The Path Sum IV problem encodes a binary tree as a flat array where each element represents a node as a 3-digit number: the first digit is the level, the second is the position within that level, and the third is the value. Find the sum of all root-to-leaf path sums. This coding problem decodes a compact tree representation using a hash map. The array, hash table, DFS, binary tree, and tree interview pattern is the core.
Alibaba and TikTok ask this because it tests encoding/decoding of tree structures — a skill relevant to serialization, database storage, and compressed data formats. The ability to reconstruct tree relationships from an encoded format demonstrates strong data structure reasoning.
Hash map reconstruction + DFS. Decode each 3-digit number: level = num // 100, pos = (num % 100) // 10, val = num % 10. Store in map[(level, pos)] = val. DFS from root (1, 1): pass the current running sum. At each node, check if children (level+1, 2*pos-1) and (level+1, 2*pos) exist. If a node has no children (leaf), add the running sum to total.
nums=[113,215,221]. Decode: (1,1,3),(2,1,5),(2,2,1). Tree: root=3 at level 1. Children: 5 at (2,1), 1 at (2,2). Path 3→5: sum=8. Path 3→1: sum=4. Total = 12.
(level+1, 2*pos-1), right = (level+1, 2*pos).Compact tree encodings appear in competitive programming and data engineering. Practice decoding tree structures from various formats: array-of-3-digit-codes, BFS-level arrays, parent-pointer arrays. The hash map approach generalizes any flat encoding to parent-child lookups. Path Sum IV is a great problem for understanding how tree algorithms adapt to non-standard representations.
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Delete Nodes And Return Forest | Medium | Solve | |
| Count Nodes With the Highest Score | Medium | Solve | |
| Create Binary Tree From Descriptions | Medium | Solve | |
| Find Duplicate Subtrees | Medium | Solve | |
| Lowest Common Ancestor of a Binary Tree IV | Medium | Solve |