Mastering Dynamic Programming: 53 Coding Interview Questions Unveiled

Dynamic programming is a powerful technique that every aspiring software engineer should master to excel in coding interviews. It’s a problem-solving approach that breaks down complex problems into simpler sub-problems, solves them recursively, and stores the solutions for future use. This strategy not only optimizes solutions but also saves valuable time during interviews.

In this comprehensive guide, we’ve curated 53 dynamic programming interview questions, ranging from easy to hard difficulty levels. Whether you’re a beginner or an experienced programmer, this article will help you prepare for your next coding interview with confidence.

Easy Dynamic Programming Interview Questions

Let’s start with some easy questions to warm up:

1. Maximum Subarray
2. Climbing Stairs
3. Pascal’s Triangle
4. Pascal’s Triangle II
5. Best Time to Buy and Sell Stock
6. Counting Bits
7. Is Subsequence
8. Fibonacci Number
9. Min Cost Climbing Stairs
10. Divisor Game
11. N-th Tribonacci Number
12. Get Maximum in Generated Array

These questions are often asked during the “phone screen” stage, so you should be comfortable answering them without being able to write code or use a whiteboard. Practice solving these problems within a fixed amount of time to simulate an actual interview scenario.

Medium Dynamic Programming Interview Questions

As you progress, you’ll encounter slightly more challenging questions that require you to write code or sketch out solutions on a whiteboard. Here are some medium-level dynamic programming questions:

1. Longest Palindromic Substring
2. Unique Paths
3. Unique Paths II
4. Minimum Path Sum
5. Decode Ways
6. Triangle
7. Unique Binary Search Trees
8. Best Time to Buy and Sell Stock II
9. Unique Binary Search Trees II
10. Interleaving String
11. Palindrome Partitioning
12. Maximal Square
13. House Robber
14. Word Break
15. House Robber II
16. Maximum Product Subarray
17. Longest Increasing Subsequence
18. Perfect Squares
19. Partition Equal Subset Sum
20. Coin Change

These questions often require you to write code or sketch solutions on a whiteboard, so practicing them in a similar environment will help you prepare for the real interview setting.

Hard Dynamic Programming Interview Questions

Brace yourself for the most challenging dynamic programming questions. These questions may be asked in an onsite or video call interview, and you’ll likely be given more time to create a full solution:

1. Regular Expression Matching
2. Maximal Rectangle
3. Edit Distance
4. Wildcard Matching
5. Distinct Subsequences
6. Palindrome Partitioning II
7. Scramble String
8. Best Time to Buy and Sell Stock III
9. Burst Balloons
10. Best Time to Buy and Sell Stock IV
11. Dungeon Game
12. Frog Jump
13. Arithmetic Slices II – Subsequence
14. Russian Doll Envelopes
15. Freedom Trail
16. Cherry Pickup
17. Concatenated Words
18. Remove Boxes
19. Student Attendance Record II
20. K Inverse Pairs Array
21. Decode Ways II

These questions are designed to test your problem-solving abilities, algorithmic thinking, and understanding of dynamic programming at a deeper level. Don’t be discouraged if you find them challenging; with practice and persistence, you’ll be able to tackle even the most complex problems.

Dynamic Programming Basics

To truly master dynamic programming, it’s essential to understand its fundamentals. Here’s a brief overview of what you need to know:

What is Dynamic Programming?

Dynamic programming is an algorithmic paradigm that creates optimal solutions for complex problems by breaking them down into simpler sub-problems that can be solved recursively. It is applicable to problems that have the following two properties:

• Optimal Substructure: The optimal solution builds on the optimal solutions of smaller pieces.
• Overlapping Sub-problems: The broken-down versions of the problem are repeated.

Dynamic programming allows you to solve problems efficiently by storing the solutions to sub-problems and reusing them later, avoiding redundant calculations.

Use Cases for Dynamic Programming

Dynamic programming can be applied to a wide range of problems, including:

• Fibonacci problems
• Finding if a word can be built from a set of strings
• Coin change problem
• Min cost path problem
• Assembly line scheduling
• Tile stacking/box stacking problem
• Travelling salesman problem
• Palindrome problems
• Wildcard pattern matching
• Graph coloring problems
• Levenshtein distance
• Diff programs

Example Implementation

There are two main approaches to implementing dynamic programming: