Exercise Sheet 3 - Master Solution Exercise 1 - Comparisons in Quicksort
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چکیده
Exercise 1 Comparisons in Quicksort To begin with, note that when we talk about the ’number of comparisons’, we mean the number of times one element is compared to another element of the sequence to sort. We do not count internal comparisons of the algorithm (like when the algorithm compares the index of an element to another index). Let a, b be two distinct elements of rank i and j, respectively. In the script (cf. page 22), a mapping is described from the possible runs of quicksort(S) to binary search trees (with the same distribution as our random search trees). According to that mapping, a, b are compared in quicksort(S) if and only if in the corresponding search tree, either b is the ancestor of a or a is the ancestor of b. We have denoted these events using indicator variables by Aji = 1 and A i j = 1, respectively.
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