
Problem Statement
In this problem, we are provided with a binary tree which has initially been constructed with specific value assignment rules. These rules are such that the value of any node in the tree can be determined by its position and the value of its parent node in an uncompromised tree. Specifically:
- The root node starts with a value of 0.
- The left child of a node with value
x
is assigned the value2 * x + 1
. - The right child of a node with value
x
is given the value2 * x + 2
.
However, due to some contamination, all node values in the tree are overwritten with -1
.
To tackle the problem, one needs to implement the FindElements
class that:
- Takes the root of this contaminated tree upon initialization and recovers the original values of the tree nodes using the known rules.
- Includes a method
find(int target)
that checks if a target value exists in the recovered tree.
This contamination-recovery and search mechanism would enable us to utilize the tree structure once again for various operations, such as search.
Examples
Example 1
Input
["FindElements","find","find"] [[[-1,null,-1]],[1],[2]]
Output
[null,false,true]
Explanation
FindElements findElements = new FindElements([-1,null,-1]); findElements.find(1); // return False findElements.find(2); // return True
Example 2
Input
["FindElements","find","find","find"] [[[-1,-1,-1,-1,-1]],[1],[3],[5]]
Output
[null,true,true,false]
Explanation
FindElements findElements = new FindElements([-1,-1,-1,-1,-1]); findElements.find(1); // return True findElements.find(3); // return True findElements.find(5); // return False
Example 3
Input
["FindElements","find","find","find","find"] [[[-1,null,-1,-1,null,-1]],[2],[3],[4],[5]]
Output
[null,true,false,false,true]
Explanation
FindElements findElements = new FindElements([-1,null,-1,-1,null,-1]); findElements.find(2); // return True findElements.find(3); // return False findElements.find(4); // return False findElements.find(5); // return True
Constraints
TreeNode.val == -1
- The height of the binary tree is less than or equal to
20
- The total number of nodes is between
[1, 104]
- Total calls of
find()
is between[1, 104]
0 <= target <= 106
Approach and Intuition
Given the contamination in the binary tree, our primary task is to rebuild or recover the original values of the tree nodes. This recovery is based on certain given deterministic rules that define how node values are derived from their parent node's values. Intuitively, our steps can be categorized into two main parts: recovery and search.
Recovering the Tree:
- Initialize the root node value to 0 since that remains unchanged.
- Use a traversal method, preferably level-order traversal (BFS), to go through each node starting from the root.
- For each node that is visited, set the value for the left and right children using the rules provided (
2 * x + 1
for left and2 * x + 2
for right). - This traversing and setting of values will reconstruct the values of all accessible nodes following the original rules of node values assignment based on the node's position.
Finding the Target Value:
- To check for a particular value, once recovery is done, typically, we could:
- Use search methods on the tree, but given the deterministic nature of value assignments, a set or hash table can be utilized during the rebuilding phase to store values.
- During the
find(int target)
method call, simply check if the target value exists in this hash set. - This provides a constant time complexity for the search operation, optimizing our method.
- To check for a particular value, once recovery is done, typically, we could:
The constraints give us bounds that ensure our method will work efficiently. Implementing the steps outlined guarantees that all operations are completed using optimal approaches regarding complexity and feasibility offered by the deterministic structure of the binary tree.
Solutions
- C++
- Java
- Python
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 anunordered_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 value2*v + 1
, and its right child is assigned the value2*v + 2
.
- The method
search(int target)
checks if a target value exists in the stored set of recovered values, returningtrue
if it does andfalse
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 aHashSet
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 aQueue
to iteratively traverse the tree in a level-order fashion (BFS—Breadth First Search). Each node's left child is calculated and set as2 * value of current node + 1
, and the right child as2 * value of current node + 2
. Each visited node's value is added to theHashSet
. - 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 theHashSet
.
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 assignsnode.left.val
asnode.val * 2 + 1
. - If
node.right
exists, it assignsnode.right.val
asnode.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.
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