Explain the procedure for transforming a binary tree to eliminate redundant data and ensure the uniqueness of elements.

To eliminate redundant data and ensure the uniqueness of elements in a binary tree, a data structure transformation called a binary search tree (BST) or its variations is usually applied.

The procedure may include the following steps:

1. Tree traversal — for example, using in-order traversal to obtain all elements.
2. Removing duplicates — during traversal, elements can be stored in a data structure that does not allow repeats (e.g., a set).
3. Building a new tree — based on the unique elements, a new binary search tree is created, where each element is placed so that for each node, all elements in the left subtree are smaller, and in the right — larger.

This ensures:

• Uniqueness of elements.
• Fast search, insertion, and deletion of elements.

Example in Swift (iOS):

class TreeNode {
    var value: Int
    var left: TreeNode?
    var right: TreeNode?

    init(_ value: Int) {
        self.value = value
    }
}

func inorderTraversal(_ root: TreeNode?, _ result: inout [Int]) {
    guard let node = root else { return }
    inorderTraversal(node.left, &result)
    result.append(node.value)
    inorderTraversal(node.right, &result)
}

func buildBST(_ values: [Int]) -> TreeNode? {
    var root: TreeNode?
    for value in values {
        root = insertIntoBST(root, value)
    }
    return root
}

func insertIntoBST(_ root: TreeNode?, _ value: Int) -> TreeNode? {
    guard let node = root else { return TreeNode(value) }
    if value < node.value {
        node.left = insertIntoBST(node.left, value)
    } else if value > node.value {
        node.right = insertIntoBST(node.right, value)
    }
    return node
}

// Usage:
var elements = [Int]()
inorderTraversal(originalRoot, &elements)
let uniqueElements = Array(Set(elements)).sorted()
let newRoot = buildBST(uniqueElements)

Thus, the transformation of a binary tree involves traversal, filtering unique values, and constructing a new tree with unique elements.