## Dyck Word Generator

Dyck word generator is a utility that lexicographically generate a sequence of Dyck words for specific length`n`

. The algorithm used was designed by Kostas Manes and me.
## Catalan Number & Dyck Words

Source: wikipedia - Catalan numberThere are many counting problems in combinatorics whose solution is given by the Catalan numbers. The book

*Enumerative Combinatorics: Volume 2*by combinatorialist Richard P. Stanley contains a set of exercises which describe 66 different interpretations of the Catalan numbers. Following are some examples, with illustrations of the case

*C*

_{3}= 5.

*C*_{n}is the number of**Dyck words**of length 2*n*. A Dyck word is a string consisting of*n*X's and*n*Y's such that no initial segment of the string has more Y's than X's (see also Dyck language). For example, the following are the Dyck words of length 6:

- Re-interpreting the symbol X as an open parenthesis and Y as a close parenthesis,
*C*_{n}counts the number of expressions containing*n*pairs of parentheses which are correctly matched:

*C*_{n}is the number of different ways*n*+ 1 factors can be completely parenthesized (or the number of ways of associating*n*applications of a binary operator). For*n*= 3 for example, we have the following five different parenthesizations of four factors:

## Download & Usage

Here you can download binaries for:- Windows
- Mac OS X (intel)
- Linux

nsp <length>For the output a binary format is used and the result are stored in file

`output.result`

. The source code is not available. Be advised that this implementation uses `double`

for the calculation of the Catalan number. Consequently, this will not work accurately when the length exceeds the data type's capacity. This will be fixed in future releases.