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<codewalk title="Generating arbitrary text: a Markov chain algorithm">

<step title="Introduction" src="doc/codewalk/markov.go:/Generating/,/line\./">
	This codewalk describes a program that generates random text using
	a Markov chain algorithm. The package comment describes the algorithm
	and the operation of the program. Please read it before continuing.
</step>

<step title="Modeling Markov chains" src="doc/codewalk/markov.go:/	chain/">
	A chain consists of a prefix and a suffix. Each prefix is a set
	number of words, while a suffix is a single word.
	A prefix can have an arbitrary number of suffixes.
	To model this data, we use a <code>map[string][]string</code>.
	Each map key is a prefix (a <code>string</code>) and its values are
	lists of suffixes (a slice of strings, <code>[]string</code>).
	<br/><br/>
	Here is the example table from the package comment
	as modeled by this data structure:
	<pre>
map[string][]string{
	" ":          {"I"},
	" I":         {"am"},
	"I am":       {"a", "not"},
	"a free":     {"man!"},
	"am a":       {"free"},
	"am not":     {"a"},
	"a number!":  {"I"},
	"number! I":  {"am"},
	"not a":      {"number!"},
}</pre>
	While each prefix consists of multiple words, we
	store prefixes in the map as a single <code>string</code>.
	It would seem more natural to store the prefix as a
	<code>[]string</code>, but we can't do this with a map because the
	key type of a map must implement equality (and slices do not).
	<br/><br/>
	Therefore, in most of our code we will model prefixes as a
	<code>[]string</code> and join the strings together with a space
	to generate the map key:
	<pre>
Prefix               Map key

[]string{"", ""}     " "
[]string{"", "I"}    " I"
[]string{"I", "am"}  "I am"
</pre>
</step>

<step title="The Chain struct" src="doc/codewalk/markov.go:/type Chain/,/}/">
	The complete state of the chain table consists of the table itself and
	the word length of the prefixes. The <code>Chain</code> struct stores
	this data.
</step>

<step title="The NewChain constructor function" src="doc/codewalk/markov.go:/func New/,/}/">
	The <code>Chain</code> struct has two unexported fields (those that
	do not begin with an upper case character), and so we write a
	<code>NewChain</code> constructor function that initializes the
	<code>chain</code> map with <code>make</code> and sets the
	<code>prefixLen</code> field.
	<br/><br/>
	This is constructor function is not strictly necessary as this entire
	program is within a single package (<code>main</code>) and therefore
	there is little practical difference between exported and unexported
	fields. We could just as easily write out the contents of this function
	when we want to construct a new Chain.
	But using these unexported fields is good practice; it clearly denotes
	that only methods of Chain and its constructor function should access
	those fields. Also, structuring <code>Chain</code> like this means we
	could easily move it into its own package at some later date.
</step>

<step title="The Prefix type" src="doc/codewalk/markov.go:/type Prefix/">
	Since we'll be working with prefixes often, we define a
	<code>Prefix</code> type with the concrete type <code>[]string</code>.
	Defining a named type clearly allows us to be explicit when we are
	working with a prefix instead of just a <code>[]string</code>.
	Also, in Go we can define methods on any named type (not just structs),
	so we can add methods that operate on <code>Prefix</code> if we need to.
</step>

<step title="The String method" src="doc/codewalk/markov.go:/func[^\n]+String/,/}/">
	The first method we define on <code>Prefix</code> is
	<code>String</code>. It returns a <code>string</code> representation
	of a <code>Prefix</code> by joining the slice elements together with
	spaces. We will use this method to generate keys when working with
	the chain map.
</step>

<step title="Building the chain" src="doc/codewalk/markov.go:/func[^\n]+Build/,/\n}/">
	The <code>Build</code> method reads text from an <code>io.Reader</code>
	and parses it into prefixes and suffixes that are stored in the
	<code>Chain</code>.
	<br/><br/>
	The <code><a href="/pkg/io/#Reader">io.Reader</a></code> is an
	interface type that is widely used by the standard library and
	other Go code. Our code uses the
	<code><a href="/pkg/fmt/#Fscan">fmt.Fscan</a></code> function, which
	reads space-separated values from an <code>io.Reader</code>.
	<br/><br/>
	The <code>Build</code> method returns once the <code>Reader</code>'s
	<code>Read</code> method returns <code>io.EOF</code> (end of file)
	or some other read error occurs.
</step>

