Maximum Subtree of the Same Color

Maximum Subtree of the Same Color

1. What is this problem about?

The Maximum Subtree of the Same Color problem asks you to analyze a tree where each node has an assigned color. A "subtree" in this context is usually defined as a node and all of its descendants. The goal is to find the largest subtree where every single node within that subtree has the exact same color. If no such subtree exists beyond individual nodes, the answer would be 1. It is a structural problem that combines tree traversal with property verification.

2. Why is this asked in interviews?

This "Maximum Subtree of the Same Color interview question" is often used by Microsoft and BlackRock to test recursion and tree data structure knowledge. It evaluates whether you can pass information effectively up the tree from leaf nodes to the root. It’s not just about traversing the tree; it’s about aggregating results (size and color consistency) and making decisions at each parent node based on the properties of its children.

3. Algorithmic pattern used

The "Array, Depth-First Search, Dynamic Programming, Tree interview pattern" is the primary approach. You use a post-order Depth-First Search (DFS). For each node, the DFS returns two things: whether the entire subtree rooted at that node is monochromatic (same color) and the size of that subtree. A parent node is part of a monochromatic subtree only if all its children are monochromatic and they all share the same color as the parent. You keep track of a global maximum size during the traversal.

4. Example explanation

Imagine a tree: Node 0 (Red) is the root. Children: Node 1 (Red), Node 2 (Blue). Node 1 has Child: Node 3 (Red).

• DFS at Node 3: Color Red, Size 1, Valid.
• DFS at Node 1: Its child (Node 3) is Red and Valid. Parent Node 1 is also Red. So Node 1's subtree is Valid, Size 2.
• DFS at Node 2: Blue, Size 1, Valid.
• DFS at Node 0: One child is Red, one is Blue. The root (Red) matches Node 1 but not Node 2. So the subtree at Node 0 is NOT monochromatic. The maximum monochromatic subtree size is 2 (the one rooted at Node 1).

5. Common mistakes candidates make

A common mistake in the "Maximum Subtree of the Same Color coding problem" is confusing a "monochromatic subtree" with a "monochromatic connected component." In a subtree, every descendant must match the color. Another error is not handling the base case of leaf nodes correctly or failing to stop the "monochromatic" flag from propagating if even one child has a different color or is not monochromatic itself. Candidates also sometimes use an O(N^2) approach by running a separate DFS for every node instead of the optimal O(N) single-pass DFS.

6. Interview preparation tip

Master the "Post-Order Traversal" pattern. In many tree problems, the answer for a node depends on the answers from its children. Practice returning multiple values from a recursive function (like a custom object or a pair). This skill is essential for tree DP problems. Also, remember to clarify the definition of "subtree" with your interviewer, as some problems define it as any connected subgraph, which would change the required approach significantly.