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L = h: This means that f (n) grows at a faster rate than g(n), and hence that f = <(g) (indeed, f = \(g) and f | 6 (g)). L | 0 is finite: This means that f (n) and g(n) grow at the same rate, to within a constant factor, and hence that f = 6(g), or equivalently, g = 6( f ). Notice that this also means that f = O(g), g = O( f ), f = <(g), and g = <( f ). f ( n) There is no limit: In the case where lim does not exist, this technique nqh g ( n ) cannot be used to determine the asymptotic relationship between f(n) and g(n).

This minimum element is swapped with the current second item (3). The procedure continues until n – 1 items have been properly ordered because this forces all n items to be properly ordered. 13 32 Chapter 1 Asymptotic Analysis Subprogram SelectionSort(List) Input: array List[1… n] , to be sorted in ascending order according to the key field of the records Output: the ordered List Algorithm: SelectionSort, as follows For each position in the List, we a. Determine the index corresponding to the entry from the unsorted portion of the List that is a minimum.

D) Although both the array-based and linked-list-based implementations of InsertionSort have worst case running times of 6(n2), in practice, we usually find that the linked-list-based implementation (assuming the same data, in the same input order) is faster. Why should this be? ) 10. Array implementations of both InsertionSort and SelectionSort have 6(n2) worst case running times. Which is likely to be faster if we time both in the same hardware/software environment for the same input data? Why?

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