Week 9 Practice
After reading this week's notes and engaging in the embedded activities and reflections, you should be able to:
- Understand balance factors and height-balanced trees.
- Apply single and double rotations to rebalance AVL trees.
- Trace AVL insertions with automatic rebalancing.
- Identify which rotations are needed based on balance factor patterns.
- Set up 1D and 2D DP tables with proper base cases.
- Formulate recurrence relations from problem structure.
- Apply DP to optimization problems (maximization, minimization).
- Solve grid traversal problems using 2D DP.
- Optimize DP solutions for space complexity.
Please refer to this week's readings to review these concepts and skills.
Practice Problems Overview
This week's practice includes 4 problems covering AVL trees and dynamic programming:
- Identifying Required Rotations in AVL Trees - Analyze unbalanced configurations and determine which rotation fixes them
- Maximum Subarray Sum (Kadane's Algorithm) - Find the contiguous subarray with maximum sum using 1D DP
- Unique Paths in Grid - Count paths in a grid using 2D DP (from Day 40)
- Minimum Path Sum - Find minimum-cost path through grid using 2D DP
Key Patterns: The AVL problems test your understanding of tree balancing and rotation mechanics—critical for implementing self-balancing trees. The DP problems build on Days 38-40, applying 1D and 2D DP patterns to classic optimization problems. Together, these problems reinforce Week 9's focus on advanced tree structures and systematic problem-solving with dynamic programming.