fix(challenge-md): Fix file names and preserve challenge order in meta.json
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---
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title: Execute a Markov algorithm
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id: 59e09e6d412c5939baa02d16
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challengeType: 5
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---
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## Description
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<section id='description'>
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Task:
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<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>
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<p><ruleset> ::= ((<comment> | <rule>) <newline>+)*</p>
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<p><comment> ::= # {<any character>}</p>
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<p><rule> ::= <pattern> <whitespace> -> <whitespace> [.] <replacement></p>
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<p><whitespace> ::= (<tab> | <space>) [<whitespace>]</p>
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<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>
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<p><big><big> Rulesets </big></big></p><p>Use the following tests on entries:</p>
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Ruleset 1:
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<pre>
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This rules file is extracted from Wikipedia:
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http://en.wikipedia.org/wiki/Markov_AlgorithmA -> apple
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B -> bag
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S -> shop
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T -> the
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the shop -> my brother
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a never used -> .terminating rule
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</pre>
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<p>Sample text of:</p>
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<p> <code> I bought a B of As from T S. </code></p>
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<p>Should generate the output:</p>
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<p> <code> I bought a bag of apples from my brother. </code></p>
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Ruleset 2:
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<p>A test of the terminating rule</p>
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<pre>
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Slightly modified from the rules on WikipediaA -> apple
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B -> bag
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S -> .shop
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T -> the
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the shop -> my brother
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a never used -> .terminating rule</pre>
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<p>Sample text of:</p>
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<p> <code>I bought a B of As from T S.</code></p>
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<p>Should generate:</p>
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<p> <code>I bought a bag of apples from T shop.</code></p>
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Ruleset 3:
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<p>This tests for correct substitution order and may trap simple regexp based replacement routines if special regexp characters are not escaped.</p>
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<pre>
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BNF Syntax testing rulesA -> apple
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WWWW -> with
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Bgage -> ->.*
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B -> bag
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->.* -> money
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W -> WW
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S -> .shop
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T -> the
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the shop -> my brother
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a never used -> .terminating rule
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</pre>
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<p>Sample text of:</p>
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<p> <code>I bought a B of As W my Bgage from T S.</code></p>
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<p>Should generate:</p>
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<p> <code>I bought a bag of apples with my money from T shop.</code></p>
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Ruleset 4:
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<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>
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<pre>
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## Unary Multiplication Engine, for testing Markov Algorithm implementations
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## By Donal Fellows.
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Unary addition engine_+1 -> _1+
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1+1 -> 11+
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Pass for converting from the splitting of multiplication into ordinary
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addition1! -> !1
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,! -> !+
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_! -> _
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Unary multiplication by duplicating left side, right side times1*1 -> x,@y
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1x -> xX
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X, -> 1,1
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X1 -> 1X
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_x -> _X
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,x -> ,X
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y1 -> 1y
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y_ -> _
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Next phase of applying1@1 -> x,@y
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1@_ -> @_
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,@_ -> !_
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++ -> +
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Termination cleanup for addition_1 -> 1
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1+_ -> 1
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_+_ ->
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</pre>
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<p>Sample text of:</p>
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<p> <code> _1111*11111_ </code></p>
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<p>should generate the output:</p>
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<p> <code> 11111111111111111111 </code></p>
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Ruleset 5:
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<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>
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<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>
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<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>
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<pre>
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Turing machine: three-state busy beaver
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# state A, symbol 0 => write 1, move right, new state BA0 -> 1B
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state A, symbol 1 => write 1, move left, new state C0A1 -> C01
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1A1 -> C11
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state B, symbol 0 => write 1, move left, new state A0B0 -> A01
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1B0 -> A11
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state B, symbol 1 => write 1, move right, new state BB1 -> 1B
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state C, symbol 0 => write 1, move left, new state B0C0 -> B01
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1C0 -> B11
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state C, symbol 1 => write 1, move left, halt0C1 -> H01
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1C1 -> H11
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</pre>
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<p>This ruleset should turn</p>
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<p> <code> 000000A000000 </code></p>
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<p>into</p>
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<p> <code> 00011H1111000 </code></p>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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- text: <code>markov</code> is a function.
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testString: 'assert(typeof markov === ''function'', ''<code>markov</code> is a function.'');'
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- 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.".'
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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.".'');'
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- 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.".'
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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.".'');'
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- 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.".'
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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.".'');'
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- 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".'
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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".'');'
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- 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".'
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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".'');'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function markov (rules,test) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function markov(rules,test) {
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let pattern = new RegExp("^([^#]*?)\\s+->\\s+(\\.?)(.*)");
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let origTest = test;
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let captures = [];
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rules.forEach(function(rule){
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let m = pattern.exec(rule);
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for (let j = 0; j < m.length; j++)
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m[j] = m[j + 1];
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captures.push(m);
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});
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test = origTest;
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let copy = test;
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for (let j = 0; j < captures.length; j++) {
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let c = captures[j];
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test = test.replace(c[0], c[2]);
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if (c[1]==".")
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break;
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if (test!=copy) {
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j = -1;
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copy = test;
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}
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}
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return test;
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}
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// tail:
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let rules=[["A -> apple","B -> bag","S -> shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],
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["A -> apple","B -> bag","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],
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["A -> apple","WWWW -> with","Bgage -> ->.*","B -> bag","->.* -> money","W -> WW","S -> .shop","T -> the","the shop -> my brother","a never used -> .terminating rule"],
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["_+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","_+_ -> "],
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["A0 -> 1B","0A1 -> C01","1A1 -> C11","0B0 -> A01","1B0 -> A11","B1 -> 1B","0C0 -> B01","1C0 -> B11","0C1 -> H01","1C1 -> H11"]];
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let tests=["I bought a B of As from T S.",
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"I bought a B of As from T S.",
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"I bought a B of As W my Bgage from T S.",
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"_1111*11111_",
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"000000A000000"];
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let outputs=["I bought a bag of apples from my brother.",
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"I bought a bag of apples from T shop.",
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"I bought a bag of apples with my money from T shop.",
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"11111111111111111111",
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"00011H1111000"];
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```
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</section>
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