I feel like if I'm being asked this in an interview, they're not asking me to use a constraint solver, they're asking me to _write_ a constraint solver. Just for a specific constraint problem, not a more general constraint solver.
Great insight. But this is sadly not applicable to interviews.
> It's easy to do in O(n^2) time, or if you are clever, you can do it in O(n). Or you could be not clever at all and just write it as a constraint problem
This nails it. The point of these problems is to test your cleverness. That's it. Presenting a not-clever solution of using constraint solvers shows that you have experience and your breadth of knowledge is great. It doesn't show any cleverness.
Most interviews are based on the premise that if a diabetic can't synthesize their own insulin in their basement, they are somehow cheating at the game of life.
If my wife's blood sugar is high, she takes insulin. If you need to solve a constraint problem, use a constraint solver.
If your company doesn't make and sell constraint solving software, why do you need me to presume that software doesn't exist and invent it from scratch?
> The "smart" answer is to use a dynamic programming algorithm, which I didn't know how to do. So I failed the interview.
Really? This kind of interview needs to go away.
However, coding interviews are useful. It's just that "knowing the trick" shouldn't be the point. The point is whether the candidate knows how to code (without AI), can explain themselves and walk through the problem, explain their thought processes, etc. If they do a good enough reasoning job but fail to solve the problem (they run out of time, or they go on an interesting tangent that ultimately proves fruitless) it's still a "passed the test" situation for me.
Failure would mean: "cannot code anything at all, not even a suboptimal solution. Cannot reason about the problem at all. Cannot describe a single pitfall. When told about a pitfall, doesn't understand it nor its implications. Cannot communicate their thoughts."
Reminder that the research says the interview process should match the day to day expectations as closely as possible, even to a trial day/week/month. All these brain teasers are low on signal, not to mention bad for women and minorities.
My beef with someone using a constraint solver here is that they almost certainly wouldn't be able to guarantee anything about their solution other than that, if it produces an output, it will be correct. They won't be able to guarantee running time, space usage, or (probably for most tools) even a useful progress indicator. The problem isn't merely that they used another tool - the problem is that they abstracted away critical details. Had they provided a handwritten solution from scratch with the same characteristics, it would've exhibited the same problems.
This doesn't mean they can't provide a constraint solver solution, but if they do, they'd better be prepared to address the obvious follow-ups. If they're prepared to give an efficient solution afterward in the time left, then more power to them.
I agree with the other comments here that using a constraint solver defeats the purpose of the interview. But this seems like a good case for learning how to use a constraint solver! Instead of spending hours coding a custom solution to a tricky problem, you could use a constraint solver at first and only write a custom solution if it turns out to be a bottleneck.
Terrible question for an interview, and further highlights how our interviews are broken.
Greedy algorithms tell you nearly nothing about the candidate's ability to code. What are you going to see? A single loop, some comparison and an equality. Nearly every single solution that can be solved with a greedy algorithm is largely a math problem disguised as programming. The entire question hinges on the candidate finding the right comparison to conduct.
The author himself finds that these are largely math problems:
> Lots of similar interview questions are this kind of mathematical optimization problem
So we're not optimizing to find good coders, we're optimizing to find mathematicians who have 5 minutes of coding experience.
At the risk of self-promotion, I'm fairly opinionated on this subject. I have a podcast episode where I discuss exactly this problem (including discuss greedy algorithms), and make some suggestions where we could go as an industry to avoid these kind of bad-signal interviews:
Here’s my empirical evidence based on several recent “coding session” interviews with a variety of software companies. Background: I have been developing software for over 30 years, I hold a few patents, I’ve had a handful of modestly successful exits. I kind of know a little bit about what I am doing. At this stage in my career, I am no longer interested in the super early stage startup lifestyle, I’m looking at IC/staff engineer type roles.
The mature, state-of-the-art software companies do not give me leetcode problems to solve. They give me interesting & challenging problems that force me to both a) apply best practices of varying kinds and yet b) be creative in some aspects of the solution. And these problems are very amenable to “talking through” what I’m doing, how I’m approaching the solution, etc. Overall, I feel like they are effective and give the company a good sense of how I develop software as an engineer. I have yet to “fail” one of these.
It is the smaller, less mature companies that give me stupid leetcode problems. These companies usually bluntly tell me their monolithic codebase (always in a not-statically-typed language), is a total mess and they are “working on domain boundaries”.
I fail about 50% of these leetcode things because I don’t know the one “trick” to yield the right answer. As a seasoned developer, I often push back on the framing and tell them how I would do a better solution by changing one of the constraints, where the change would actually better match the real world problem they’re modeling.
And they don’t seem to care at all. I wonder if they realize that their bullshit interviewing process has both a false positive and a false negative problem.
The false negatives exclude folks like myself who could actually help to improve their codebase with proper, incremental refactorings.
The false positives are the people who have memorized all the leetcode problems. They are hired and write more shitty monolithic hairball code.
Their interviewing process reinforces the shittiness of their codebase. It’s a spiral they might never get out of.
The next time I get one of these, I think I’m going to YOLO it, pull the ripcord early and politely tell them why they’re fucked.
