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2013-09-26T22:26:43.673
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<p>Your question is quite challenging, but i found a working (maybe not the most performant) solution. My Example is written in PHP, but you should be able to adapt it. I'll try to explain the "thoughts" behind the code.</p> <p><strong>Note:</strong> It seems like you added the "10 persons, 3 Jobs" constraint later - or i simple did overread it. However, my code should give you an example that you <em>might</em> be able to adapt to that constraint. My Code currently is assuming that there are <code>n</code> jobs for <code>n</code> persons. (The most easiest way of adapting it to the 10/3 criteria, would be to split up the 3 Jobs into 10 equal units of work, when assuming 10 workers!)</p> <p><strong>First</strong>, lets create some basic architecture stuff. We need <code>person</code>, <code>job</code> and obviously a matrix, representing the satisfaction of a person towards a job. The following snipped does exactly that:</p> <pre><code><?php class Person{ var $name; var $prim; var $sec; function __construct($name, $prim, $sec){ $this->name = $name; $this->prim = $prim; $this->sec = $sec; } function likes($job){ if ($job->type == $this->prim) return 2; if ($job->type == $this->sec) return 1; else return -1; } } class Job{ var $name; var $type; function __construct($name, $type){ $this->name = $name; $this->type = $type; } } $persons = array( "Max" => new Person("Max", "programing", "testing"), "Peter" => new Person("Peter", "testing", "docu"), "Sam" => new Person("Sam", "designing", "testing") ); $jobs = array( "New Classes" => new Job("New Classes", "programing"), "Theme change" => new Job("Theme change", "designing"), "Test Controller" => new Job("Test Controller", "testing") ); // debug: draw it: echo "<h2>Happines with Jobs</h2> "; echo "<table border=1>"; $p=0; echo "<tr>"; foreach ($jobs AS $job){ $j=0; foreach ($persons as $person){ if ($p++==0){ echo "<tr><td></td>"; foreach ($persons as $per) { echo "<td>".$per->name."</td>"; } echo "</tr>"; } if ($j++==0){ echo "<td>".$job->name."</td>"; } echo "<td>".$person->likes($job)."</td>"; } echo "</tr>"; } echo "</table>"; </code></pre> <p>This will give you a table like this: </p> <p><img src="https://i.stack.imgur.com/5iYvD.jpg" alt="Happiness with Jobs"></p> <p><strong>Second</strong>, we need to create ALL permutations of jobs and persons. (actually we don't need to, but doing so, will show you the reason, why we don't need to!)</p> <p>To create all permutations, we are using just the <strong>name</strong> of a person or job. (we can resolve the name back to the actual object later)</p> <pre><code>//build up all permutations $personNames = array(); foreach ($persons AS $person){ $personNames[] = $person->name; } $jobNames = array(); foreach ($jobs AS $job){ $jobNames[] = $job->name; } $personsPerms = array(); pc_permute($personNames,$personsPerms); $jobsPerms = array(); pc_permute($jobNames,$jobsPerms); function pc_permute($items, &$result, $perms = array( )) { if (empty($items)) { $result[] = join('/', $perms); } else { for ($i = count($items) - 1; $i >= 0; --$i) { $newitems = $items; $newperms = $perms; list($foo) = array_splice($newitems, $i, 1); array_unshift($newperms, $foo); pc_permute($newitems,$result, $newperms); } } } </code></pre> <p>Now, we have 2 Arrays: All job permutations and all person permutations. For the Example given above, the arrays will look like this (3 Elements each, makes 3*2*1=6 Permutations per Array):</p> <pre><code>Array ( [0] => Max/Peter/Sam [1] => Peter/Max/Sam [2] => Max/Sam/Peter [3] => Sam/Max/Peter [4] => Peter/Sam/Max [5] => Sam/Peter/Max ) Array ( [0] => New Classes/Theme change/Test Controller [1] => Theme change/New Classes/Test Controller [2] => New Classes/Test Controller/Theme change [3] => Test