jacc question

questions/Jacc.md

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+# The P versus NP Problem
+
+## Background Info
+
+Imagine, for instance, that you have an unsorted list of numbers, and you want to write an algorithm to find the largest one. 
+The algorithm has to look at all the numbers in the list: there’s no way around that. But if it simply keeps a record of the largest 
+number it’s seen so far, it has to look at each entry only once. The algorithm’s execution time is thus directly proportional to the 
+number of elements it’s handling — which computer scientists designate N. Of course, most algorithms are more complicated, and thus 
+less efficient, than the one for finding the largest number in a list; but many common algorithms have execution times proportional 
+to N2, or N times the logarithm of N, or the like.
+
+A mathematical expression that involves N’s and N2s and N’s raised to other powers is called a polynomial, and that’s what the “P” in 
+“P = NP” stands for. P is the set of problems whose solution times are proportional to polynomials involving N's.
+
+Obviously, an algorithm whose execution time is proportional to N3 is slower than one whose execution time is proportional to N. But such 
+differences dwindle to insignificance compared to another distinction, between polynomial expressions — where N is the number being raised 
+to a power — and expressions where a number is raised to the Nth power, like, say, 2N.
+
+If an algorithm whose execution time is proportional to N takes a second to perform a computation involving 100 elements, an algorithm whose 
+execution time is proportional to N3 takes almost three hours. But an algorithm whose execution time is proportional to 2N takes 300 
+quintillion years. And that discrepancy gets much, much worse the larger N grows.
+
+NP (which stands for nondeterministic polynomial time) is the set of problems whose solutions can be verified in polynomial time. But as far as 
+anyone can tell, many of those problems take exponential time to solve. Perhaps the most famous exponential-time problem in NP, for example, is 
+finding prime factors of a large number. Verifying a solution just requires multiplication, but solving the problem seems to require systematically 
+trying out lots of candidates.
+
+## Question
+Does P equal NP?
+or
+If the solution to a problem can be verified in polynomial time, can it be found in polynomial time?
+
+