# What Is Tree Sort in Data Structure?

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Heather Bennett

What Is Tree Sort in Data Structure?

Tree sort is a sorting algorithm that utilizes the concept of a binary search tree (BST) to efficiently sort an array of elements. It is based on the principle of creating a binary search tree from the given elements and then traversing the tree in an in-order manner to obtain a sorted sequence.

The process begins by inserting all the elements of the array into an initially empty BST. The insertion process maintains the property where all elements to the left of a node are smaller, and all elements to the right are greater. This property ensures that when we perform an in-order traversal of the BST, we get a sorted sequence.

Let’s take a closer look at how tree sort works:

Step 1: Building the Binary Search Tree

• Iterate through each element in the input array.
• For each element, insert it into the binary search tree.

The insertion process involves comparing each element with the existing nodes in the BST until a suitable position is found.

Step 2: In-Order Traversal

• Perform an in-order traversal of the binary search tree.
• During this traversal, visit each node in ascending order.
• Store or output each visited node value to obtain a sorted sequence.

In essence, performing an in-order traversal means visiting nodes in the order: left subtree, current node, right subtree. This order ensures that we obtain a sorted sequence when applied to a BST.

It is worth noting that tree sort has an average time complexity of O(n log n) for both best and worst cases. However, it can exhibit poor performance if the initial array is already sorted or nearly sorted, as it may result in an imbalanced tree.

Using tree sort can be advantageous in scenarios where the input data is continuously changing or when we need to maintain a dynamic, sorted sequence. The ability to efficiently insert elements into a BST makes tree sort a suitable choice for such cases.

In conclusion, tree sort is a sorting algorithm that utilizes the concept of a binary search tree. It involves building a BST from the given elements and then performing an in-order traversal on the tree to obtain a sorted sequence. By leveraging the properties of BSTs, tree sort provides an efficient way to sort arrays of elements.