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Joe has a free choice between implementing either an O ( n 2 ) or an O ( n 3 ) worst case running time
Joe has a free choice between implementing either an On or an On worst case running time algorithm to serve as an important subroutine inside his personal larger project. Joe does indeed have several good reasons to implement the On algorithm, but which one of the following would not be a good argument to support Joe's design decision
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The first algorithm is far simpler and shorter and can be practically copypasted from Stack Overflow, whereas the second algorithm would require careful implementation to guarantee its correctness in all possible edge and corner cases.
The second algorithm is On only in the worst case, and on average it runs in On linear time for the overwhelming majority for possible inputs, whereas the first algorithm is always guaranteed to be quadratic for all inputs.
The hidden lower order terms inside the asymptotic running time of the first algorithm are of higher order than the hidden lower order terms of the second algorithm.
Inside Joe's project, the value of n is guaranteed to always be small enough as not to make any real difference in the overall running time of the program.
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