## Gwen McKinley's A Problem in Card Shuffling PDF

By Gwen McKinley

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Additional info for A Problem in Card Shuffling

Sample text

6 NB. by the meaning of () 6 NB. by the meaning of >. 6 6 6 6 6 Monadic >: is informally called "Increment". 3 Dyadic >: is "Larger or Equal" 3 >: 1 3 5 1 1 0 This is the end of Chapter 1. NEXT Table of Contents Index Copyright © Roger Stokes 2003. This material may be freely reproduced, provided that this copyright notice is also reproduced. last updated 18 Jul 2003 Chapter 2: Lists and Tables Computations need data. So far we have seen data only as single numbers or lists of numbers. We can have other things by way of data, such as tables for example.

An empty, or zero-length, string is entered as two successive single quotes, and displays as nothing. 5 Some Functions for Arrays At this point it will be useful to look at some functions for dealing with arrays. J is very rich in such functions: here we look at a just a few. 1 Joining The built-in function , (comma) is called "Append". It joins things together to make lists. a =: 'rear' b =: 'ranged' a,b rear ranged rearranged The "Append" function joins lists or single items. x =: 1 2 3 0 , x x , 0 0 , 0 x , x 1 2 3 0 1 2 3 1 2 3 0 0 0 1 2 3 1 2 3 The "Append" function can take two tables and join them together end-to-end to form a longer table: T1=: 2 3 \$ 'catdog' T2=: 2 3 \$ 'ratpig' T1,T2 cat dog rat pig cat dog rat pig Now a table can be regarded as a list where each item of the list is a row of the table.

Thus A is a list of scalars. A \$ A s =: 1 { A # \$ s +-------------+-+ |The answer is| 42| +-------------+--+ 2 +--+ |42| +--+ 0 The main purpose of an array of boxes is to assemble into a single variable several values of possibly different kinds. 99|baked beans| +----------+----+-----------+ 'baked beans' Note the difference between "Link" and "Append". While "Link" joins values of possibly different kinds, "Append" always joins values of the same kind. That is, the two arguments to "Append" must both be arrays of numbers, or both arrays of characters, or both arrays of boxes.