freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/execute-a-markov-algorithm.english.md

---
title: Execute a Markov algorithm
id: 59e09e6d412c5939baa02d16
challengeType: 5
---

## Description
<section id='description'>
Task:
<p>Create an interpreter for a <a href="https://en.wikipedia.org/wiki/Markov algorithm" title="wp: Markov algorithm">Markov Algorithm</a>.</p><p>Rules have the syntax:</p>
<p><ruleset> ::= ((<comment> | <rule>) <newline>+)*</p>
<p><comment> ::= # {<any character>}</p>
<p><rule> ::= <pattern> <whitespace> -> <whitespace> [.] <replacement></p>
<p><whitespace> ::= (<tab> | <space>) [<whitespace>]</p>
<p>There is one rule per line.</p><p>If there is a  <b>.</b>  (period)  present before the  <replacement>,  then this is a terminating rule in which case the interpreter must halt execution.</p><p>A ruleset consists of a sequence of rules, with optional comments.</p>
<p><big><big> Rulesets </big></big></p><p>Use the following tests on entries:</p>
Ruleset 1:
<pre>
This rules file is extracted from Wikipedia:
http://en.wikipedia.org/wiki/Markov_AlgorithmA -> apple
B -> bag
S -> shop
T -> the
the shop -> my brother
a never used -> .terminating rule
</pre>
<p>Sample text of:</p>
<p> <code> I bought a B of As from T S. </code></p>
<p>Should generate the output:</p>
<p> <code> I bought a bag of apples from my brother. </code></p>
Ruleset 2:
<p>A test of the terminating rule</p>
<pre>
Slightly modified from the rules on WikipediaA -> apple
B -> bag
S -> .shop
T -> the
the shop -> my brother
a never used -> .terminating rule</pre>
<p>Sample text of:</p>
<p> <code>I bought a B of As from T S.</code></p>
<p>Should generate:</p>
<p> <code>I bought a bag of apples from T shop.</code></p>
Ruleset 3:
<p>This tests for correct substitution order and may trap simple regexp based replacement routines if special regexp characters are not escaped.</p>
<pre>
BNF Syntax testing rulesA -> apple
WWWW -> with
Bgage -> ->.*
B -> bag
->.* -> money
W -> WW
S -> .shop
T -> the
the shop -> my brother
a never used -> .terminating rule
</pre>
<p>Sample text of:</p>
<p> <code>I bought a B of As W my Bgage from T S.</code></p>
<p>Should generate:</p>
<p> <code>I bought a bag of apples with my money from T shop.</code></p>
Ruleset 4:
<p>This tests for correct order of scanning of rules, and may trap replacement routines that scan in the wrong order.  It implements a general unary multiplication engine.  (Note that the input expression must be placed within underscores in this implementation.)</p>
<pre>
## Unary Multiplication Engine, for testing Markov Algorithm implementations
## By Donal Fellows.
Unary addition engine_+1 -> _1+
1+1 -> 11+
Pass for converting from the splitting of multiplication into ordinary
addition1! -> !1
,! -> !+
_! -> _
Unary multiplication by duplicating left side, right side times1*1 -> x,@y
1x -> xX
X, -> 1,1
X1 -> 1X
_x -> _X
,x -> ,X
y1 -> 1y
y_ -> _
Next phase of applying1@1 -> x,@y
1@_ -> @_
,@_ -> !_
++ -> +
Termination cleanup for addition_1 -> 1
1+_ -> 1
_+_ -> 
</pre>
<p>Sample text of:</p>
<p> <code> _1111*11111_ </code></p>
<p>should generate the output:</p>
<p> <code> 11111111111111111111 </code></p>
Ruleset 5:
<p>A simple <a href="http://en.wikipedia.org/wiki/Turing_machine" title="link: http://en.wikipedia.org/wiki/Turing_machine">Turing machine</a>,</p>
<p>implementing a three-state <a href="http://en.wikipedia.org/wiki/Busy_beaver" title="link: http://en.wikipedia.org/wiki/Busy_beaver">busy beaver</a>.</p><p>The tape consists of 0s and 1s,  the states are A, B, C and H (for Halt), and the head position is indicated by writing the state letter before the character where the head is.</p>
<p>All parts of the initial tape the machine operates on have to be given in the input.</p><p>Besides demonstrating that the Markov algorithm is Turing-complete, it also made me catch a bug in the C++ implementation which wasn't caught by the first four rulesets.</p>
<pre>
Turing machine: three-state busy beaver
# state A, symbol 0 => write 1, move right, new state BA0 -> 1B
state A, symbol 1 => write 1, move left, new state C0A1 -> C01
1A1 -> C11
state B, symbol 0 => write 1, move left, new state A0B0 -> A01
1B0 -> A11
state B, symbol 1 => write 1, move right, new state BB1 -> 1B
state C, symbol 0 => write 1, move left, new state B0C0 -> B01
1C0 -> B11
state C, symbol 1 => write 1, move left, halt0C1 -> H01
1C1 -> H11
</pre>
<p>This ruleset should turn</p>
<p> <code> 000000A000000 </code></p>
<p>into</p>
<p> <code> 00011H1111000 </code></p>
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>markov</code> is a function.
    testString: 'assert(typeof markov === ''function'', ''<code>markov</code> is a function.'');'
  - text: '<code>markov(["A -> apple","B -> bag","S -> shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],"I bought a B of As from T S.")</code> should return "I bought a bag of apples from my brother.".'
    testString: 'assert.deepEqual(markov(rules[0],tests[0]),outputs[0],''<code>markov(["A -> apple","B -> bag","S -> shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],"I bought a B of As from T S.")</code> should return "I bought a bag of apples from my brother.".'');'
  - text: '<code>markov(["A -> apple","B -> bag","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],"I bought a B of As from T S.")</code> should return "I bought a bag of apples from T shop.".'
    testString: 'assert.deepEqual(markov(rules[1],tests[1]),outputs[1],''<code>markov(["A -> apple","B -> bag","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],"I bought a B of As from T S.")</code> should return "I bought a bag of apples from T shop.".'');'
  - text: '<code>markov(["A -> apple","WWWW -> with","Bgage -> ->.*","B -> bag","->.* -> money","W -> WW","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],"I bought a B of As W my Bgage from T S.")</code> should return "I bought a bag of apples with my money from T shop.".'
    testString: 'assert.deepEqual(markov(rules[2],tests[2]),outputs[2],''<code>markov(["A -> apple","WWWW -> with","Bgage -> ->.*","B -> bag","->.* -> money","W -> WW","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],"I bought a B of As W my Bgage from T S.")</code> should return "I bought a bag of apples with my money from T shop.".'');'
  - text: '<code>markov(["_+1 -> _1+","1+1 -> 11+","1! -> !1",",! -> !+","_! -> _","1*1 -> x,@y","1x -> xX","X, -> 1,1","X1 -> 1X","_x -> _X",",x -> ,X","y1 -> 1y","y_ -> _","1@1 -> x,@y","1@_ -> @_",",@_ -> !_","++ -> +","_1 -> 1","1+_ -> 1","_+_ -> "],"_1111*11111_")</code> should return "11111111111111111111".'
    testString: 'assert.deepEqual(markov(rules[3],tests[3]),outputs[3],''<code>markov(["_+1 -> _1+","1+1 -> 11+","1! -> !1",",! -> !+","_! -> _","1*1 -> x,@y","1x -> xX","X, -> 1,1","X1 -> 1X","_x -> _X",",x -> ,X","y1 -> 1y","y_ -> _","1@1 -> x,@y","1@_ -> @_",",@_ -> !_","++ -> +","_1 -> 1","1+_ -> 1","_+_ -> "],"_1111*11111_")</code> should return "11111111111111111111".'');'
  - text: '<code>markov(["A0 -> 1B","0A1 -> C01","1A1 -> C11","0B0 -> A01","1B0 -> A11","B1 -> 1B","0C0 -> B01","1C0 -> B11","0C1 -> H01","1C1 -> H11"],"")</code> should return "00011H1111000".'
    testString: 'assert.deepEqual(markov(rules[4],tests[4]),outputs[4],''<code>markov(["A0 -> 1B","0A1 -> C01","1A1 -> C11","0B0 -> A01","1B0 -> A11","B1 -> 1B","0C0 -> B01","1C0 -> B11","0C1 -> H01","1C1 -> H11"],"")</code> should return "00011H1111000".'');'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function markov (rules,test) {
  // Good luck!
}
```

</div>



</section>

## Solution
<section id='solution'>


