Number of Good Leaf Nodes Pairs

Problem Description

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.

Key Insights

• Leaf nodes are nodes without children.
• The shortest path between two leaf nodes can be determined using their lowest common ancestor (LCA).
• We can use depth-first search (DFS) to traverse the tree and collect information about leaf nodes.
• The distance between two leaf nodes can be calculated based on their depth in the tree and the path taken to reach their LCA.
• Since the maximum distance is small (up to 10), we can use a counting array to keep track of leaf nodes at different depths.

Space and Time Complexity

Time Complexity: O(N), where N is the number of nodes in the tree, since we visit each node once. Space Complexity: O(H), where H is the height of the tree, due to the recursion stack used during DFS.

Solution

We can solve this problem using a depth-first search (DFS) approach. The idea is to traverse the tree and count the number of leaf nodes at various depths. When we reach a leaf node, we can check the counts of leaf nodes at different depths in relation to the given distance. The key steps are:

1. Perform a DFS traversal of the tree.
2. For each leaf node encountered, record its depth.
3. Use an array to count the number of leaf nodes found at each depth.
4. For each pair of leaf nodes at depths that are within the given distance, increment a counter for good pairs.

Code Solutions