Leetcode 1261: Find Elements in a Contaminated Binary Tree
Given a contaminated binary tree, recover it and implement a class to search for specific values in the tree.
Problem
Approach
Steps
Complexity
Input: The input is a list of operations. Each operation is either the initialization of a tree or a search for a target value.
Example: [[[-1, null, -1]], [1], [2]]
Constraints:
• The tree has at most 10^4 nodes.
• Each node value is -1 initially.
Output: The output is a list where each entry corresponds to the result of a 'find' operation, indicating whether the target exists in the tree.
Example: [null, false, true]
Constraints:
• The result of the 'find' operation is either true or false.
Goal: Recover the tree's original values and search for specific targets efficiently.
Steps:
• 1. Initialize the tree with the given contaminated root.
• 2. Recover the values of each node using depth-first traversal.
• 3. Implement the 'find' operation by checking if the target exists in the recovered set of values.
Goal: The constraints for the problem involve tree size and the values to search for.
Steps:
• 1 <= tree size <= 10^4
• Target value is between 0 and 10^6
Assumptions:
• The input tree has been contaminated (all node values are initially -1).
• Each node follows the given value rules in the original uncontaminated tree.
• Input: [[[-1, null, -1]], [1], [2]]
• Explanation: In this example, after recovering the tree, the result of searching for 1 is 'false' and 2 is 'true'.
Approach: The problem can be solved by first recovering the tree values using a recursive depth-first search and then using a set to store these values for efficient lookups.
Observations:
• The binary tree follows a specific value pattern which allows for recursive recovery.
• Use recursion to recover each node value, starting from the root. Then, store the recovered values in a set for efficient querying.
Steps:
• 1. Define a helper function to recover the tree values using depth-first traversal.
• 2. Use a set to store recovered values as we traverse the tree.
• 3. Implement the 'find' function to check if a target exists in the set of recovered values.
Empty Inputs:
• The input tree is empty, which should not happen according to the problem constraints.
Large Inputs:
• The solution should efficiently handle trees with up to 10^4 nodes.
Special Values:
• The root value is always 0 and must be recovered first.
Constraints:
• Handle up to 10^4 nodes efficiently in both time and space.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class FindElements {
unordered_set<int> set;
public:
void recover(TreeNode* root, int x) {
if(root == NULL) return;
root->val = x;
set.emplace(x);
recover(root->left, 2*x+1);
recover(root->right, 2*x+2);
}
FindElements(TreeNode* root) {
recover(root, 0);
}
bool find(int target) {
return set.count(target);
}
};
/**
* Your FindElements object will be instantiated and called as such:
* FindElements* obj = new FindElements(root);
* bool param_1 = obj->find(target);
1 : Class Definition
class FindElements {
This defines the `FindElements` class, which is used to recover the binary tree and search for specific elements.
2 : Data Member
unordered_set<int> set;
This declares an unordered set `set` to store the recovered values from the binary tree for fast look-up.
3 : Access Modifier
public:
This sets the section following it to public access, making the methods accessible outside the class.
4 : Function Definition
void recover(TreeNode* root, int x) {
This defines the `recover` function, which is used to traverse the tree and recover the values by assigning values based on the binary tree's structure.
5 : Base Case
if(root == NULL) return;
This is the base case of the recursion: if the node is `NULL`, the function returns without performing any operations.
6 : Node Value Assignment
root->val = x;
This assigns the current node's value to `x`.
7 : Insert to Set
set.emplace(x);
This inserts the node's value `x` into the `set` for fast lookup during search operations.
8 : Recursive Call (Left Child)
recover(root->left, 2*x+1);
This recursively calls the `recover` function to process the left child of the current node, assigning it the value `2*x+1`.
9 : Recursive Call (Right Child)
recover(root->right, 2*x+2);
This recursively calls the `recover` function to process the right child of the current node, assigning it the value `2*x+2`.
10 : Constructor Definition
FindElements(TreeNode* root) {
This defines the constructor of the `FindElements` class, which initializes the tree recovery process.
11 : Call to recover
recover(root, 0);
This calls the `recover` function to recover the tree starting from the root node with an initial value of 0.
12 : Function Definition
bool find(int target) {
This defines the `find` function, which checks if a given target value exists in the recovered tree.
13 : Set Lookup
return set.count(target);
This checks if the `target` value is present in the `set` and returns `true` if it is, or `false` otherwise.
Best Case: O(N), where N is the number of nodes in the tree (for the recovery operation).
Average Case: O(1) for each 'find' operation (due to the set lookup).
Worst Case: O(N) for the recovery operation and O(1) for each 'find' operation.
Description: The time complexity of the recovery operation is O(N), where N is the number of nodes in the tree. The time complexity of each 'find' operation is O(1) due to the set lookup.
Best Case: O(N) for the space used by the set storing the recovered values.
Worst Case: O(N), where N is the number of nodes in the tree (for storing the recovered values).
Description: The space complexity is O(N) for storing the recovered tree values in the set.
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