Dynamic programming is an essential algorithmic technique that comes up frequently in coding interviews, Being able to efficiently solve dynamic programming problems demonstrates strong analytical abilities and coding skills to interviewers
In this comprehensive guide, we will explore some of the most common dynamic programming interview questions, provide tips to ace them, and walk through detailed solutions and sample code. Read on to boost your confidence in tackling any dynamic programming question during the interview process.
Why Dynamic Programming Questions Matter
Dynamic programming questions test various abilities that are key for success in a coding role
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Algorithmic Thinking – The process of breaking down a complex problem into sub-problems and solving it by combining solutions systematically
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Memoization – Storing results of solved sub-problems to avoid recomputing them, optimizing efficiency.
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Mathematical Analysis – Analyzing the recurrence relations and computational complexity.
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Coding Implementation – Translating the algorithm into clean and efficient code.
Preparing dynamic programming solutions demonstrates your strong foundation in key programming principles. Let’s look at some common pattern types asked.
Optimization Problems
These problems aim to find the optimal solution, like maximum profit or minimum cost. Classic examples include:
Maximum subarray problem – Given an array, find the contiguous subarray with the largest sum.
- Break into subproblems of maximum sum ending at each index.
- Use memoization to store results for each subproblem.
- Calculate maximum from stored results.
0/1 knapsack problem – Given weights and values for items, find the items to include in a knapsack of fixed capacity for maximum value.
- Break into subproblems of maximum value for capacities up to target capacity.
- Use memoization to store optimal solutions for each sub-capacity.
- Return memoized solution for target capacity.
Counting Problems
These involve counting the number of ways to reach a desired outcome, like:
Coin change problem – Given coin denominations and target amount, count total number of ways to make change.
- Break into subproblems of number of ways to make change for amounts below target.
- Use memoization to store results for each sub-amount.
- Add memoized results to get final count.
Unique paths problem – Count number of unique paths from top left to bottom right of a grid.
- Break into subproblems of number of paths to each position.
- Store results in memoization grid and add results.
String Problems
String manipulation challenges like:
Longest common subsequence – Find longest subsequence common to two strings.
- Break into subproblems of LCS of shorter prefixes of strings.
- Use memoization to store LCS length for each subproblem.
- Return longest result.
Edit distance – Find minimum edits to convert string A to string B.
- Break into subproblems of edit distances between shorter prefixes.
- Store results in memoization grid.
- Return final grid value.
Key Strategies to Ace Dynamic Programming Interview Questions
To master dynamic programming interview questions, keep these proven strategies in mind:
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Identify optimal substructure – Spot repeated subproblems you can optimize.
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Map out memoization cache – Decide what intermediate results to store.
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Implement top-down approach – Recursively solve subproblems.
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Analyze time/space complexity – Strive for efficient solutions.
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Test thoroughly with examples – Verify your logic and code handles all cases.
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Explain your approach clearly – Walk through each step verbally.
Preparing go-to dynamic programming patterns will enable you to systematically unravel any tricky problem.
Sample Dynamic Programming Interview Question
Let’s walk through a sample problem to see dynamic programming in action:
Problem: Given a flight of stairs where you can climb 1 or 2 steps each move, count the number of unique ways to climb to the top.
Approach:
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Break into subproblem of number of ways to each step.
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Use memoization to store the subproblem results.
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Calculate the result for current step using results of 2 prior steps.
Pseudocode:
waysToStep(n) if n == 0 or n == 1 return 1 if memo[n] is defined: return memo[n] memo[n] = waysToStep(n-1) + waysToStep(n-2) return memo[n]This demonstrates the optimization, bottom-up building of solutions, and memoization that exemplify dynamic programming.
Take the Time to Master Dynamic Programming
Many programmers dread dynamic programming questions. But learning recurring patterns and practice implementing them in code will give you the confidence to tackle these problems in interviews.
Use this guide as a starting point to analyze practice problems, identify techniques to optimize solutions, and code efficient algorithms. Mastering dynamic programming opens up an immense range of coding challenges to you and proves you have the analytical approach needed to thrive in software roles. Show interviewers what a dynamic problem solver you are!
Heuristics for Identifying Dynamic Programming Problems
The first heuristic comes from considering the problem statement. Does it ask for the smallest and largest options in a list, the best and worst options in a list, or maybe the total number of options? This doesn’t mean that dynamic programming is right or even the best way to do things, but it does mean that DP is something that should be looked into.
