algorithms on S Anand

Picking books to read

Wed, 11 Jan 2023 03:20:39 +0000

I add book recommendations to my GoodReads – To-read list. Then I sort by rating and pick the first one I like to read.

In 2023, I’m reshaping my environment. Picking books I usually won’t pick. (Read The Unknown Unknown: Bookshops and the Delight of Not Getting What You Wanted if you want to be similarly inspired.)

So here are 4 approaches I’m adding to my process.

Algorithmic. Sort Kaggle books based on popularity, rating, and age. Pick the top 10 (or 50)
Serendipitous. Go to bookstores and libraries. Pick the most popular books
Award-winning. Pick from the Pulitzer, Booker, Nobel, Hugo, and other award winners
Challenges. Pick from Popsugar, Book Riot, Goodreads, The 52 Book Club, and other challenges

FYI, here are algorithmic results (for books with 100+ ratings and a 4+ average on Goodreads):

Top rated books

Most popular books

Oldest books

Managing the data deluge

Sat, 10 Feb 2007 12:00:00 +0000

Peter Norvig’s brilliant talk on Managing the Data Deluge. Among other things, he talks about how having lots of data is sometimes better than having a carefully designed algorithm.

Knuth Volume 4

Mon, 24 Jul 2006 12:00:00 +0000

The Art of Computer Programming, Volume 4 by Donald Knuth. Pre-fascicles are available for download.

Math will rock your world

Sat, 14 Jan 2006 12:00:00 +0000

It’s a good time to be a mathematician.

Compare Yahoo and Google searches

Thu, 14 Apr 2005 12:00:00 +0000

Compare Yahoo and Google searches. This site lets you compare the rankings of each site on identical searches with Yahoo and Google.

Prime factorisation algorithm

Sun, 10 Nov 2002 12:00:00 +0000

An update on the IIT-K prime factorisation algorithm. via Matthai Markose

Tetris is NP-Hard

Sat, 26 Oct 2002 12:00:00 +0000

Tetris is NP-Hard. Let me explain, in English, what that means.

The toughness of problems is how much time it takes to solve them.

Adding two 3-digit number takes less time than adding two 30-digit numbers, and hence is easier. Similarly, figuring out if a 3-digit number is prime or not is easier than a 30-digit number.

Some problems grow tough very quickly.

Adding two 30-digit numbers is 10-times slower than adding two 3-digit numbers. But checking if a 30-digit number is prime is several trillions of times slower than checking a 3-digit number. That is because, to check if a number is prime, you need to repeatedly divide it by numbers smaller than it. For a 3-digit number, you need to divide by around 1,000 numbers. For a 30 digit number, it’s several trillions.

Problems that grow tough at a constant rate are ‘P’.

What this means is: if you keep on doubling the number of digits, the problem repeatedly becomes twice as tough (or 3 times as tough, or whatever – some constant rate). Adding of numbers is an example. (‘P’ stands for polynomial time.)

Problems that grow tough at a constant rate if you already know how to solve them are ‘NP’.

For instance, to check if a 30-digit number is a prime, you needn’t check with all numbers below the number. You just need to check with all primes below the number. That takes about 10-times as much time as for a 3-digit number. Hence, if you knew which primes were below the number, it would be ‘P’.

‘P’ is a subset of ‘NP’.

The real question is, are there any problems that are ‘NP’ and not ‘P’. That is, are there problems for which you really need to know how to solve the problem to be able to solve them in polynomial time? Or is it that we’ve just not been smart enough to come up with solutions that are fast enough? We don’t know. The first step is to make a list of NP problems that are not obviously in ‘P’. Then, we try converting these problems into each other in polynomial time.

NP problems that can be converted into each other in polynomial time are ‘NP-hard’.

So, if you solve any one of these ‘NP-hard’ problems in polynomial time, you can solve all NP-hard problems in polynomial time. Figuring out the right moves in Tetris is one such problem.

Microsoft interview question

Mon, 15 Jan 2001 12:00:00 +0000

“Write a one-line C expression to determine if a number is a power of 2”. Microsoft is famous for asking such questions to their programmers. Or you might want to find out what the assembly code

CWD
XOR AX, DX
SUB AX, DX

does. Satish’s site has the answer, but not the question. More questions: 1 2