Data structures and algorithms interview questions and their solutions(techiedelight.quora.com) |
Data structures and algorithms interview questions and their solutions(techiedelight.quora.com) |
"Implement multiplication without using loops."
"Uh, okay. What do you mean by loops?"
"Don't use a conditional loop."
"What do you mean by a conditional loop?"
"Oh, you know, the standard definition."
Time passes.
"I'm stuck. What is the answer?"
"Oh, you just have a loop on b dividing it by 2 using shift operators until it is zero."
"Wait a minute, you said you couldn't use loops."
"Did I? Ah, well."
Hackerrank/leetcode exercises are written the same way. So many times that a problem asks "Output the indexes of two numbers in the array such that their sum is K" and you write your code and the website says "INCORRECT! You said [3,6] but the right answer was [6,3]". Addition is commutative! The two are equal! And both right!
That page is both hilarious and sad at the same time. Hilarious because the second "solution" clearly has a loop, and sad because sites like those don't really help anyone. Some of the pages on that site are downright WTFs:
Can you elaborate on this? I understand the shifting but didn't understand the "loop unrolling fixed iteration part"
Uh, ok:
a * b = b != 0 ? a/(1/b) : 0
Done.
EDIT: handle division by zero.
I would argue that a loop constructs an answer, while recursion deconstructs input.
There's a duality, so you can port algorithms between the two models, but there is an actual distinction.
I never understood why anyone would ask say DP questions in an interview. We don’t use that in 99.9% of software (I’ve never once in my career found a use case). What you’re really testing is whether or not the candidate had enough time to refresh that material. Worse still, it involves a very rigid solution pattern that’s over-specified to that class of problem and tells you nothing about what you want to know: can a candidate synthesize concepts to devise a solution to problems we actually encounter?
"Replace each element of array with product of every other element without using / operator"
use the / operator?
My solution would involve summing the log() of the values in the array.
Edit: how about
(Math.Pow(a+b, 2) - Math.Pow(a,2) - Math.Pow(b,2))/2
For one thing, all loops can be trivially unrolled into a tail-recursive function that most languages will trivially transform back into a loop. Clearly these transforms have no bearing on the nature of the computation.
If asked such a question, I’d probably just use goto. (Bonus points if candidates use a goto on one part of one question I ask, since it saves a minute or two of whiteboard cut and paste, BTW).
That there's a transform between them doesn't make them the same thing, it makes them possible to use for each other in programming. You even seem aware that there's still a distinction -- you're just not sure why it matters.
> Clearly these transforms have no bearing on the nature of the computation.
Depending on the nature of the job, not understanding why you can transform between loops and recursion is big points off. (You can go back and forth because while not the same thing, they're duals, which means you'll be able to find similar structures in both for certain classes of problems.)
That's why you need to understand what induction vs co-induction is -- so you can prove things about the transforms between them, such as that it doesn't impact the result to change the algorithm in a particular manner.
Similarly, you're only talking about really simple inductive or recursive behaviors -- what about complex cases? Are all inductive structures transformable to co-inductive (or the other direction)? What does it do to computational complexity when you make the transform?
That there's an uninteresting kernel in the transform doesn't make the entire transform trivial -- it just means you're only used to working in the "well-behaved" portion of it. (And that there is such a kernel is itself an interesting fact about computation!)
> Clearly these transforms have no bearing on the nature of the computation.
Just to reiterate how off-base I find this comment: there's entire huge collaborations in mathematics and academic computer science exploring the nature of those transforms because understanding how they can be applied is essential for moving forward with things like mechanically/formally verified software.
I get that not everyone is going to know that distinction and its impact -- but the distinction absolutely matters. As you astutely point out, it's used by compilers routinely -- and they certainly need to be sure the transform is well-behaved in the cases they apply it!
I’m not sure what you’re trying to get at...
Assuming you mean the and not a, they're still not the same, as equivalent algorithms need not be identical. Example: 5-3 and 1+1 both compute the result 2, making them equivalent but non-identical algorithms.
There's a way to transform any subtractive recipe for a number into an additive recipe so they're equivalent classes, but addition and subtraction aren't identical as operations.