Dynamic Programming: A Complete Roadmap for Cracking Coding Interviews

Introduction

• What is Dynamic Programming?
  • Brief introduction to DP and its significance in coding interviews.
  • Common DP applications in real-world problems.
  • Why DP is often considered challenging and how this roadmap simplifies it.

Prerequisites

• Basic Concepts You Should Know Before Diving Into DP:
  • Recursion and Backtracking
  • Time and Space Complexity
  • Understanding Memoization and Tabulation
  • Basic Mathematical Concepts (like Fibonacci sequence, combinatorics)

References:

• Recursion vs. Iteration
• Memoization and Tabulation

Section 1: Introduction to Dynamic Programming

1.1. Understanding the Basic Concepts

• Theory:
  • Definition and importance of DP
  • Overlapping Subproblems and Optimal Substructure
• LeetCode Problems:
  • Fibonacci Number (Easy)
  • Climbing Stairs (Easy)

1.2. Classical DP Problems:

• Theory:
  • Steps to identify if a problem can be solved using DP.
  • Bottom-up vs Top-down approaches.
• LeetCode Problems:
  • House Robber (Medium)
  • Coin Change (Medium)

Section 2: Intermediate Dynamic Programming

2.1. 1D DP Problems

• Theory:
  • Understanding state transition and the role of variables.
• LeetCode Problems:
  • Maximum Subarray (Medium)
  • Jump Game (Medium)

2.2. 2D DP Problems

• Theory:
  • Introduction to Grid-based DP problems.
• LeetCode Problems:
  • Unique Paths (Medium)
  • Longest Common Subsequence (Medium)

2.3. Subset and Knapsack Problems

• Theory:
  • Detailed explanation of Knapsack variations.
• LeetCode Problems:
  • Partition Equal Subset Sum (Medium)
  • 0/1 Knapsack Problem (On GeeksforGeeks)

Section 3: Advanced Dynamic Programming

3.1. Advanced Techniques:

• Theory:
  • Understanding DP with Bitmasking
  • DP on Trees
• LeetCode Problems:
  • Travelling Salesman Problem (On GeeksforGeeks)
  • Burst Balloons (Hard)

3.2. Advanced Problems & Mixed Topics:

• Theory:
  • DP on Graphs
  • Optimization techniques using DP
• LeetCode Problems:
  • Edit Distance (Hard)
  • Interleaving String (Hard)

Section 4: Dynamic Programming Patterns and Tips

4.1. DP Patterns

• Theory:
  • Identifying common DP patterns.
• Examples:
  • Knapsack, Subsequence, Palindromic, Grid-based, etc.

4.2. Tips for Interviews

• Theory:
  • How to discuss DP problems in interviews.
  • Common pitfalls and how to avoid them.

Section 5: Final Preparations

5.1. Practicing Mixed Problems

• Strategy:
  • Mix up problems from different sections.
• LeetCode Problem Sets:
  • Top 50 Dynamic Programming Problems (Custom LeetCode List)

5.2. Mock Interviews and Resources

• Strategy:
  • Practice with a friend or use platforms like Pramp.
• References:
  • Pramp for Mock Interviews
  • LeetCode Weekly Contests

Conclusion

• Summary:
  • Recap the importance of mastering DP.
  • Emphasize consistency in practice.
  • Final words of encouragement for the upcoming interviews.