<step title="Buffering the input" src="doc/codewalk/markov.go:/bufio\.NewReader/">
	This function does many small reads, which can be inefficient for some
	<code>Readers</code>. For efficiency we wrap the provided
	<code>io.Reader</code> with
	<code><a href="/pkg/bufio/">bufio.NewReader</a></code> to create a
	new <code>io.Reader</code> that provides buffering.
</step>

<step title="The Prefix variable" src="doc/codewalk/markov.go:/make\(Prefix/">
	At the top of the function we make a <code>Prefix</code> slice
	<code>p</code> using the <code>Chain</code>'s <code>prefixLen</code>
	field as its length.
	We'll use this variable to hold the current prefix and mutate it with
	each new word we encounter.
</step>

<step title="Scanning words" src="doc/codewalk/markov.go:/var s string/,/\n		}/">
	In our loop we read words from the <code>Reader</code> into a
	<code>string</code> variable <code>s</code> using
	<code>fmt.Fscan</code>. Since <code>Fscan</code> uses space to
	separate each input value, each call will yield just one word
	(including punctuation), which is exactly what we need.
	<br/><br/>
	<code>Fscan</code> returns an error if it encounters a read error
	(<code>io.EOF</code>, for example) or if it can't scan the requested
	value (in our case, a single string). In either case we just want to
	stop scanning, so we <code>break</code> out of the loop.
</step>

<step title="Adding a prefix and suffix to the chain" src="doc/codewalk/markov.go:/	key/,/key\], s\)">
	The word stored in <code>s</code> is a new suffix. We add the new
	prefix/suffix combination to the <code>chain</code> map by computing
	the map key with <code>p.String</code> and appending the suffix
	to the slice stored under that key.
	<br/><br/>
	The built-in <code>append</code> function appends elements to a slice
	and allocates new storage when necessary. When the provided slice is
	<code>nil</code>, <code>append</code> allocates a new slice.
	This behavior conveniently ties in with the semantics of our map:
	retrieving an unset key returns the zero value of the value type and
	the zero value of <code>[]string</code> is <code>nil</code>.
	When our program encounters a new prefix (yielding a <code>nil</code>
	value in the map) <code>append</code> will allocate a new slice.
	<br/><br/>
	For more information about the <code>append</code> function and slices
	in general see the
	<a href="http://blog.golang.org/2011/01/go-slices-usage-and-internals.html">Slices: usage and internals</a> article.
</step>

<step title="Pushing the suffix onto the prefix" src="doc/codewalk/markov.go:/p\.Shift/">
	Before reading the next word our algorithm requires us to drop the
	first word from the prefix and push the current suffix onto the prefix.
	<br/><br/>
	When in this state
	<pre>
p == Prefix{"I", "am"}
s == "not" </pre>
	the new value for <code>p</code> would be
	<pre>
p == Prefix{"am", "not"}</pre>
	This operation is also required during text generation so we put
	the code to perform this mutation of the slice inside a method on
	<code>Prefix</code> named <code>Shift</code>.
</step>

<step title="The Shift method" src="doc/codewalk/markov.go:/func[^\n]+Shift/,/\n}/">
	The <code>Shift</code> method uses the built-in <code>copy</code>
	function to copy the last len(p)-1 elements of <code>p</code> to
	the start of the slice, effectively moving the elements
	one index to the left (if you consider zero as the leftmost index).
	<pre>
p := Prefix{"I", "am"}
copy(p, p[:1])
// p == Prefix{"am", "am"}</pre>
	We then assign the provided <code>word</code> to the last index
	of the slice:
	<pre>
// suffix == "not"
p[len(p)-1] = suffix
// p == Prefix{"am", "not"}</pre>
</step>

<step title="Generating text" src="doc/codewalk/markov.go:/func[^\n]+Generate/,/\n}/">
	The <code>Generate</code> method is similar to <code>Build</code>
	except that instead of reading words from a <code>Reader</code>
	and storing them in a map, it reads words from the map and
	appends them to a slice (<code>words</code>).
	<br/><br/>
	<code>Generate</code> uses a conditional for loop to generate
	up to <code>n</code> words.
</step>

