Assignment 12: Binary Search Trees

Assignment 12 Binary Search Trees

In this assignment, you are tasked with implementing essential functions for a binary search tree (BST) data structure coded in C++. The class provided manages a binary tree comprising nodes that store integer values, with a focus on correctly inserting nodes, computing the tree height, and clearing the tree structure. The functions you will develop include insert(), height(), as well as a private recursive helper for each, and clear() with its recursive counterpart.

The insert() function is the starting point, designed to add new integers into the BST while maintaining its ordered property. The public insert() calls the private recursive version, which traverses down the tree until it finds the appropriate null position for the new node. You must implement the recursive insert() so that if the current node is NULL, a new node is dynamically allocated with the given item, initialized with null left and right children. Otherwise, if the item to insert is less than or equal to the current node’s item, recursive insertion proceeds into the left subtree; if greater, into the right subtree. After the recursive call, the newly created or existing node pointer should be assigned back to the left or right child pointer accordingly to maintain the correct links. At each level, the recursive function returns the node pointer, culminating in assigning the final root back into the main root pointer, and incrementing the nodeCount variable.

Next, the height() function calculates the depth of the tree. The public height() simply invokes the private recursive version with the root node. The recursive height() checks if the current node is NULL; if so, it returns 0, indicating no height at that branch. Otherwise, it recursively computes the height of the left and right subtrees, takes the maximum of these two, adds one for the current level, and returns this value. This process results in an accurate measure of the tree's height, which is useful for understanding the tree's balance and efficiency.

Finally, the clear() method deallocates all nodes in the tree, ensuring no memory leaks. Both the public clear() and private recursive clear() functions have void return types. The recursive clear() checks if the current node is NULL; if not, it invokes itself recursively on both left and right children before deleting the current node. This post-order traversal guarantees all child nodes are deleted before their parent node, maintaining proper memory management. The public clear() then resets the root pointer to NULL; this process empties the tree completely.

Implementing these functions properly will enable comprehensive testing of the BinaryTree class, including inserting multiple items, computing the height after various insertions, and clearing the entire tree. These methods form the core functionality of a binary search tree, offering ordered data storage and efficient operations.

Paper For Above instruction

The implementation of core binary search tree operations such as insertion, height calculation, and clearing is fundamental to creating an efficient and reliable data structure in C++. The insert() method is crucial because it establishes the ordered property of the BST, organizing data to allow for quick searches, insertions, and deletions. By employing a recursive approach, the insert() method traverses the tree from the root to the appropriate null leaf where the new node is to be inserted, maintaining the binary search order at each step. This approach simplifies the logic and makes the code more elegant, as each recursive call handles a smaller subtree, halting when a null position is found, and creating a new node there.

The recursive insert() function takes a node pointer and the item to insert as parameters. If the current node pointer is NULL, it instantiates a new BinaryTreeNode with the item, setting its left and right children to NULL, and returns this node pointer so that it can be linked appropriately. If the current node is not NULL, the function compares the item to be inserted with the current node's item. If the item is less than or equal to the current node's item, the function recursively inserts into the left subtree and assigns the returned node to node->left; if greater, it goes into the right subtree similarly. This recursive process ensures that each insertion maintains the binary search tree property.

The height() function determines the depth of the tree, which can reflect the efficiency of the BST; a lower height indicates a more balanced tree, leading to faster search operations. The public height() calls the private recursive function with the root node. The recursive function base case occurs when the node parameter is NULL, returning 0, indicating the height of an empty subtree. For non-null nodes, the function computes the height of both left and right subtrees recursively. It then takes the maximum of these two heights and adds one to account for the current node, thus building up the overall height from the bottom up. This recursive height calculation gracefully manages all nodes, providing a reliable measure of the tree's depth.

The clear() method is important for efficient memory management, especially when the tree is no longer needed or needs to be reset. The public clear() method initiates the process, calling the private recursive function passing the root node. The recursive clear() function, following a post-order traversal, first calls itself recursively for the left and right children, ensuring all descendants are deallocated before deleting the current node with delete. This pattern prevents dangling pointers and ensures proper resource deallocation. After the recursive process completes, the public method resets the root pointer to NULL, signifying an empty tree and preventing access to deleted nodes.

Effectively implementing these core functions allows the binary search tree to be robust, efficient, and ready for further extensions such as deletion or balancing. Proper recursive implementations for insert(), height(), and clear() leverage the natural recursive structure of trees, simplify code, and enhance maintainability. These mechanisms form the backbone of many database indexes, in-memory caches, and other data storage solutions where ordered and dynamic data manipulations are required.

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