Question: 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 or an 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
algorithm, but which one of the following would not be a good argument to support
Joe's design decision
Inside Joe's project, the value of is guaranteed to always be small enough as
not to make any real difference in the overall running time of the program.
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 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.
The second algorithm is only in the worst case, and on average it runs in
linear time for the overwhelming majority for possible inputs, whereas the
first algorithm is always guaranteed to be quadratic for all inputs.
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