<step title="Getting potential suffixes" src="doc/codewalk/markov.go:/choices/,/}\n/">
	At each iteration of the loop we retrieve a list of potential suffixes
	for the current prefix. We access the <code>chain</code> map at key
	<code>p.String()</code> and assign its contents to <code>choices</code>.
	<br/><br/>
	If <code>len(choices)</code> is zero we break out of the loop as there
	are no potential suffixes for that prefix.
	This test also works if the key isn't present in the map at all:
	in that case, <code>choices</code> will be <code>nil</code> and the
	length of a <code>nil</code> slice is zero.
</step>

<step title="Choosing a suffix at random" src="doc/codewalk/markov.go:/next := choices/,/Shift/">
	To choose a suffix we use the
	<code><a href="/pkg/rand/#Intn">rand.Intn</a></code> function.
	It returns a random integer up to (but not including) the provided
	value. Passing in <code>len(choices)</code> gives us a random index
	into the full length of the list.
	<br/><br/>
	We use that index to pick our new suffix, assign it to
	<code>next</code> and append it to the <code>words</code> slice.
	<br/><br/>
	Next, we <code>Shift</code> the new suffix onto the prefix just as
	we did in the <code>Build</code> method.
</step>

<step title="Returning the generated text" src="doc/codewalk/markov.go:/Join\(words/">
	Before returning the generated text as a string, we use the
	<code>strings.Join</code> function to join the elements of
	the <code>words</code> slice together, separated by spaces.
</step>

<step title="Command-line flags" src="doc/codewalk/markov.go:/Register command-line flags/,/prefixLen/">
	To make it easy to tweak the prefix and generated text lengths we
	use the <code><a href="/pkg/flag/">flag</a></code> package to parse
	command-line flags.
	<br/><br/>
	These calls to <code>flag.Int</code> register new flags with the
	<code>flag</code> package. The arguments to <code>Int</code> are the
	flag name, its default value, and a description. The <code>Int</code>
	function returns a pointer to an integer that will contain the
	user-supplied value (or the default value if the flag was omitted on
	the command-line).
</step>

<step title="Program set up" src="doc/codewalk/markov.go:/flag.Parse/,/rand.Seed/">
	The <code>main</code> function begins by parsing the command-line
	flags with <code>flag.Parse</code> and seeding the <code>rand</code>
	package's random number generator with the current time.
	<br/><br/>
	If the command-line flags provided by the user are invalid the
	<code>flag.Parse</code> function will print an informative usage
	message and terminate the program.
</step>

<step title="Creating and building a new Chain" src="doc/codewalk/markov.go:/c := NewChain/,/c\.Build/">
	To create the new <code>Chain</code> we call <code>NewChain</code>
	with the value of the <code>prefix</code> flag.
	<br/><br/>
	To build the chain we call <code>Build</code> with
	<code>os.Stdin</code> (which implements <code>io.Reader</code>) so
	that it will read its input from standard input.
</step>

<step title="Generating and printing text" src="doc/codewalk/markov.go:/c\.Generate/,/fmt.Println/">
	Finally, to generate text we call <code>Generate</code> with
	the value of the <code>words</code> flag and assigning the result
	to the variable <code>text</code>.
	<br/><br/>
	Then we call <code>fmt.Println</code> to write the text to standard
	output, followed by a carriage return.
</step>

<step title="Using this program" src="doc/codewalk/markov.go">
	To use this program, first compile and link it.
	If you are using <code>6g</code> as your compiler, the command
	would look something like this:
	<pre>
$ 6g markov.go &amp;&amp; 6l -o markov markov.6</pre>
	And then execute it while piping in some input text:
	<pre>
$ echo "a man a plan a canal panama" | ./markov -prefix=1
a plan a man a plan a canal panama
	</pre>
	Here's a transcript of generating some text using the Go distribution's
	README file as source material:
	<pre>
$ ./markov -words=10 &lt $GOROOT/go/README
This is the source code repository for the Go source
$ ./markov -prefix=1 -words=10 &lt $GOROOT/go/README
This is the go directory (the one containing this README).
$ ./markov -prefix=1 -words=10 &lt $GOROOT/go/README
This is the variable if you have just untarred a</pre>
</step>

<step title="An exercise for the reader" src="doc/codewalk/markov.go">
	The <code>Generate</code> function does a lot of allocations when it
	builds the <code>words</code> slice. As an exercise, modify it to
	take an <code>io.Writer</code> to which it incrementally writes the
	generated text with <code>Fprint</code>.
	Aside from being more efficient this makes <code>Generate</code>
	more symmetrical to <code>Build</code>.
</step>

</codewalk>