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Have you ever asked yourself questions to which you can’t find the answer, no matter how much time you spend on it, or reason about it. I know I have.
“Should I break-up with my girlfriend?”
“Should I quit my job and start a company?”
“Should I shut down my company and take a job?”
These questions are hard, we know that. But why are they hard?
I argue they are hard not because it’s tough to answer them, but because there is no right answer.
Computer Science to the rescue!
Surprisingly, this applies to not only to life’s philosophical questions but also to well-defined Computer Science problems. Scientists have been studying them for hundreds of years. Lets talk about what they have learnt.
This video explains it like you were five (or you can just skip it and jump to TL;DR):
P set of problems are easy to solve and check (like multiplication).
NP includes P, but also includes problems that are tough to solve, but easy to verify if a solution is correct; like Su Do Ku.
NP-complete is the hard parts of NP. Or, NP is superset of P and NP-complete.
EXP is exponential. Not only is it ridiculously hard to solve, but also equally hard to check if your answer is correct. Like the best move in chess.
NP-hard can be thought of as a super set of P, NP, and EXP.
TL;DR:
NP-complete: problems that are tough to solve, but easy to verify if a solution is correct. Example: Su Do Ku.
NP-hard: problems that are ridiculously hard to solve, and, even if someone game you the answer, its ridiculously hard to verify if they’re correct. Example: The next best move in a chess game.
Note: when computer scientists say “Ridiculously hard” or “will take a long time”, they mean it’s not possible to find out in the lifetime of the universe! They just don’t want to say it’s impossible, even though it is practically impossible.
How it applies to life
For life decisions you’ll never know if you made the right choice. You can reason, ask people who have been through that, but still you’ll never know for sure. Sometimes, in hindsight, you’ll learn you made the right decision couple of years back. Sometimes, even with hindsight, you’ll never know.
“Should I goto college?” is probably a NP-complete problem. You may feel its not worth it during the program but later in life, you’ll realize you’re much better off than your friends who didn’t attend college.
“Should I break-up or not?” is probably a NP-hard. Even with years of hindsight you still won’t be sure if you made the correct choice (in either case). It’s exactly like asking what’s the best move of a particular chess game.
Want to know a surprising fact above the hard problems
Proving a problem is NP-hard, is a NP-hard itself!
There. You can’t even be sure if the problem is easily solvable or not.
I guess you could use the life analogy to understand the complexity zoo, but that would mean you have a good grip on life. Please share your enlightment with me on my twitter @vedantsopinions.
For those of you, who still argue there must be an answer to every question, you’re effectively saying P = NP. If you can prove this, the Clay Mathematics Institute will award you with a million dollars (and lots of high accolades and respect).
It’s not a dystopia
I don’t feel sad that there are important questions to which I’ll never know the correct answer to. It just means
there is no correct answer!
In this case, just take your best guess and assume its the best. You (or anyone else) can’t prove it otherwise anyway- NP-hard problems are ridiculously hard to verify, remember.
For those of you won’t agree with my life = NP-hard analogy, I can’t prove it you that it is- Proving a problem is NP-hard, is a NP-hard itself. Unless you prove to me that life decisions are easy, I’ll assume I am correct.
Life is like chess! Rather than worrying about the current best move, focus on winning the game and, more importantly, have fun playing it!
(I know I have oversimplified, and maybe even wrongly stated some technical facts in this story. Let me know it the comments!)
Life decisions are like NP hard problems was originally published in Hacker Noon on Medium, where people are continuing the conversation by highlighting and responding to this story.
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