Lecture14 - Divide and Conquer Algorithms CSE 421...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 CSE 421 Algorithms Richard Anderson Lecture 14 Inversions, Multiplication, FFT Divide and Conquer Algorithms • Mergesort, Quicksort • Strassen’s Algorithm • Closest Pair Algorithm (2d) • Inversion counting • Integer Multiplication (Karatsuba’s Algorithm) • FFT – Polynomial Multiplication – Convolution Inversion Problem • Let a 1 , . . . a n be a permutation of 1 . . n •( a i , a j ) is an inversion if i < j and a i > a j • Problem: given a permutation, count the number of inversions • This can be done easily in O(n 2 ) time – Can we do better? 4, 6, 1, 7, 3, 2, 5 Counting Inversions 14 10 13 6 8 16 5 9 15 3 2 7 1 4 12 11 Count inversions on lower half Count inversions on upper half Count the inversions between the halves 1 4 12 11 15 3 2 7 15 3 2 7 1 4 12 11 8 16 5 9 14 10 13 6 14 10 13 6 8 16 5 9 Count the Inversions 14 10 13 6 8 16 5 9 15 3 2 7 1 4 12 11 4 1 2 3 14 10 19 8 6 43 Problem – how do we count inversions between sub problems in O(n) time?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/25/2012 for the course CSE 421 taught by Professor Richardanderson during the Fall '06 term at University of Washington.

Page1 / 4

Lecture14 - Divide and Conquer Algorithms CSE 421...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online