## Sorting with Trees:

Sorting algorithms are fundamental in computer science, offering ways to arrange data efficiently. Among the plethora of sorting methods, Tree Sort stands out for its simplicity and elegance. Unlike traditional comparison-based sorting algorithms, Tree Sort utilizes the hierarchical structure of trees to sort elements. This article aims to explore the Tree Sort algorithm, its steps, implementation in pseudo code and C, advantages, disadvantages, and complexities.

## Tree Sort Algorithm:

Tree Sort leverages the properties of binary search trees (BSTs) to sort elements. The algorithm follows these general steps: Building the Binary Search Tree (BST): Insert each element of the input array into a BST. If an element is less than the current node, it goes to the left subtree; otherwise, it goes to the right subtree. In-order Traversal: Perform an in-order traversal of the BST. This traversal visits nodes in non-decreasing order, effectively sorting the elements.

## Source Code

#include <stdio.h>
#include <stdlib.h>

struct TreeStruct
{
int value;
struct TreeStruct *left;
struct TreeStruct *right;
};

struct TreeStruct *
NewNode (int value)
{
struct TreeStruct *Node =
(struct TreeStruct *) malloc (sizeof (struct TreeStruct));
Node->value = value;
Node->left = Node->right = NULL;
return Node;
}

struct TreeStruct *
InsertNode (struct TreeStruct *root, int value)
{
if (root == NULL)
return NewNode (value);
if (value < root->value)
root->left = InsertNode (root->left, value);
else
root->right = InsertNode (root->right, value);
return root;
}

void
InOrderTraversal (struct TreeStruct *root)
{
if (root != NULL)
{
InOrderTraversal (root->left);
printf ("%d ", root->value);
InOrderTraversal (root->right);
}
}

void
TreeSort (int arr[], int n)
{
struct TreeStruct *root = NULL;
for (int i = 0; i < n; i++)
root = InsertNode (root, arr[i]);
InOrderTraversal (root);
}

int
main (int argc, char *argv[])
{
int arr[] = { 11, 35, 25, 43, 57, 5, 3, 7 };
int n = sizeof (arr) / sizeof (arr[0]);
int i;
printf ("Unsorted array: \n");
for (= 0; i < n; i++)
printf ("%d ", arr[i]);

printf ("\nSorted array: \n");
TreeSort (arr, n);
return 0;
}

## Output:

```Unsorted array:
11 35 25 43 57 5 3 7
Sorted array:
3 5 7 11 25 35 43 57
```

Tree Sort offers average-case time complexity similar to Quick Sort and Merge Sort (O(n log n)).

Suitable for sorting large datasets efficiently.

Provides stable sorting, preserving the order of equal elements.

Can be modified to accommodate additional operations like searching or deleting elements.

Inefficient for small datasets due to the overhead of building and traversing the tree.

The performance heavily depends on the balance of the tree; an unbalanced tree can degrade sorting efficiency to O(n^2).

## Time Complexity:

The average-case time complexity of Tree Sort is O(n log n), similar to other efficient sorting algorithms. However, in the worst-case scenario (unbalanced tree), it can degrade to O(n^2).

## Space Complexity:

Tree Sort has a space complexity of O(n) due to the auxiliary space required for the tree structure.

## Conclusion:

Tree Sort, although not as widely used as some other sorting algorithms, offers a unique approach to sorting data using binary search trees. Its efficiency and stability make it a valuable tool in scenarios where a stable sorting order is required for large datasets. By understanding its principles and complexities, developers can leverage Tree Sort effectively to tackle sorting tasks in various applications.