Give a complete justification of Proposition 11.1. Data from in Proposition 11.1 The merge-sort tree associated with
Question:
Give a complete justification of Proposition 11.1.
Data from in Proposition 11.1
The merge-sort tree associated with an execution of mergesort on a sequence of size n has height ⌈log n⌉. We leave the justification of Proposition 11.1 as a simple exercise (R-11.4). We use this proposition to analyze the running time of the merge-sort algorithm. Having given an overview of merge-sort and an illustration of how it works, let us consider each of the steps of this divide-and-conquer algorithm in more detail. The divide and recur steps of the merge-sort algorithm are simple; dividing a sequence of size n involves separating it at the element with index ⌈n/2⌉, and the recursive calls simply involve passing these smaller sequences as parameters. The difficult step is the conquer step, which merges two sorted sequences into a single sorted sequence. Thus, before we present our analysis of merge-sort, we need to say more about how this is done.
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Data Structures And Algorithms In C++
ISBN: 9780470383278
2nd Edition
Authors: Michael T. Goodrich, Roberto Tamassia, David M. Mount