Long time ago, just for fun, I wrote a constraint solver problem that could figure out which high yield banks to put money into that were recommended on doctor of credit(https://www.doctorofcredit.com/high-interest-savings-to-get/) based on <= `X` money and <= `Y` # of transactions on debit cards maximize the yield and other constraints(boolean and real valued)
I played it for a while when interest rates were really low and used the thing for my own rainy day savings(I did get tired changing accounts all the time)
I've always maintained that solving LeetCode is more about finding the hidden "trick" that makes the solution,
if not easy,
one that is already "solved" in the general sense.
Look at the problem long enough and realize "oh that's a sliding window problem" or somesuch known solution,
and do that.
SAT, SMT, and constraint solvers are criminally underutilized in the software industry. We need more education about what they are, how they work, and what sorts of problems they can solve.
A loonnngggg time ago when I was green, and wasn't taught about constraint solving in my State University compsci program, I encountered the problem when trying to help a friend with his idea.
He wanted to make an app to help sports club owners schedule players for the day based on a couple simple rules. I thought this was going to be easy, and failed after not realizing what I was up against. At the time I didn't even know what I didn't know.
I often look back on that as a lesson of my own hubris. And it's helped me a lot when discussing estimates and timelines and expectations.
> This was a question in a different interview (which I thankfully passed):
> Given a list of stock prices through the day, find maximum profit you can get by buying one stock and selling one stock later.
It was funny to see this, because I give that question in our interviews. If someone suggested a constraint solver... I don't know what I'd have done before reading this post (since I had only vaguely even heard of a constraint solver), but after reading it...
Yeah, I would still expect them to be able to produce a basic algorithm, but even if their solution was O(n^2) I would take it as a strong sign we should hire them, since I know there are several different use cases for our product that require generalized constraint solving (though I know it by other names) and having a diverse toolset on hand is more important in our domain than writing always-optimal code.
Whenever constraint programming languages come up, you can’t miss mentioning Håkan Kjellerstrand. He’s put together an amazing collection of problems and examples—including plenty for MiniZinc—on his site: https://www.hakank.org/minizinc/
My biggest problem with leetcode type questions is that you can't ask clarifying questions. My mind just doesn't work like most do, and leetcode to some extent seems to rely on people memorizing leetcode type answers. On a few, there's enough context that I can relate real understanding of the problem to, such as the coin example in the article... for others I've seen there's not enough there for me to "get" the question/assignment.
Because of this, I've just started rejecting outright leetcode/ai interview steps... I'll do homework, shared screen, 1:1, etc, but won't do the above. I tend to fail them about half the time. It only feels worse in instances, where I wouldn't even mind the studying on leetcode types sites if they actually had decent explainers for the questions and working answers when going through them. I know this kind of defeats the challenge aspect, but learning is about 10x harder without it.
It's not a matter of skill, it's just my ability to take in certain types of problems doesn't work well. Without any chance of additional info/questions it's literally a setup to fail.
edit: I'm mostly referring to the use of AI/Automated leetcode type questions as a pre-interview screening. If you haven't seen this type of thing, good for you. I've seen too much of it. I'm fine with relatively hard questions in an actual interview with a real, live person you can talk to and ask clarifying questions.
> Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.
Maybe it's my graphics programmer brain firing on all cylinders, but isn't this just a linear scan, maintaining a list of open rectangles?
I find this post interesting independent of the question of whether leetcode problems are a good tool for interviews. It's: here are some kinds or problems constraint solvers are useful for. I can imagine a similar post about non-linear least squared solvers like ceres.
I implemented the simple greedy algorithm and immediately fell into the trap of the question: the greedy algorithm only works for "well-behaved" denominations. If the coin values were [10, 9, 1], then making 37 cents would take 10 coins in the greedy algorithm but only 4 coins optimally (10+9+9+9).
That's a bad algorithm, then, not a greedy algorithm. Wouldn't a properly-implemented greedy algorithm use as many coins as possible of a given large denomination before dropping back to the next-lower denomination?
If a candidate's only options are to either use a constraint solver or to implement a naïver-than-usual greedy algorithm, well, sorry, but that's a no-hire.
67 comments
[ 2.9 ms ] story [ 73.9 ms ] thread> It's easy to do in O(n^2) time, or if you are clever, you can do it in O(n). Or you could be not clever at all and just write it as a constraint problem
This nails it. The point of these problems is to test your cleverness. That's it. Presenting a not-clever solution of using constraint solvers shows that you have experience and your breadth of knowledge is great. It doesn't show any cleverness.
If my wife's blood sugar is high, she takes insulin. If you need to solve a constraint problem, use a constraint solver.
If your company doesn't make and sell constraint solving software, why do you need me to presume that software doesn't exist and invent it from scratch?
Really? This kind of interview needs to go away.
However, coding interviews are useful. It's just that "knowing the trick" shouldn't be the point. The point is whether the candidate knows how to code (without AI), can explain themselves and walk through the problem, explain their thought processes, etc. If they do a good enough reasoning job but fail to solve the problem (they run out of time, or they go on an interesting tangent that ultimately proves fruitless) it's still a "passed the test" situation for me.
