
Problem Statement
Given a binary tree and a specific node u
within the tree, the task is to determine the nearest node on the same tree level but situated immediately on the right side of node u
. If node u
does not have any nodes to its right on the same level, the function should return null
. This scenario tests understanding and manipulation of tree data structures, focusing on level-order traversal to identify positional relationships among nodes.
Examples
Example 1
Input:
root = [1,2,3,null,4,5,6], u = 4
Output:
5
Explanation:
The nearest node on the same level to the right of node 4 is node 5.
Example 2
Input:
root = [3,null,4,2], u = 2
Output:
null
Explanation:
There are no nodes to the right of 2.
Constraints
- The number of nodes in the tree is in the range
[1, 105]
. 1 <= Node.val <= 105
- All values in the tree are distinct.
u
is a node in the binary tree rooted atroot
.
Approach and Intuition
To solve this problem efficiently, we can employ a breadth-first traversal (BFT) using a queue. This traversal method ensures that nodes are processed level by level from left to right, which is ideal for checking neighbors on the same level:
- Start by initializing a queue and pushing the root of the tree alongside its level index (e.g.,
(root, 0)
). The level index helps in determining when we move to a new level in the tree. - Use a loop to process each node and its level from the queue:
- For each node extracted, check if this node matches the target node
u
. - If it matches and there's a subsequent node within the same level in the queue, that node is our answer—return it.
- If it matches but no subsequent node exists in the same level, return
null
. - Push the current node's children to the queue with an incremented level index.
- For each node extracted, check if this node matches the target node
- If the loop completes without finding node
u
, returnnull
as the node doesn't exist in the tree based on given constraints.
This approach effectively checks each node's right neighbor by leveraging the natural left-to-right processing of nodes within the same level in a BFT. Use of a queue guarantees that each node and its immediate right neighbor (if it exists) are checked consecutively.
Edge Case Considerations:
- If
u
is the only node at its level, or positioned at the end (i.e., no nodes to its right), the function should returnnull
. - Efficient handling is pivotal, given the high potential number of nodes (up to 100,000), which mandates an algorithm efficient both in terms of time (ideally O(n)) and space.
Solutions
- C++
- Java
- Python
class Solution {
private:
int search_depth;
TreeNode* subsequent_node;
TreeNode* search_target;
public:
TreeNode* locateAdjacentRightNode(TreeNode* root, TreeNode* target) {
this->search_depth = -1;
this->search_target = target;
this->subsequent_node = nullptr;
traverse(root, 0);
return this->subsequent_node;
}
void traverse(TreeNode* current, int level) {
if (current == this->search_target) {
this->search_depth = level;
return;
}
if (level == this->search_depth) {
if (this->subsequent_node == nullptr) {
this->subsequent_node = current;
}
return;
}
if (current->left != nullptr) {
traverse(current->left, level + 1);
}
if (current->right != nullptr) {
traverse(current->right, level + 1);
}
}
};
This C++ solution defines a class Solution
that provides the functionality to find the nearest right node of a given target node in a binary tree. The critical class members include search_depth
, subsequent_node
, and search_target
, used during the traversal of the binary tree.
- The
locateAdjacentRightNode
function initializes the search parameters and begins the tree traversal starting from the root node with an intial level of 0. - The
traverse
function performs a recursive depth-first search through the tree. During traversal:- It checks if the current node matches the target node and updates the
search_depth
. - If the current level matches
search_depth
andsubsequent_node
is not set, it captures the current node as the nearest right node. - Recursively moves to the left and right children of the current node, incrementing the level by 1 each time to accurately track the depth of traversal.
