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How to Solve Dynamic Programming Interview Questions?

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Learning to answer dynamic programming interview questions is essential if you want to be a serious contender for the best software engineering jobs available. DP is a technique that helps solve complex problems by breaking them down into simpler subproblems, solving them once, and storing their solutions. Dynamic Programming (DP) can thus be seen as a more efficient recursive algorithm in which the same subproblem is not solved twice. This article explains how to approach Dynamic Programming questions and provides sample Dynamic Programming interview questions.

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In this article, you’ll learn:

  • How to Start with Dynamic Programming?
  • How to Solve Interview Questions on Dynamic Programming?
  • Problems on Dynamic Programming for Coding Interviews
  • Cracking the Dynamic Programming Coding Interview
  • Grokking Dynamic Programming Patterns for Coding Interviews
  • FAQs on How to Solve Dynamic Programming Interview Questions

How to Start with Dynamic Programming?

To start with Dynamic Programming, you need to learn the following topics thoroughly: 

  • Overlapping subproblems
  • Optimal substructure property
  • Memoization
  • Tabulation
  • Recursive solution 
  • Memoized solution 
  • Tabulated solution
  • Dynamic Programming basic concepts

How to Solve Interview Questions on Dynamic Programming?

You can use the following steps to solve Dynamic Programming interview questions: 

Step 1: Identifying the problem can be solved using DP

Step 2: Identifying problem variables

Step 3: Clearly expressing the recurrence relation

Step 4: Identifying the base cases

Step 5: Deciding whether to implement recursive or iterative

Step 6: Adding memoization

Step 7: Determining time complexity

Problems on Dynamic Programming for Coding Interviews

Here are some interview questions on Dynamic Programming you should definitely consider solving before your DP interview:

Dynamic Programming Questions asked in Facebook, Amazon, Apple, and Google Interviews

  • 0–1 Knapsack Problem
  • Shortest Common Supersequence Problem
  • Longest Common Subsequence Problem
  • Dice Throw Problem
  • Minimum Partition Problem
  • Ways to Cover a Distance 
  • Longest Path In Matrix
  • Subset Sum Problem
  • Optimal Strategy for a Game
  • Matrix Chain Multiplication Problem
  • Longest Increasing Subsequence Problem
  • Word Break Problem
  • Maximal Product when Cutting Rope Problem
  • The Levenshtein/Edit Distance Problem
  • Partition Problem
  • Rod Cutting Problem
  • Coin Change Problem
  • Egg Dropping Puzzle
  • Partition Problem
  • Box Stacking Problem
  • Boolean Parenthesization Problem

Cracking the Dynamic Programming Coding Interview

A repeatable strategy to get to the most optimal DP solution can help you get an edge over your competitors. The FAST method for Dynamic Programming provides just that. As the acronym suggests, the FAST method has four steps:

  • Find the first solution
  • Analyze the first solution
  • Identify the Subproblems
  • Turn the solution around

Using the FAST method when solving DP problems can help you crack your coding interview more smoothly.

Grokking Dynamic Programming Patterns for Coding Interviews

Here are some Grokking Dynamic Programming Patterns you should explore for your DP coding interview:

  • 0/1 Knapsack
  • 0/1 Knapsack Problem
  • Subset Sum
  • Equal Subset Sum Partition
  • Count Of Subset Sum
  • Minimum Subset Sum Difference
  • Target Sum
  • Unbounded Knapsack
  • Minimum Coin Change
  • Maximum Ribbon Cut
  • Rod Cutting
  • Coin Change
  • Fibonacci Numbers
  • Fibonacci Number
  • Minimum Jumps To Reach End
  • Minimum Jumps With Fee 
  • Staircase
  • Number Divisors 
  • House Thief
  • Palindromic Subsequence
  • Longest Palindromic Subsequence
  • Longest Palindromic Substring
  • Palindromic Partitioning
  • Count Of Palindromic Substrings
  • Minimum Deletions To Make A String Palindrome
  • Longest Common Substring
  • Longest Common Subsequence
  • Longest Repeating Subsequence
  • Longest Alternating Subsequence
  • Longest Bitonic Subsequence
  • Longest Increasing Subsequence
  • Shortest Common Supersequence
  • Maximum Sum Increasing Subsequence
  • Minimum Deletions To Make Sequence Sorted
  • Minimum Deletions And Insertions To Transform A String Into A Different String
  • Edit Distance
  • Subsequence Pattern Matching 
  • String Interleaving

FAQs on How to Solve Dynamic Programming Interview Questions

Q1 Can Dynamic Programming solve all problems?

No, DP can’t solve all the problems. The DP approach is applicable if the problem has the following two attributes: optimal substructure and overlapping sub-problems.

Q2 What are the two key attributes that a problem must have for dynamic programming to be applicable?

The two key attributes a problem must have for DP to be applicable are optimal substructure and overlapping sub-problems. When a solution to the problem can be found by combining optimal solutions to non-overlapping sub-problems, we call it the divide and conquer strategy instead.

Q3 What are the drawbacks of dynamic programming over recursion?

Some of the drawbacks of dynamic programming over recursion are: a significant amount of memory is needed to store the calculated result of every subproblem. There’s no guarantee whether all the stored values will be used or not. Often the result that gets stored is never utilized in the subsequent subproblems.

Q4. Why is dynamic programming important?

DP as a technique helps us solve difficult problems efficiently. That’s the reason why it’s so popular in academia, industry, and software engineering interviews in top roles.

Q5. How is dynamic programming different from recursion?

In recursion, a method calls itself again, while problems with an optimal substructure that can be broken down into similar subproblems are solved in dynamic programming.

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