// Numbas version: exam_results_page_options
{"name": "Find all words within given Hamming distance", "extensions": ["codewords", "permutations"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"answer": "", "displayAnswer": "{sphere_string}", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>Enter your answer as a list of codewords, separated by commas. For example:&nbsp;<code>0000, 0001, 0002</code>.</p>", "unitTests": [], "matchMode": "regex", "showFeedbackIcon": true, "scripts": {"mark": {"script": "// check student's answer is a comma-separated list of codewords\nthis.valid = /^\\s*\\d+(\\s*,\\s*\\d+)*\\s*$/.test(this.studentAnswer);\nif(!this.valid) {\n  this.setCredit(0,\"Your answer is not a comma-separated list of codewords\");\n}\n\n// split up into individual codewords\nvar strings = this.studentAnswer.trim().split(/\\s*,\\s*/g);\n\n// parse each string as a codeword object\nvar Codeword = Numbas.extensions.codewords.Codeword;\nvar TCodeword = Numbas.jme.types.TCodeword;\nvar words = strings.map(function(s) {\n  var field_size = variables.field_size;\n  for(var i=0;i<s.length;i++) {\n    field_size = Math.max(parseInt(s[i])+1,field_size);\n  }\n  return new TCodeword(Codeword.fromString(s,field_size)); \n});\n\n// from here, we know the student has entered a valid answer\nthis.answered = true;\n\n// remove duplicates\nvar olength = words.length\nwords = Numbas.util.distinct(words);\n\n// tell the student if they've entered a duplicate word.\nif(olength!=words.length) {\n  this.markingComment(\"Your answer contains duplicate codewords.\");\n}\n\nvar sphere = question.scope.variables.sphere.value;\n\n// if the student's answer is the same set as the calculated answer\nif(Numbas.setmath.eq(words,sphere)) {\n  this.setCredit(1,\"Your answer is correct.\");\n} else {\n  // otherwise, give feedback on what went wrong\n  \n  var hamming_distance = Numbas.extensions.codewords.hamming_distance;      \n  var p = this;\n  \n  words.map(function(tword) {\n    var word = tword.value;\n    // if length is wrong or an invalid digit is used, this word doesn't belong to the field\n    if(word.length!=variables.word_length || word.field_size!=variables.field_size) {\n      p.markingComment(word+\" does not belong to $\\\\mathbb{Z}_{\"+variables.field_size+\"}^{\"+variables.word_length+\"}$.\");\n      return;\n    }\n    \n    // work out if the Hamming distance is wrong\n    var d = hamming_distance(word,variables.base_word);\n    if(d!=variables.radius) {\n      p.markingComment(\"$d_\\\\mathrm{H}(\"+word+\", \"+variables.base_word+\") = \"+d+\"$\");\n    }\n  });\n  \n  this.setCredit(0,\"Your answer is incorrect.\");\n}", "order": "instead"}}, "type": "patternmatch", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": "2"}], "variables": {"word_length": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..6)", "name": "word_length", "description": "<p>Length of words</p>"}, "sphere": {"templateType": "anything", "group": "Ungrouped variables", "definition": "hamming_sphere(base_word,radius)", "name": "sphere", "description": "<p>All words&nbsp;whose Hamming distance from&nbsp;<code>base_word</code> is <code>radius</code>.</p>"}, "field_size": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4)", "name": "field_size", "description": "<p>Number of&nbsp;choices of digit</p>"}, "sphere_string": {"templateType": "anything", "group": "Ungrouped variables", "definition": "join(map(string(x),x,sphere),', ')", "name": "sphere_string", "description": "<p>The list of words in <code>sphere</code>, as a string to be used as the displayed answer to the question.</p>"}, "base_word": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random_word(word_length,field_size)", "name": "base_word", "description": "<p>The centre of the ball.</p>"}, "radius": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..word_length-1)", "name": "radius", "description": "<p>Radius of the Hamming&nbsp;sphere</p>"}}, "ungrouped_variables": ["word_length", "field_size", "base_word", "radius", "sphere", "sphere_string"], "name": "Find all words within given Hamming distance", "variable_groups": [], "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "len(sphere)<15 and len(sphere)>3", "maxRuns": 100}, "statement": "<p>Find all words $w \\in \\mathbb{Z}_{\\var{field_size}}^{\\var{word_length}}$ for which $d_\\mathrm{H}(w,\\var{base_word}) = \\var{radius}$.</p>", "tags": [], "rulesets": {}, "extensions": ["codewords", "permutations"], "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find all words with given Hamming distance from a given codeword.</p>"}, "functions": {}, "advice": "<p>Each word $w$ must differ from the word $\\var{base_word}$ in $\\var{radius}$ {pluralise(radius,\"place\",\"places\")}.</p>\n<p>There are $\\simplify{comb({word_length},{radius}) = {comb(word_length,radius)}}$ ways of choosing $\\var{radius}$ {pluralise(radius,\"digit\",\"digits\")} to change, and $\\var{field_size}-1 = \\var{field_size-1}$ {pluralise(field_size-1,\"choice\",\"choices\")}&nbsp;for each changed digit.</p>\n<p>That means that there are $\\simplify[]{{comb(word_length,radius)}*{field_size-1}^{radius}} = \\var{comb(word_length,radius)*(field_size-1)^radius}$ words $w$ with $d_\\mathrm{H}(w,\\var{base_word}) = \\var{radius}$.</p>", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas-editor.mas.ncl.ac.uk/accounts/profile/3/"}, {"name": "Chris Graham", "profile_url": "https://numbas-editor.mas.ncl.ac.uk/accounts/profile/73/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas-editor.mas.ncl.ac.uk/accounts/profile/3/"}, {"name": "Chris Graham", "profile_url": "https://numbas-editor.mas.ncl.ac.uk/accounts/profile/73/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}