If a program executes in 2seconds with n=10, how much time will it take to execute n=100 with complexity n * log(n)? I thought about it and I think it’s probably 4seconds, but how can I prove it?
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If a program executes in 2seconds with n=10, how much time will it take to execute n=100 with complexity n * log(n)? I thought about it and I think it’s probably 4seconds, but how can I prove it?
Assuming the time taken is exactly proportional to n*log(n), and not just an upper bound (see http://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachmann.E2.80.93Landau_notations), you’d have:
Plug in n=10 and solve for the constant. Now you have an expression for the execution time at every n.