## Binary Search Trees for Efficient Data Management in C

This C code offers a comprehensive Binary Search Tree (BST) implementation, essential for organizing and managing data efficiently. The provided functions enable the creation, insertion, search, deletion, minimum value retrieval, and height calculation within a BST. These operations are critical for tasks such as data organization, retrieval, and analysis. The code's ability to traverse the tree using inorder, preorder, and postorder methods enhances its practicality. Furthermore, it conducts experiments to evaluate the tree's height under varying conditions. This implementation can serve as a valuable resource to help with your C assignment, aiding in understanding and applying data structures for diverse applications where ordered data storage and retrieval are paramount.

## Block 1: Includes and Function Declarations

```
#include < stdio.h >
#include < stdlib.h >
#include " bst.h "
```

This block includes necessary header files for standard input/output, dynamic memory allocation, and a custom header file "bst.h" that likely contains data structure and function declarations related to a Binary Search Tree (BST).

## Block 2: newBST Function

```
BST* newBST()
{
BST* bst;
bst = (BST*) malloc(sizeof(BST));
bst->root = NULL;
return bst;
}
```

This function creates a new empty Binary Search Tree (BST) and returns a pointer to it. It allocates memory for a BST structure, initializes the root node to NULL, and returns a pointer to the newly created BST.

## Block 3: deleteBST Function

```
void deleteBST(BST* T)
{
if (T != NULL)
{
T->root = deleteNode(T->root);
free(T);
}
}
```

This function is responsible for freeing all the memory allocated to a BST. It takes a pointer to a BST as an argument, checks if it's not NULL, and then calls deleteNode to recursively delete all nodes in the tree. Afterward, it frees the memory allocated for the BST structure itself.

## Block 4: insert Function

```
void insert(BST* T, int target)
{
if (T != NULL)
T->root = insertValue(target, T->root);
}
```

This function is used to insert a value into the BST. It takes a pointer to a BST and an integer value to insert. If the BST is not NULL, it calls the insertValue function to perform the insertion, passing the target value and the root node of the tree.

## Block 5: find Function

```
bool find(BST* T, int target)
{
if (T != NULL)
return findValue(target, T->root);
else
return false;
}
```

This function searches for a value in the BST. It takes a pointer to a BST and a target value to search for. If the BST is not NULL, it calls the findValue function, passing the target value and the root node of the tree, and returns true if the value is found, otherwise, it returns false.

## Block 6: deleteFromTree Function

```
void deleteFromTree(BST* T, int target)
{
if (T != NULL)
T->root = deleteValue(target, T->root);
}
```

This function is used to delete a specific value from the BST. It takes a pointer to a BST and a target value to delete. If the BST is not NULL, it calls the deleteValue function to perform the deletion, passing the target value and the root node of the tree.

## Block 7: min Function

```
int min(BST* T)
{
if (T != NULL)
return findMin(T->root);
else
return 10000;
}
```

This function finds the minimum value in the BST. If the BST is not NULL, it calls the findMin function, passing the root node of the tree, and returns the minimum value found. If the tree is empty (NULL), it returns a default value of 10000.

## Block 8: inorder, preorder, and postorder Functions

```
void inorder(BST* T)
{
if (T != NULL)
inorderWalker(T->root);
printf("\n");
}
void preorder(BST* T)
{
if (T != NULL)
preorderWalker(T->root);
printf("\n");
}
void postorder(BST* T)
{
if (T != NULL)
postorderWalker(T->root);
printf("\n");
}
```

These three functions (inorder, preorder, and postorder) are responsible for printing the elements of the BST in different traversal orders. They call corresponding walker functions (inorderWalker, preorderWalker, and postorderWalker) that traverse and print the tree nodes accordingly.

## Block 9: height Function

```
int height(BST* T)
{
if (T != NULL)
return nodeHeight(T->root);
else
return -1;
}
```

This function calculates the height of the BST, which is the number of edges in the longest path from a node to the root. It calls the nodeHeight function, passing the root node of the tree. If the tree is empty (NULL), it returns -1.

## Block 10: Deletion of a Specific Node

```
Node* deleteNode(Node* current)
{
if (current != NULL)
{
deleteNode(current->left);
deleteNode(current->right);
free(current);
}
return NULL;
}
```

The deleteNode function is used to delete a specific node. It recursively deletes all nodes in the tree starting from the given node and frees their memory. It returns NULL as an updated pointer to replace the node in the tree.

## Conclusion

In conclusion, this Binary Search Tree (BST) implementation in C serves as a powerful tool for efficient data management and retrieval. With its array of functions for tree creation, value manipulation, traversal, and height calculation, it provides a solid foundation for understanding and applying data structures in real-world applications. Whether you are a student seeking assistance with a C programming assignment or a developer looking to enhance your data handling capabilities, this code offers valuable insights and practical solutions. Its experimental capabilities to assess tree heights under various scenarios add an extra layer of depth to its educational and analytical value. Overall, this BST implementation embodies the essence of structured and organized data storage, unlocking the potential for streamlined data management in a wide range of contexts.