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Q. Calculate that how many key comparisons and assignments an insertion sort makes in its worst case?
Ans:
The worst case performance occurs in insertion sort occurs when the elements of the input array are in descending order. In that case, the first pass requires one comparison, the second pass requires two comparisons, third pass three comparisons till the kth pass requires (k-1), and in the end the last pass requires (n-1) comparisons. Therefore, we obtain the total numbers of comparisons as follows : f(n) = 1+2+3+.........+(n-k)+.....+(n-2)+(n-1) = n(n-1)/2 = O(n2)
The worst case performance occurs in insertion sort occurs when the elements of the input array are in descending order. In that case, the first pass requires one comparison, the second pass requires two comparisons, third pass three comparisons till the kth pass requires (k-1), and in the end the last pass requires (n-1) comparisons. Therefore, we obtain the total numbers of comparisons as follows :
f(n) = 1+2+3+.........+(n-k)+.....+(n-2)+(n-1)
= n(n-1)/2
= O(n2)
Asymptotic notation Let us describe a few functions in terms of above asymptotic notation. Example: f(n) = 3n 3 + 2n 2 + 4n + 3 = 3n 3 + 2n 2 + O (n), as 4n + 3 is of
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