with the rightmost one. This property makes inorder traversal particularly useful for applications where ordered data retrieval is necessary, like when displaying sorted data.

Preorder Traversal

Preorder traversal is another technique to navigate through a binary tree. This time, the approach shifts, focusing on the root node first before any subtrees are traversed. Specifically, you begin by visiting the root node, then recursively perform a preorder traversal of the left subtree, and conclude with a preorder traversal of the right subtree. The sequence can be denoted as Root, Left, Right.

Preorder traversal is especially useful for creating a copy of the tree. It is also used when saving the tree structure to a file or array — an operation known as 'serialization' that allows for the tree to be reconstructed or 'deserialized' later. Undeniably, the preorder traversal offers a straightforward snapshot of the tree's structure, starting from the very top.

Postorder Traversal

The last common traversal technique for binary trees is postorder traversal. This method takes a different tact by processing a node only after its subtrees have been dealt with. To be precise, you first traverse the left subtree, then the right subtree, and finally, the root node is visited. The visiting sequence here is Left, Right, Root.

An application of postorder traversal is to delete or free nodes from a binary tree cleanly; it ensures that the children are dealt with before their parents, thereby avoiding dangling references. Postorder traversal is also used in certain mathematical evaluations, like in expression trees, where operators are represented by nodes; in such cases, postorder traversal ensures that operand nodes are evaluated before the operator nodes.