Tree Sort

Tree sort is a sorting algorithm that is based on Binary Search Tree data structure. It first creates a binary search tree from the elements of the input list or array and then performs an in-order traversal on the created binary search tree to get the elements in sorted order. 

Algorithm: 

• Step 1: Take the elements input in an array.
• Step 2: Create a Binary search tree by inserting data items from the array into the binary search tree.
• Step 3: Perform in-order traversal on the tree to get the elements in sorted order.

Applications of Tree sort:

• Its most common use is to edit the elements online: after each installation, a set of objects seen so far is available in a structured program.
• If you use a splay tree as a binary search tree, the resulting algorithm (called splaysort) has an additional property that it is an adaptive sort, which means its working time is faster than O (n log n) for virtual inputs.

Below is the implementation for the above approach:

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Complexity Analysis:

Average Case Time Complexity: O(n log n) Adding one item to a Binary Search tree on average takes O(log n) time. Therefore, adding n items will take O(n log n) time

Worst Case Time Complexity: O(n²). The worst case time complexity of Tree Sort can be improved by using a self-balancing binary search tree like Red Black Tree, AVL Tree. Using self-balancing binary tree Tree Sort will take O(n log n) time to sort the array in worst case. 

Auxiliary Space: O(n)