```js
function markov(rules,test) {
    let pattern = new RegExp("^([^#]*?)\\s+->\\s+(\\.?)(.*)");
    let origTest = test;

    let captures = [];
    
    rules.forEach(function(rule){
		let m = pattern.exec(rule);
		for (let j = 0; j < m.length; j++)
		    m[j] = m[j + 1];
		captures.push(m);
    });

    test = origTest;
    let copy = test;
    for (let j = 0; j < captures.length; j++) {
        let c = captures[j];
        test = test.replace(c[0], c[2]);
        if (c[1]==".")
            break;
        if (test!=copy) {
            j = -1;
            copy = test;
        }
    }
    return test;
}

// tail:
let rules=[["A -> apple","B -> bag","S -> shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],
			["A -> apple","B -> bag","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],
			["A -> apple","WWWW -> with","Bgage -> ->.*","B -> bag","->.* -> money","W -> WW","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],
			["_+1 -> _1+","1+1 -> 11+","1! -> !1",",! -> !+","_! -> _","1*1 -> x,@y","1x -> xX","X, -> 1,1","X1 -> 1X","_x -> _X",",x -> ,X","y1 -> 1y","y_ -> _","1@1 -> x,@y","1@_ -> @_",",@_ -> !_","++ -> +","_1 -> 1","1+_ -> 1","_+_ -> "],
			["A0 -> 1B","0A1 -> C01","1A1 -> C11","0B0 -> A01","1B0 -> A11","B1 -> 1B","0C0 -> B01","1C0 -> B11","0C1 -> H01","1C1 -> H11"]];
let tests=["I bought a B of As from T S.",
			"I bought a B of As from T S.",
			"I bought a B of As W my Bgage from T S.",
			"_1111*11111_",
			"000000A000000"];
let outputs=["I bought a bag of apples from my brother.",
			"I bought a bag of apples from T shop.",
			"I bought a bag of apples with my money from T shop.",
			"11111111111111111111",
			"00011H1111000"];
```

</section>