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The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
One important drawback for applications of the solution of the classical secretary problem is that the number of applicants must be known in advance, which is rarely the case. One way to overcome this problem is to suppose that the number of applicants is a random variable N {\displaystyle N} with a known distribution of P ( N = k ) k = 1 , 2 ...
Many students work in groups to solve them and help get a better understanding of the material, [6] [7] but most professors require each student to hand in their own individual problem set. Some professors explicitly encourage collaboration, [ 5 ] [ 6 ] some allow it, and some explicitly disallow it [ 3 ] or consider it cheating.
There are several basic elements that can be built into every problem statement. The problem statement should focus on the end user, and the statement should not be too broad or narrow. [7] Problem statements usually follow a format. While there are several options, the following is a template often used in business analysis.
Insight is the sudden aha! solution to a problem, the birth of a new idea to simplify a complex situation. Solutions found through insight are often more incisive than those from step-by-step analysis. A quick solution process requires insight to select productive moves at different stages of the problem-solving cycle.
Conversely, in every solution of S u, since the target sum is 7 T and each element is in ( T /4, 7 T /2), there must be exactly 3 elements per set, so it corresponds to a solution of S r. The ABC-partition problem (also called numerical 3-d matching) is a variant in which, instead of a set S with 3 m integers, there are three sets A, B, C with ...
The answer to a research question will help address a research problem or question. [5] Specifying a research question, "the central issue to be resolved by a formal dissertation, thesis, or research project," [6] is typically one of the first steps an investigator takes when undertaking research.
For every solution of the problem, not only applying an isometry or a time shift but also a reversal of time (unlike in the case of friction) gives a solution as well. [ citation needed ] In the physical literature about the n -body problem ( n ≥ 3 ), sometimes reference is made to "the impossibility of solving the n -body problem" (via ...