- It checks if the current node matches the target node and updates the
By maintaining a targeted search level (search_depth
) and updating the nearest right node (subsequent_node
), the algorithm efficiently identifies the right neighboring node in relation to a specified target node within the binary tree.
class Solution {
private int nodeDepth;
private TreeNode siblingNode, soughtNode;
public TreeNode findNearestRightNode(TreeNode root, TreeNode u) {
nodeDepth = -1;
soughtNode = u;
siblingNode = null;
traverse(root, 0);
return siblingNode;
}
public void traverse(TreeNode currentNode, int depth) {
if (currentNode == soughtNode) {
nodeDepth = depth;
return;
}
if (depth == nodeDepth) {
if (siblingNode == null) siblingNode = currentNode;
return;
}
if (currentNode.left != null) traverse(currentNode.left, depth + 1);
if (currentNode.right != null) traverse(currentNode.right, depth + 1);
}
}
In this solution, you are tasked with finding the nearest right node to a given node u in a binary tree. This code defines a Java class named Solution
which includes two primary functions to accomplish this task.
Here's a breakdown of the implemented functionality:
Global Variables:
nodeDepth
- stores the depth of the node u.siblingNode
- holds the nearest right node found during the traversal.soughtNode
- stores the reference to the node u for which the nearest right node is sought.
findNearestRightNode(TreeNode root, TreeNode u):
- Initializes the global variables.
- Begins the tree traversal with the root node at depth 0.
- Returns the
siblingNode
, which will either be the nearest right node to u ornull
if no such node is found at the same depth.
traverse(TreeNode currentNode, int depth):
- Handles the tree traversal recursively.
- Checks if the current node is the sought-after node u. If so, it captures the depth and stops further operations in this branch (via return).
- If currently at the depth of u and the
siblingNode
is not yet found, sets thesiblingNode
ascurrentNode
. - Recursively calls itself for left and right children of the current node, incrementing the depth for each.
This method efficiently finds the nearest right node at the same depth as node u without additional data structures like queues. However, it relies on the recursive stack, and its performance depends on the height and structure of the binary tree. It’s a direct and straightforward approach, leveraging depth-first search principles.
class Solution:
def findNextRightNode(self, root: TreeNode, target: TreeNode) -> TreeNode:
def traverse(node, level):
nonlocal target_level, right_node
if node == target:
target_level = level
return
if level == target_level:
if right_node is None:
right_node = node
return
if node.left:
traverse(node.left, level + 1)
if node.right:
traverse(node.right, level + 1)
target_level, right_node = -1, None
traverse(root, 0)
return right_node
The provided Python code defines a solution for finding the nearest right node of a given target node within a binary tree. The solution uses a depth-first traversal approach to explore the tree and identify the target node and its corresponding right neighbor at the same depth. Here's how the code accomplishes this task:
The
findNextRightNode
function expects two parameters:root
, the root node of the binary tree, andtarget
, the node for which you want to find the nearest right node.Inside
findNextRightNode
, the nested helper functiontraverse
is defined. This function performs the actual traversal and comparison. It takesnode
, representing the current node being processed, andlevel
, indicating its depth within the tree.Two non-local variables,
target_level
andright_node
, track the level of the target node and the earliest visited node at the same level to the right of the target, respectively.As
traverse
executes, it first checks if the current node matches the target. If it does, it updatestarget_level
with the current level of the target.If the current
level
matchestarget_level
andright_node
is unset,right_node
gets updated to point to this node, marking it as the nearest right node.The exploration continues to the left and right children of the current node, incrementing the level by 1 to reflect the move down the tree.
Finally,
findNextRightNode
initializestarget_level
andright_node
and invokestraverse
starting from theroot
node at level 0. The result stored inright_node
(either a node orNone
if no right node is found) is returned as the output.
When using this code:
- Ensure that the
TreeNode
class is appropriately defined elsewhere in your environment, as it represents the structure of nodes in your binary tree. - The function expects a binary tree and operates correctly under the assumption of a consistent tree structure without cycles.
This solution efficiently finds the closest right node to a given target node without traversing unnecessary parts of the tree, leveraging depth-first search (DFS) to maintain optimal space and time complexity given the problem constraints.
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