## Look And Say

### March 15, 2011

The “Look and Say” sequence, Sloane number A005150, begins 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …. Each term is constructed from its predecessor by stating the frequency and number of each group of like digits. For instance, the term after 1211 is “one 1, one 2, and two 1s”, or 111221. This sequence was studied by the British mathematician John Horton Conway, and has some fascinating properties; see MathWorld or follow the references at Sloane’s if you are interested.

Your task is to write a program to compute the look and say sequence. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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Here’s a quick solution in ghci:

Prelude> import Data.List

Prelude Data.List> let n = concatMap (\x -> (show $ length x) ++ [head x]) . group

Prelude Data.List> take 10 $ iterate n “1”

["1","11","21","1211","111221","312211","13112221","1113213211","31131211131221","13211311123113112211"]

My Haskell solution (see http://bonsaicode.wordpress.com/2011/03/15/programming-praxis-look-and-say/ for a version with comments):

[...] today’s Programming Praxis exercise, our task is to generate the Look and Say sequence (1, 11, 21, 1211, [...]

A Python solution:

Using the

`groupby()`

function from Python’s itertools module:Looks like Dave beat me to it :-) I should have refreshed the page before posting.

Clojure solution:

(defn lookandsay [s]

(mapcat (juxt count first)

(partition-by identity s)))

(take 10 (iterate lookandsay [1]))

A listless solution, integer to integer, in Scheme.

Output using iterate from that Standard Prelude.

Because Sloane’s is a catalogue of integer sequences, I wrote a generator that return successive integers of the sequence.

My first version is basically the same as Webb’s and Graham’s above, so I also did a second version using the regular expression library.

I was somewhat suprised that the second version appears to be slightly faster, based on using the timeit module.

My try in REXX

[...] autre petit exercice de Programming Praxis, programmer la suite Look and Say. Ce n’est pas très difficile : import Data.List import [...]

My Haskell solution

in scala:

def lookAndSay(previous:List[Int]) : Stream[List[Int]] = {

def next(num : List[Int]) : List[Int] = num match {

case Nil => Nil

case head :: Nil => 1 :: head :: Nil

case head :: tail => {

val size = (num takeWhile{_ == head}).size

List(size, head) ::: next(num.drop(size))

}

}

val x = next(previous)

x #:: lookAndSay(x)

}

lookAndSay(1::Nil) take 10 foreach (println _)

Here’s a JS solution. I’ve only been programming for about a year, mostly JS and PHP. Going to attempt a PHP version next, then subsequently, ajax-ify it.

Look and Say Sequence

var start = false;

var result;

function lookSay(int, repeat) {

for (t=1; t<=repeat; t++) {

if (!start) {

start = int;

result = start+"”;

}

newNumber = “”;

digit = start.charAt(0);

count = 1;

for (var i = 1; i < start.length; i++) {

if (digit == start.charAt(i)) {

count++;

}

else {

newNumber = newNumber + count + digit;

digit = start.charAt(i);

count = 1;

}

}

start = newNumber + count + digit;

if (t == repeat) {

result+=start;

document.getElementById('result').innerHTML=result;

start = false;

result = '';

}

else {

result +=start+"”;

}

}

}

function returnResult() {

s = document.getElementById(‘start’).value;

r = document.getElementById(‘repeat’).value;

lookSay(s, r);

}

Start Integer:

Repeat Amount:

Submit

A Scheme solution using lists is:

A ruby version:

sloane = [1]

puts sloane.inspect

8.times.each do |iteration|

new_sloane = []

rep_digit = 1

last_sum = sloane.inject(0) do |sum, digit|

next sum + 1 if digit == rep_digit

new_sloane << rep_digit

new_sloane << sum

rep_digit = digit

1

end

new_sloane << rep_digit

new_sloane << last_sum

puts sloane.replace(new_sloane).reverse.inspect

end

[/sourcecode]

Mine in F#

Here is a solution in Factor:

http://re-factor.blogspot.com/2011/03/look-and-say.html

For the curious, Factor looks like this:

: look-and-say ( n — n’ )

number>string [ = ] monotonic-split [

[ length ] [ first ] bi "%d%c" sprintf

] map concat string>number ;

is anybody have solution in c plz upload here

Rohit, check my website link here for a version in C. Please note that it is NOT written for clarity. But it is in C, and it works. Increase the ‘M’ constant if you want more numbers in the series; for example, 1000000 gives you the first 49 terms.