Longest Special Path II

Longest Special Path II

What is this problem about?

The Longest Special Path II is a complex graph problem where you are given a tree structure. Each node in the tree is assigned a specific "value" or "color." The task is to find the maximum length of a downward path (from an ancestor to a descendant) such that all the node values along this specific path are completely unique.

Why is this asked in interviews?

This is a Hard-level problem that tests a candidate's mastery of Depth-First Search (DFS) combined with sliding window concepts on a graph. Interviewers ask this to evaluate your ability to manage state during deep recursion. It assesses whether you can maintain a history of visited node values and elegantly backtrack, avoiding massive memory duplications.

Algorithmic pattern used

This problem leverages DFS with a Hash Table / Sliding Window state tracker. As you traverse down the tree, you keep track of the current path and a Hash Map storing the most recent depth (index) at which each node value was seen. If you encounter a value that already exists in your current valid window, you must "shrink" your valid path from the top by updating your valid starting depth to be just below the previous occurrence of that value. When backtracking, you restore the state.

Example explanation

Imagine a path down a tree: Node A(val 1) -> Node B(val 2) -> Node C(val 3) -> Node D(val 2).

1. At Node A (1): Map {1: depth 0}. Valid start depth is 0. Length = 1.
2. At Node B (2): Map {1: 0, 2: 1}. Valid start depth is 0. Length = 2.
3. At Node C (3): Map {1: 0, 2: 1, 3: 2}. Valid start depth is 0. Length = 3.
4. At Node D (2): We see '2' again! The last '2' was at depth 1. Our valid path must now start after depth 1. The valid start depth becomes 2. The map updates to {1: 0, 2: 3, 3: 2}. The valid path is now just nodes C and D (Length 2). The global maximum length recorded during this traversal is 3.

Common mistakes candidates make

A major pitfall is forgetting to backtrack the Hash Map state when returning up the DFS call stack. If you branch left, update the map, and then return to branch right, the right branch must not be contaminated by the left branch's values! Candidates often use a global set and fail to remove elements upon returning, breaking the logic for sibling subtrees.

Interview preparation tip

For the Longest Special Path II coding problem, practice writing DFS functions that pass a "state" object. Instead of cloning a massive Hash Map for every recursive call (which causes Memory Limit Exceeded), use a single shared Hash Map, but rigorously record the previous value associated with the key before you overwrite it, so you can perfectly restore it during the backtracking phase.