Closed mah-shamim closed 3 hours ago
We'll follow these steps:
Let's implement this solution in PHP: 2583. Kth Largest Sum in a Binary Tree
<?php
// Definition for a binary tree node.
class TreeNode {
public $val;
public $left;
public $right;
public function __construct($val = 0, $left = null, $right = null) {
$this->val = $val;
$this->left = $left;
$this->right = $right;
}
}
/**
* @param TreeNode $root
* @param Integer $k
* @return Integer
*/
function kthLargestLevelSum($root, $k) {
if ($root === null) {
return -1;
}
// Use BFS to traverse the tree level by level
$queue = [];
array_push($queue, $root);
$levelSums = [];
// BFS loop
while (!empty($queue)) {
$levelSize = count($queue);
$currentLevelSum = 0;
// Process each node in the current level
for ($i = 0; $i < $levelSize; $i++) {
$node = array_shift($queue);
$currentLevelSum += $node->val;
// Add left and right children to the queue for the next level
if ($node->left !== null) {
array_push($queue, $node->left);
}
if ($node->right !== null) {
array_push($queue, $node->right);
}
}
// Store the sum of the current level
array_push($levelSums, $currentLevelSum);
}
// Sort the level sums in descending order
rsort($levelSums);
// Return the k-th largest level sum
return isset($levelSums[$k - 1]) ? $levelSums[$k - 1] : -1;
}
// Example 1:
// Input: root = [5,8,9,2,1,3,7,4,6], k = 2
$root1 = new TreeNode(5);
$root1->left = new TreeNode(8);
$root1->right = new TreeNode(9);
$root1->left->left = new TreeNode(2);
$root1->left->right = new TreeNode(1);
$root1->right->left = new TreeNode(3);
$root1->right->right = new TreeNode(7);
$root1->left->left->left = new TreeNode(4);
$root1->left->left->right = new TreeNode(6);
echo kthLargestLevelSum($root1, 2); // Output: 13
// Example 2:
// Input: root = [1,2,null,3], k = 1
$root2 = new TreeNode(1);
$root2->left = new TreeNode(2);
$root2->left->left = new TreeNode(3);
echo kthLargestLevelSum($root2, 1); // Output: 3
?>
TreeNode Class: We define the TreeNode
class to represent a node in the binary tree, where each node has a value (val
), a left child (left
), and a right child (right
).
BFS Traversal: The function kthLargestLevelSum
uses a queue to perform a BFS traversal. For each level, we sum the values of the nodes and store the result in an array ($levelSums
).
Sorting Level Sums: After traversing the entire tree and calculating the level sums, we sort the sums in descending order using rsort
. This allows us to easily access the k-th largest sum.
Edge Case Handling: If there are fewer than k
levels, we return -1
.
This approach ensures that we traverse the tree efficiently and return the correct kth largest level sum.
Discussed in https://github.com/mah-shamim/leet-code-in-php/discussions/735
kth
**largest** level sum in the tree (not necessarily distinct)_. If there are fewer than `k` levels in the tree, return _`-1`_. **Note** that two nodes are on the same level if they have the same distance from the root. **Example 1:** ![binaryytreeedrawio-2](https://assets.leetcode.com/uploads/2022/12/14/binaryytreeedrawio-2.png) - **Input:** root = [5,8,9,2,1,3,7,4,6], k = 2 - **Output:** 13 - **Explanation:** The level sums are the following: - Level 1: 5. - Level 2: 8 + 9 = 17. - Level 3: 2 + 1 + 3 + 7 = 13. - Level 4: 4 + 6 = 10. The 2nd largest level sum is 13. **Example 2:** ![treedrawio-3](https://assets.leetcode.com/uploads/2022/12/14/treedrawio-3.png) - **Input:** root = [1,2,null,3], k = 1 - **Output:** 3 - **Explanation:** The largest level sum is 3. **Constraints:** - The number of nodes in the tree is `n`. -2 <= n <= 105
-1 <= Node.val <= 106
- `1 <= k <= n` **Hint:** 1. Find the sum of values of nodes on each level and return the kth largest one. 2. To find the sum of the values of nodes on each level, you can use a DFS or BFS algorithm to traverse the tree and keep track of the level of each node.