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1c - Sorting1

# Programming 4 6 9 8 7 2 5 1 3 insertion sort insertion

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Unformatted text preview: on Sort Insertion Sort Applied Programming Applied 34 6 1 7 8 9 5 1 2 Applied Programming 3 4 6 7 8 9 5 1 2 Insertion Sort Insertion Sort Applied Programming 34 6 7 8 9 5 1 Applied Programming 234 6 7 8 9 5 1 2 Insertion Sort Insertion Sort Applied Programming Applied Programming 234 6 7 8 1 9 234 5 6 7 8 9 5 Insertion Sort Insertion Sort Applied Programming Applied 234 5 6 7 1 8 9 1 Applied Programming 234 5 6 7 8 9 1 Insertion Sort Insertion Sort Applied Programming 234 5 6 7 8 9 Applied Programming 1 234 5 6 7 8 9 1 Insertion Sort Insertion Sort Applied Programming Applied Programming Guarantees So, how good is this algorithm? On average, the value being inserted will go in the On middle. So we need only about half of the comparisons of Selection Sort. comparisons W e have to be sure that, if we follow the procedure We described, by the completion of the process the data will be sorted. data Just because some test runs produce the correct Just result is not a proof of correctness. result That is, about n(n-1)/4 on average. That n(n Now let's look at how we generally compare the Now efficiency of algorithms efficiency . . . and how we must ensure that the algorithm and actually works. actually Applied Programming Applied The advantage of standard algorithms – tried-andThe tested methods – iis that we can be assured that s tested the procedure will work. the Efficiency We said Selection Sort needed n(n-1)/2 comparisons (always). What algorithm is best for a particular purpose? How does runtime change as the size of the How dataset increases? dataset For sorting, the number of comparisons of the For data is a good measure. data Applied Programming W e say that such an expression is of order n2 We order It behaves like a constant times n2 when n is when large (the n2 term overpowers the n term so the large term latter is ignored). latter * the expression is bounded above by a the bounded by constant times n2 for n > some value. constant Start with Selection Sort. Applied Programming W...
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