April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
Computation Models and Design by Refi nement 111
Algorithm design and analysis We can now develop a functional algorithm for primality testing
based on the Fermat’s Little theorem. We start by defi ning an iterative function prime(n, q) of the type
prime : P × N → {true, false}, where n is the number whose primality is to be tested and q is the maximum
number of times the Fermat’s test is to be applied.
prime(n, q) =
if 2
_(,
, )otherwise
true n
prime test n q false
=
⎧
⎨
⎩
where the iterative function prime test : P × N × {true, false} → {true, false} is defi ned using the invariant
P = (¬ failed = (n has passed the Fermat’s test (q
0
− q) times) )
(where q
0
is the initial value of q) as
prime_test(n, q, failed) =
if 0
if failed
_(,1, _())otherwise
true
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access
More than 5,000 organizations count on O’Reilly
O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.