The above image represents something completely un-understandable to me during my college years. I couldn’t understand what the professor tried to explain during my algorithms class when the topic of P vs NP vs NP-Complete problems came.
Finally I understood it from a video by “Up and Atom”. The problems are grouped according to these 2 criteria:
Can a solution to the problem be found in polynomial time?
Can a given solution for the problem be verified in polynomial time?
These are the problems for which condition 2 holds true. If given a solution to such problem, the correctness of that solution can be verified in polynomial time. Condition 1 being true or false for such problems doesn’t affect whether they can fall under NP category or not.
These are the problems for which condition 2 holds true but condition 1 is false. A valid solution to the problem can’t be verified in polynomial time, but if given a solution to the problem the correctness of that solution can be verified in polynomial time.
For these problems, both conditions 1 & 2 hold true. There exist methods by which a valid solution to any of these problem can be found under polynomial time. And also, any given solution for such problem can be verified in polynomial time.
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