Controller/New Classes/Theme change [4] => Theme change/Test Controller/New Classes [5] => Test Controller/Theme change/New Classes ) </code></pre> <p>Now, We can create a <code>nXn</code> Table, containing ALL Values of the overall satisfaction for ALL possible job allocations:</p> <pre><code>// debug: draw it: echo "<h2>Total Happines of Combination (full join)</h2> "; echo "<table border=1>"; $p=0; echo "<tr>"; $row = 0; $calculated = array(); foreach ($jobsPerms AS $jobComb){ $j=0; $jobs_t = explode("/", $jobComb); foreach ($personsPerms as $personComb){ if ($p++==0){ echo "<tr><td></td>"; foreach ($personsPerms as $n) { echo "<td>".$n."</td>"; } echo "</tr>"; } if ($j++==0){ echo "<td>".$jobComb."</td>"; } $persons_t = explode("/", $personComb); $h = 0; echo "<td>"; for ($i=0; $i< count($persons_t); $i++){ $h += $persons[$persons_t[$i]]->likes($jobs[$jobs_t[$i]]); } echo $h; echo "</td>"; } $col=0; $row++; echo "</tr>"; } echo "</table>"; </code></pre> <p><img src="https://i.stack.imgur.com/hJxt1.jpg" alt="enter image description here"></p> <p>Lets call this matrix "M"</p> <p>This Matrix contains a "lot" of double combinations: (a/b) TO (1/2) is equal to (b/a) to (2/1) etc...</p> <p>After all: We simple can ignore:</p> <ul> <li>Either Each row > 1</li> <li>OR Each column > 1</li> </ul> <p>Ignoring all Columns > 1:</p> <pre><code>echo "<h2>Total Happines of Combination (ignoring columns)</h2> "; echo "<table border=1>"; $p=0; echo "<tr>"; $row = 0; $calculated = array(); foreach ($jobsPerms AS $jobComb){ $j=0; $jobs_t = explode("/", $jobComb); $col = 0; $personComb = $personsPerms[0]; if ($p++==0){ echo "<tr><td></td>"; echo "<td>".$personsPerms[0]."</td>"; echo "</tr>"; } if ($j++==0){ echo "<td>".$jobComb."</td>"; } $persons_t = explode("/", $personComb); $h = 0; echo "<td>"; for ($i=0; $i< count($persons_t); $i++){ $h += $persons[$persons_t[$i]]->likes($jobs[$jobs_t[$i]]); } echo $h; echo "</td>"; $col=0; $row++; echo "</tr>"; } echo "</table>"; </code></pre> <p>Output:</p> <p><img src="https://i.stack.imgur.com/K4rui.jpg" alt="enter image description here"></p> <p>And there you go! In this Example (one of) the most satisfying Solution would be:</p> <ul> <li>Max -> New Classes (+2)</li> <li>Peter -> Test Controller (+2)</li> <li>Sam -> Theme Change (+2)</li> </ul> <p>-> Happiness: 6.</p> <p>There are other, equal distributions as well.</p> <p>Example: 6 persons / 6 jobs:</p> <pre><code>$persons = array( "Max" => new Person("Max", "programing", "testing"), "Peter" => new Person("Peter", "testing", "docu"), "Sam" => new Person("Sam", "designing", "testing"), "Jeff" => new Person("Jeff", "docu", "programing"), "Fred" => new Person("Fred", "programing", "designing"), "Daniel" => new Person("Daniel", "designing", "docu") ); $jobs = array( "New Classes" => new Job("New Classes", "programing"), "Theme change" => new Job("Theme change", "designing"), "Test Controller" => new Job("Test Controller", "testing"), "Create Manual" => new Job("Create Manual", "docu"), "Program more!" => new Job("Program more!", "programing"), "Style the frontend" => new Job("Style the frontend", "designing") ); </code></pre> <p><img src="https://i.stack.imgur.com/0FsYZ.jpg" alt="enter image description here"></p> <p>results in (Persons: Max / Peter / Sam / Jeff / Fred / Daniel)</p> <p><img src="https://i.stack.imgur.com/CoLbC.jpg" alt="enter image description here"></p>
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1. COThank you for the answer. So in case of N workers and M jobs, where M > N, you suggest subdividing M. What if this is not always the case, and workers should just be as evenly distributed as possible? (in the case of 10/3, one worker will be the 4th in a group. This odd one out should be chosen solely based on his first preference, as he has the liberty to go in whatever group)
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