1530. Number of Good Leaf Nodes Pairs

[mah-shamim]

You are given the root of a binary tree and an integer distance. A pair of two different leaf nodes of a binary tree is said to be good if the length of the shortest path between them is less than or equal to distance.

Return the number of good leaf node pairs in the tree.

Example 1:

• Input: root = [1,2,3,null,4], distance = 3
• Output: 1
• Explanation: The leaf nodes of the tree are 3 and 4 and the length of the shortest path between them is 3. This is the only good pair.

Example 2:

• Input: root = [1,2,3,4,5,6,7], distance = 3
• Output: 2
• Explanation: The good pairs are [4,5] and [6,7] with shortest path = 2. The pair [4,6] is not good because the length of ther shortest path between them is 4.

Example 3:

• Input: root = [7,1,4,6,null,5,3,null,null,null,null,null,2], distance = 3
• Output: 1
• Explanation: The only good pair is [2,5].

Constraints:

• The number of nodes in the tree is in the range [1, 210].
• 1 <= Node.val <= 100
• 1 <= distance <= 10

Hint:

1. Start DFS from each leaf node. stop the DFS when the number of steps done > distance.
2. If you reach another leaf node within distance steps, add 1 to the answer.
3. Note that all pairs will be counted twice so divide the answer by 2.

[mah-shamim]

To solve this problem, we can follow these steps:

1. Tree Representation: Define the structure of the binary tree nodes.
2. DFS Traversal: Implement a DFS traversal to gather distances of leaf nodes.
3. Counting Good Pairs: During the DFS traversal, count the number of good leaf node pairs.

Let's implement this solution in PHP: 1530. Number of Good Leaf Nodes Pairs

<?php
// Example usage:
$root = new TreeNode(1);
$root->left = new TreeNode(2);
$root->right = new TreeNode(3);
$root->left->right = new TreeNode(4);

$distance = 3;
$solution = new Solution();
echo $solution->countPairs($root, $distance); // Output: 1
?>

Explanation:

1. TreeNode Class: Defines the structure for the tree nodes.
2. Solution Class: Contains the countPairs function which initiates the DFS traversal and returns the result.
3. dfs Function:
   • It recursively traverses the tree.
   • If a leaf node is found, it returns an array with a single element representing the distance from the leaf to itself (which is 1).
   • It then merges the distances from the left and right subtrees, checking if the sum of any pair of distances is less than or equal to the given distance.
   • It returns the updated distances incremented by 1 (for the parent node).

This approach ensures that we only consider leaf nodes and efficiently count pairs using the properties of the binary tree.