Apply Binary Search Tree to create a Spanish dictionary. Develop algorithms to search a word, insert a word and delete a word with proper explanation.

1. Break Down the Problem

We need to develop a Binary Search Tree (BST) to represent a Spanish dictionary. The operations we will implement are:

1. Search for a word.
2. Insert a new word.
3. Delete a word.

2. Relevant Concepts

In a Binary Search Tree:

• Each node has a value, with left children containing values less than the node's value and right children containing values greater.
• Searching, inserting, and deleting operations maintain these properties.

Algorithms:

1. Search: Traverse the tree, comparing the target word with the current node:

   • If the target is equal to the current node, the word is found.
   • If the target is less, continue the search in the left subtree.
   • If the target is greater, continue the search in the right subtree.

2. Insert: Traverse the tree to find null (where the word should be inserted):

   • If the current node is null, insert the new word here.
   • Otherwise, follow the same comparison method as in search to find the correct position.

3. Delete: This has three cases:

   • Leaf Node: Simply remove it.
   • One Child: Remove the node and link its parent to its child.
   • Two Children: Find the in-order successor (smallest node in the right subtree), replace the node with it, then delete the original in-order successor node.

3. Analysis and Detail

Search Algorithm:

def search(root, word):
    if root is None or root.word == word:
        return root
    if word < root.word:
        return search(root.left, word)
    return search(root.right, word)

Insert Algorithm:

def insert(root, word):
    if root is None:
        return Node(word)
    if word < root.word:
        root.left = insert(root.left, word)
    elif word > root.word:
        root.right = insert(root.right, word)
    return root

Delete Algorithm:

def delete(root, word):
    if root is None:
        return root

    if word < root.word:
        root.left = delete(root.left, word)
    elif word > root.word:
        root.right = delete(root.right, word)
    else:
        # Node with only one child or no child
        if root.left is None:
            return root.right
        elif root.right is None:
            return root.left

        # Node with two children
        min_larger_node = root.right
        while min_larger_node.left:
            min_larger_node = min_larger_node.left
        root.word = min_larger_node.word
        root.right = delete(root.right, min_larger_node.word)

    return root

4. Verify and Summarize

The algorithms provided for searching, inserting, and deleting words in a binary search tree will correctly manipulate the data structure while maintaining the properties of the BST.

The search function returns the node containing the word if it exists, or null otherwise. The insert function adds a new node into the proper position to keep the BST properties. The delete function handles all three cases effectively to maintain the structure.

Final Answer

We have developed algorithms to search, insert, and delete words in a Binary Search Tree representing a Spanish dictionary.