Leetcode #2005: Subtree Removal Game with Fibonacci Tree
In this guide, we solve Leetcode #2005 Subtree Removal Game with Fibonacci Tree in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
A Fibonacci tree is a binary tree created using the order function order(n): order(0) is the empty tree. order(1) is a binary tree with only one node.
Quick Facts
- Difficulty: Hard
- Premium: Yes
- Tags: Tree, Math, Dynamic Programming, Binary Tree, Game Theory
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: n = 3
Output: true
Explanation:
Alice takes the node 1 in the right subtree.
Bob takes either the 1 in the left subtree or the 2 in the right subtree.
Alice takes whichever node Bob doesn't take.
Bob is forced to take the root node 3, so Bob will lose.
Return true because Alice wins.
Python Solution
Complexity
The time complexity is O(n·m) (typical). The space complexity is O(n·m) or optimized.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.