Learning Go

I find that a good way to figure out if I like a new language is to write a few classic algorithms in it.

Merge Sort

Insertion Sort

Quick Sort

And the unit test framework

This might not be the most idiomatic Go but I really like the spartan syntax, I like the array slices and I really like the ability to swap variable values in one line. I am impressed.

Converting a regular BIND ZONE to DNSSEC

Recently I wanted to sign a regular zone in BIND9.7. Google wasn’t very helpful so I thought I’d write up a little bit about it here.

My /etc/named.conf looks like this:

I want to keep my dnssec zones in a separate directory.

Now I sign the zone.

Finally I want to change the named.conf to the myzone.com.signed.

Make sure that all the files are owned by user “named” and reload bind

Using SVN with Git

Once I learned Git I never wanted to go back to the days of svn. The only problem is that SVN is used almost in every linux shop I worked for. Luckily there is git-svn. With git-svn I can just import an svn repositories and use git to browse, branch, merge etc.

My typical workflow:

1) Import the repository into git.

2) Get a branch to hack on

3) Keep up with svn commits:

This fetches revisions from the SVN parent of the current HEAD and rebases the current (uncommitted to SVN) work against it.

This works similarly to svn update or git pull except that it preserves linear history with git rebase instead of git merge for ease of dcommitting with git svn.

This accepts all options that git svn fetch and git rebase accept. However, –fetch-all only fetches from the current [svn-remote], and not all [svn-remote] definitions.

Like git rebase; this requires that the working tree be clean and have no uncommitted changes.

4) Commit changes back to svn

sin(n) = -1 where n is an integer in radians

I saw a fun math problem on reddit the other day.

find a number n, so that sin(n)=-1, where n is an integer in radians; so sin(270 degrees) doesn’t count. Obviously it will never be exactly -1 but close enough for the difference to be lost in rounding.

\sin(\frac{3\pi}{2} + 2\pi \cdot n) = -1
I need the argument of sin function to be as close to an integer as possible. Call this integer m.
\frac{3\pi}{2}+2\pi \cdot n \approx m
Solving for \pi leads to:
\pi \approx \frac{p}{q} \approx \frac{2m}{4n+3}

If I have a rational approximation to \pi with an even numerator I can divide it by two get my m. I also have to make sure that the denominator is in the form of 4n+3.
It’s possible to use continued fractions to approximate real numbers. Here’s a continued fraction sequence for pi: https://oeis.org/A001203

The first rational approximation I learned in elementary school is 22/7 which is perfect.

> (sin 11)
-.9999902065507035

For the others I’ll have to evaluate the continued fraction to get my approximation of a simple fraction.

> (eval-terms (list 3 7 15 1 292 1))
104348/33215

> (sin (/ 104348 2))
-.9999999999848337

> (eval-terms (list 3 7 15 1 292 1 1 1 2 1 3 1 14 2 1))
245850922/78256779

> (sin (/ 245850922 2))
-.99999999999999999532
Looks like a good candidate was found.

This is the code to evaluate a continued fraction coefficients. It’s very convenient that scheme has a native rational data type.

Exercise 2.42 of SICP

Exercise 2.42:

A solution to the eight-queens puzzle.

A solution to the eight-queens puzzle.

The “eight-queens puzzle” asks how to place eight queens on a chessboard so that no queen is in check from any other (i.e., no two queens are in the same row, column, or diagonal). One possible solution is shown in figure 2.8. One way to solve the puzzle is to work across the board, placing a queen in each column. Once we have placed k – 1 queens, we must place the kth queen in a position where it does not check any of the queens already on the board. We can formulate this approach recursively: Assume that we have already generated the sequence of all possible ways to place k – 1 queens in the first k – 1 columns of the board. For each of these ways, generate an extended set of positions by placing a queen in each row of the kth column. Now filter these, keeping only the positions for which the queen in the kth column is safe with respect to the other queens. This produces the sequence of all ways to place k queens in the first k columns. By continuing this process, we will produce not only one solution, but all solutions to the puzzle.

We implement this solution as a procedure queens, which returns a sequence of all solutions to the problem of placing n queens on an n×n chessboard. Queens has an internal procedure queen-cols that returns the sequence of all ways to place queens in the first k columns of the board.

In this procedure rest-of-queens is a way to place k – 1 queens in the first k – 1 columns, and new-row is a proposed row in which to place the queen for the kth column. Complete the program by implementing the representation for sets of board positions, including the procedure adjoin-position, which adjoins a new row-column position to a set of positions, and empty-board, which represents an empty set of positions. You must also write the procedure safe?, which determines for a set of positions, whether the queen in the kth column is safe with respect to the others. (Note that we need only check whether the new queen is safe — the other queens are already guaranteed safe with respect to each other.)

> (length (queens 8))
92
> (length (queens 11))
2680
> (length (queens 10))
724
> (queens 4)
((2 4 1 3) (3 1 4 2))

Exercise 2.41 of SICP

Exercise 2.41: Write a procedure to find all ordered triples of distinct positive integers i, j, and k less than or equal to a given integer n that sum to a given integer s.

> (sum-triples 5 9)
((4 3 2 9) (5 3 1 9))
> (sum-triples 5 10)
((5 3 2 10) (5 4 1 10))
> (sum-triples 5 11)
((5 4 2 11))
> (sum-triples 5 12)
((5 4 3 12))
> (sum-triples 5 13)
()
> (sum-triples 6 13)
((6 4 3 13) (6 5 2 13))
> (sum-triples 6 10)
((5 3 2 10) (5 4 1 10) (6 3 1 10))
> (sum-triples 6 11)
((5 4 2 11) (6 3 2 11) (6 4 1 11))
> (sum-triples 6 12)
((5 4 3 12) (6 4 2 12) (6 5 1 12))
> (sum-triples 6 13)
((6 4 3 13) (6 5 2 13))

Exercise 2.40 of SICP

Exercise 2.40: Define a procedure unique-pairs that, given an integer n, generates the sequence of pairs (i,j) with latex path not specified.: 1\le j< i\le n[/latex]. Use unique-pairs to simplify the definition of prime-sum-pairs given above.

Using Miller-Rabin primality test as well as taking advantage of some lexical scoping here is the solution:

> (prime-sum-pairs 1)
()
> (prime-sum-pairs 2)
((2 1 3))
> (prime-sum-pairs 3)
((2 1 3) (3 2 5))
> (prime-sum-pairs 4)
((2 1 3) (3 2 5) (4 1 5) (4 3 7))
> (prime-sum-pairs 5)
((2 1 3) (3 2 5) (4 1 5) (4 3 7) (5 2 7))

Exercise 2.39 of SICP

Exercise 2.39: Complete the following definitions of reverse (exercise 2.18) in terms of fold-right and fold-left from exercise 2.38:

> (reverse-right (list 1 2 3))
(3 2 1)
> (reverse-left (list 1 2 3))
(3 2 1)