'Counting inversions' presentation slideshows

Chapter 5

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Prof. Swarat Chaudhuri

COMP 482: Design and Analysis of Algorithms. Prof. Swarat Chaudhuri. Spring 2013 Lecture 11. Divide-and-Conquer. Divide-and-conquer. Break up problem into several parts. Solve each part recursively. Combine solutions to sub-problems into overall solution. Most common usage.

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Divide-and-Conquer

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Inversions

Inversions. Outline. Given an unsorted list, one measure of unsortedness is the number of inversions Review of inversions Distribution of inversions for randomly generated lists Counting inversions: Straight-forward algorithm is has a Q ( n 2 ) run time

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A Useful Recurrence Relation

A Useful Recurrence Relation. Def. T(n) = number of comparisons to mergesort an input of size n. Mergesort recurrence. Solution. T(n) = O(n log 2 n). Assorted proofs. We describe twoways to prove this recurrence. Initially we assume n is a power of 2 and replace ? with =.

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Counting Inversions I

Divid e and Conquer. Counting Inversions I. Design and Analysis of Algorithms I. The Problem. Examples and Motivation. What is the largest-possible number of inversions that a 6-element array can have?. 15. 21. High-Level Approach. High-Level Algorithm.

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