Failure would mean: "cannot code anything at all, not even a suboptimal solution. Cannot reason about the problem at all. Cannot describe a single pitfall. When told about a pitfall, doesn't understand it nor its implications. Cannot communicate their thoughts."
An interview shouldn't be an university exam.
> We can solve this with a constraint solver
Ok, using your favorite constraint solver, please write a solution for this.
> [half an hour later]
Ok, now how would you solve it if there was more than 100 data points? E.g. 10^12?
This doesn't mean they can't provide a constraint solver solution, but if they do, they'd better be prepared to address the obvious follow-ups. If they're prepared to give an efficient solution afterward in the time left, then more power to them.
Greedy algorithms tell you nearly nothing about the candidate's ability to code. What are you going to see? A single loop, some comparison and an equality. Nearly every single solution that can be solved with a greedy algorithm is largely a math problem disguised as programming. The entire question hinges on the candidate finding the right comparison to conduct.
The author himself finds that these are largely math problems:
> Lots of similar interview questions are this kind of mathematical optimization problem
So we're not optimizing to find good coders, we're optimizing to find mathematicians who have 5 minutes of coding experience.
At the risk of self-promotion, I'm fairly opinionated on this subject. I have a podcast episode where I discuss exactly this problem (including discuss greedy algorithms), and make some suggestions where we could go as an industry to avoid these kind of bad-signal interviews:
https://socialengineering.fm/episodes/the-problem-with-techn...
The mature, state-of-the-art software companies do not give me leetcode problems to solve. They give me interesting & challenging problems that force me to both a) apply best practices of varying kinds and yet b) be creative in some aspects of the solution. And these problems are very amenable to “talking through” what I’m doing, how I’m approaching the solution, etc. Overall, I feel like they are effective and give the company a good sense of how I develop software as an engineer. I have yet to “fail” one of these.
It is the smaller, less mature companies that give me stupid leetcode problems. These companies usually bluntly tell me their monolithic codebase (always in a not-statically-typed language), is a total mess and they are “working on domain boundaries”.
I fail about 50% of these leetcode things because I don’t know the one “trick” to yield the right answer. As a seasoned developer, I often push back on the framing and tell them how I would do a better solution by changing one of the constraints, where the change would actually better match the real world problem they’re modeling.
And they don’t seem to care at all. I wonder if they realize that their bullshit interviewing process has both a false positive and a false negative problem.
The false negatives exclude folks like myself who could actually help to improve their codebase with proper, incremental refactorings.
The false positives are the people who have memorized all the leetcode problems. They are hired and write more shitty monolithic hairball code.
Their interviewing process reinforces the shittiness of their codebase. It’s a spiral they might never get out of.
The next time I get one of these, I think I’m going to YOLO it, pull the ripcord early and politely tell them why they’re fucked.
I played it for a while when interest rates were really low and used the thing for my own rainy day savings(I did get tired changing accounts all the time)
(if you have enough time)
He wanted to make an app to help sports club owners schedule players for the day based on a couple simple rules. I thought this was going to be easy, and failed after not realizing what I was up against. At the time I didn't even know what I didn't know.
I often look back on that as a lesson of my own hubris. And it's helped me a lot when discussing estimates and timelines and expectations.
> Given a list of stock prices through the day, find maximum profit you can get by buying one stock and selling one stock later.
It was funny to see this, because I give that question in our interviews. If someone suggested a constraint solver... I don't know what I'd have done before reading this post (since I had only vaguely even heard of a constraint solver), but after reading it...
Yeah, I would still expect them to be able to produce a basic algorithm, but even if their solution was O(n^2) I would take it as a strong sign we should hire them, since I know there are several different use cases for our product that require generalized constraint solving (though I know it by other names) and having a diverse toolset on hand is more important in our domain than writing always-optimal code.
Because of this, I've just started rejecting outright leetcode/ai interview steps... I'll do homework, shared screen, 1:1, etc, but won't do the above. I tend to fail them about half the time. It only feels worse in instances, where I wouldn't even mind the studying on leetcode types sites if they actually had decent explainers for the questions and working answers when going through them. I know this kind of defeats the challenge aspect, but learning is about 10x harder without it.
It's not a matter of skill, it's just my ability to take in certain types of problems doesn't work well. Without any chance of additional info/questions it's literally a setup to fail.
edit: I'm mostly referring to the use of AI/Automated leetcode type questions as a pre-interview screening. If you haven't seen this type of thing, good for you. I've seen too much of it. I'm fine with relatively hard questions in an actual interview with a real, live person you can talk to and ask clarifying questions.
Maybe it's my graphics programmer brain firing on all cylinders, but isn't this just a linear scan, maintaining a list of open rectangles?
That's a bad algorithm, then, not a greedy algorithm. Wouldn't a properly-implemented greedy algorithm use as many coins as possible of a given large denomination before dropping back to the next-lower denomination?
If a candidate's only options are to either use a constraint solver or to implement a naïver-than-usual greedy algorithm, well, sorry, but that's a no-hire.