Find Elements in a Contaminated Binary Tree

class ElementFinder {
    unordered_set<int> recoveredValues;
    
public:
    ElementFinder(TreeNode* root) { levelOrderTraversal(root); }
    
    bool search(int target) { return recoveredValues.find(target) != recoveredValues.end(); }
    
private:
    void levelOrderTraversal(TreeNode* root) {
        queue<TreeNode*> nodeQueue;
        root->val = 0;
        nodeQueue.push(root);
    
        while (!nodeQueue.empty()) {
            TreeNode* node = nodeQueue.front();
            nodeQueue.pop();
            recoveredValues.insert(node->val);
            if (node->left) {
                node->left->val = 2 * node->val + 1;
                nodeQueue.push(node->left);
            }
            if (node->right) {
                node->right->val = 2 * node->val + 2;
                nodeQueue.push(node->right);
            }
        }
    }
};

The C++ program defines a class ElementFinder that reconstructs values in a binary tree which has been altered or contaminated. It then supports search operations to check if a certain value exists in the recovered tree.

• The ElementFinder class utilizes an unordered_set to keep track of the recovered values in the tree for fast lookup operations.
• The constructor initializes the object by performing a level order traversal of the tree starting from the root. During this traversal, it assigns corrected values to each tree node:
  • The root node starts with a value of 0.
  • For any given node with a value v, its left child is assigned the value 2*v + 1, and its right child is assigned the value 2*v + 2.
• The method search(int target) checks if a target value exists in the stored set of recovered values, returning true if it does and false otherwise.
• The function levelOrderTraversal(TreeNode* root) implements the traversal and value recovery mechanism, utilizing a queue to process nodes in level-order:
  • It first inserts the root's adjusted value into the queue.
  • For each node, it retrieves children (if they exist), calculates their values, and inserts them into the queue for further processing.

Ensure the overall tree structure and node connections are correctly maintained for proper functionality of this program when integrating or testing with actual tree data. Additionally, remember to define or include the TreeNode structure and necessary headers like <unordered_set> and <queue> if not already included in the surrounding project.

class ElementSeeker {
    
    HashSet<Integer> elementsRecovered;
    
    public ElementSeeker(TreeNode root) {
        elementsRecovered = new HashSet<>();
        processTree(root);
    }
    
    public boolean search(int target) {
        return elementsRecovered.contains(target);
    }
    
    private void processTree(TreeNode root) {
        Queue<TreeNode> nodesQueue = new LinkedList<>();
        root.val = 0;
        nodesQueue.add(root);
    
        while (!nodesQueue.isEmpty()) {
            TreeNode currentNode = nodesQueue.remove();
            elementsRecovered.add(currentNode.val);
            if (currentNode.left != null) {
                currentNode.left.val = currentNode.val * 2 + 1;
                nodesQueue.add(currentNode.left);
            }
            if (currentNode.right != null) {
                currentNode.right.val = currentNode.val * 2 + 2;
                nodesQueue.add(currentNode.right);
            }
        }
    }
}

The Java solution provided effectively deals with finding elements in a binary tree that has been contaminated, i.e., some of the node values are altered or lost. The solution involves two primary components: the recovery of the tree's proper element values and the ability to search through the recovered values to check for the existence of a specified target.

• The ElementSeeker class is implemented with a field, elementsRecovered, which utilizes a HashSet to store the recovered elements of the binary tree.
• In the constructor of this class, the tree is processed starting from the given root to reconstruct the correct values of each node. This is crucial since the input tree is not in its intended state.
• The processing of the tree is executed through the processTree method. Here, you set the root's value to 0 and use a Queue to iteratively traverse the tree in a level-order fashion (BFS—Breadth First Search). Each node's left child is calculated and set as 2 * value of current node + 1, and the right child as 2 * value of current node + 2. Each visited node's value is added to the HashSet.
• The search method provides a mechanism to check whether a specific target value exists within the tree's recovered elements. This is simply done through an O(1) lookup in the HashSet.

Overall, this robust approach ensures that even in a contaminated binary tree, node values can be efficiently recovered and searched using a combination of BFS and HashSet. The choice of a HashSet enhances quick lookups which are essential for frequent search operations.

class ElementFinder:
    
    def __init__(self, root: TreeNode):
        self.recorded_values = set()
        self.process_nodes(root)
    
    def exists(self, target: int) -> bool:
        return target in self.recorded_values
    
    def process_nodes(self, root: TreeNode) -> None:
        processing_queue = [root]
        root.val = 0
    
        while processing_queue:
            node = processing_queue.pop(0)
            self.recorded_values.add(node.val)
            if node.left:
                node.left.val = node.val * 2 + 1
                processing_queue.append(node.left)
            if node.right:
                node.right.val = node.val * 2 + 2
                processing_queue.append(node.right)

This solution defines a Python class, ElementFinder, designed to handle a specific problem: finding elements in a contaminated binary tree where values are reconstructed. The ElementFinder class is structured to operate efficiently by utilizing a set to record node values and a queue for processing the nodes of the tree.

Upon initialization, the class:

• Accepts a root node,
• Initializes a recorded_values set to store node values,
• Calls process_nodes to reconstruct node values starting from the root and store them.

The process_nodes method reconstructs the binary tree's values assuming the root value starts at 0 and employs the breadth-first search (BFS) strategy. This approach recalculates each node's value based on its parent:

• If node.left exists, it assigns node.left.val as node.val * 2 + 1.
• If node.right exists, it assigns node.right.val as node.val * 2 + 2.

The node values are stored in recorded_values, and the method uses a queue (processing_queue) to keep track of nodes to be processed, ensuring all nodes in the tree are visited and their values calculated appropriately.

To check the existence of a specified value target in the tree, the class provides the exists method, returning True if target is found in the recorded_values set; otherwise, it returns False.

The implementation would require the user to have a TreeNode class definition compatible with this system, where each node can store a val, left, and right attribute referring to its value and left and right children, respectively. This solution efficiently ensures each node is accessed once and the value calculation respects the tree's hierarchical structure for comprehensive tree exploration.