Unformatted text preview: invariant , i.e., a property of the boy-girl ordering of the children that does not change with time. Problem 4 Arrange the following functions in increasing order of growth rate, so that for two con-secutive functions f ( n ) , g ( n ) in your sequence, either f ( n ) = o ( g ( n )) or f ( n ) = Θ( g ( n )) . Explain the relationships of all adjacent pairs of functions in your order. Assume here that log is a logarithm to base 2 and ln is a logarithm to base e . n ! , log n, log( n 2 ) , n 5 , ln n, ± n 10 ² , 2 log n , 2 ln n , (log n ) n , n (log n ) . Note: We discussed big-Oh notation O ( .. ) in class. This problem requires you to know two other commonly used symbols in comparing the relative growth rate of functions. Here are their deﬁnitions: We say that f ( n ) = o ( g ( n )) if lim n →∞ f ( n ) g ( n ) = 0. We say that f ( n ) = Θ( g ( n )) if f ( n ) = O ( g ( n )) and g ( n ) = O ( f ( n ))....
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- Fall '07
- Natural logarithm, Binary logarithm, relative growth rate, commonly used symbols