Note 5, DM819, fall 2018

Exercises October 1

• Exercises 4.1, 4.2, 4.3, 4.15, 4.16.
• Show that RANDOMPERMUTATION generates all permutations with the same probability.
• Show that it must take at least the order of n log n to compute the intersection of n halfplanes (some model assumptions are required to make this formal, but take that lightly). Hint: reduce from sorting.
• From CLRS^[1], for instance, we know that INSERTIONSORT uses n(n-1)/2 number of comparisons in the worst case. Use backwards analysis to show that if you randomize first (using RANDOMPERMUTATION), then the expected number of comparisons is n(n-1)/4.

Lecture October 2

• Point Location (sections 6.0 - 6.3).

1. ^ Sections 2.1-2.2 of Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein. Introduction to Algorithms (third ed.). MIT Press, 2009. ISBN 978-0-262-03384-8.