As always, it’s a good idea to talk about and work through a few fairly simple examples during a technical interview. Doing so helps to clarify the interviewers requirements and expectations, plus it provides test cases for later. While working through the examples you likely identified a brute-force approach. How did you explain the brute force work that led to the result? Did you say that the more difficult example “follows on from” or “makes use of” the easier one? This is a second heuristic that shows there are sub-problems and repeated work that makes a dynamic programming approach likely to work well.
Does a recursion-based programmatic solution become clear? Where does the recursion lead? It has to “bottom out” at some point, and this is probably the norm. What are the steps or conditions that make recursive calls happen? These are likely to be part of the recurrence relation. The availability of a recursive solution is a third heuristic you can look for.
If any of these rules are present, you can be sure that you will spend time and work hard to find a dynamic programming solution.
Companies That Ask Dynamic Programming Questions
To quickly review, the Fibonacci Sequence is a set of numbers where each number is the sum of the two numbers before it:
We should also restate that the Fibonacci sequence is known to start with 0, 1. This represents the “base case” which will be covered in more detail later on.
Now, if you look from left to right, it’s pretty clear that each number and the one before it are needed to figure out the next number in the sequence. This is like a “bottom-up” method because it starts with the smallest example and works its way up to the final answer.
In other words, if you look at the sequence from right to left, you can figure out the next number by looking at the two numbers that came before it. This method is like a “top-down” approach because it starts with the end goal and works its way down to the first example.
It doesn’t matter how you look at it; the math can be written as F(n) = F(n-1) FC(n-2). This is known as a recurrence relation and is another important concept that we’ll get back to later.
Let’s now turn to some code and step through a simple top-down solution that makes use of recursion:
Consider what happens when invoked as fib(5) to determine the fourth Fibonacci number.
Since N – 1 = 4 and N – 2 = 3, this function calls back to itself many times to get fib(4) and fib(3). Notice that the invocation of fib(4) will in turn make recursive calls fib(3) and fib(2). This highlights the overlapping subproblems and where work is being repeated. The function calls can also be represented as a tree to visualize and identify the repeated work:
In the end, solving for the fifth Fibonacci number ends up solving for:
- The fourth Fibonacci number once
- The third number twice
- The second number three times
- The first number five times
This is where dynamic programming really shines because it keeps work from being done twice and gives a much better solution.
The recursive algorithm for this problem throws away right away the answer to fib(3) and all the other subproblems. What a waste!
We can use a hashmap to store the return value of fib(3) instead of doing it all over again. Then, when the same subproblem comes up again, we can quickly get the result with O(1) time complexity. For small N values, adding two numbers a few times might not seem like a big deal, but as N gets bigger, the number of times this is done quickly becomes a problem. It is called “memorization” to store the result of a function call so that you don’t have to make the same call again eventually.
To do the same thing with this problem, you can solve it from the bottom up by computing and storing each number in the sequence as you go. This style of storing and reusing results is known as “tabulation”.
When solving for Fibonacci, an array can be used for tabulation, which is actually too much because you only need to see the last two results. However, this shows that the idea of using arrays in more than one dimension to solve more complicated problems often needs to be expanded.
Now that we’ve looked at Fibonacci from two different points of view and seen two different approaches, we’ve been introduced to all the main ideas behind dynamic programming:
- Recurrence relations are shown by base cases and the subproblems that happen over and over again.
- Top-down approaches which typically involve recursion and memoization
- Bottom-up approaches that are usually iterative and use tabulation
Let’s move on to look at when and how to apply Dynamic programming in interviews.
Top 5 Dynamic Programming Patterns for Coding Interviews – For Beginners
FAQ
Is dynamic programming asked in an interview?
Are dynamic programming questions hard?
What is a real life example of dynamic programming?
Are dynamic programming problems important for coding interview preparation?
Dynamic programming problems are absolutely vital for your coding interview preparation. Some of the most difficult technical questions in the coding interview demand dynamic programming solutions. Dynamic programming is a complex optimization process applied to recursive solutions.
How many dynamic programming interview questions & problems are there?
Check 12 Dynamic Programming Interview Questions and Problems (SOLVED) and Land Your Next Six-Figure Job Offer! 100% Tech Interview Success!
How does dynamic programming work?
Explore a range of commonly asked interview questions and their well-explained answers. Dynamic Programming (DP) is a powerful algorithmic paradigm that solves a complex problem by breaking it down into simpler subproblems and utilizes the fact that the optimal solution to the overall problem depends upon the optimal solution to its subproblems.
