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<p>Functions for the Gale-Shapley Algorithm.
<a href="#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a6d7e84df47dcf19e88f95f8f9040306c" id="r_a6d7e84df47dcf19e88f95f8f9040306c"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a6d7e84df47dcf19e88f95f8f9040306c">gale_shapley</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> &gt; &gt; &amp;secondary_preferences, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> &gt; &gt; &amp;primary_preferences)</td></tr>
<tr class="memdesc:a6d7e84df47dcf19e88f95f8f9040306c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function that finds the stable matching between two sets of elements using the Gale-Shapley Algorithm. <br /></td></tr>
<tr class="separator:a6d7e84df47dcf19e88f95f8f9040306c"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Functions for the Gale-Shapley Algorithm. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a6d7e84df47dcf19e88f95f8f9040306c" name="a6d7e84df47dcf19e88f95f8f9040306c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a6d7e84df47dcf19e88f95f8f9040306c">&#9670;&#160;</a></span>gale_shapley()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> &gt; greedy_algorithms::stable_matching::gale_shapley </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>secondary_preferences</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> &gt; &gt; &amp;</td> <td class="paramname"><span class="paramname"><em>primary_preferences</em></span>&#160;)</td>
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<p>The main function that finds the stable matching between two sets of elements using the Gale-Shapley Algorithm. </p>
<dl class="section note"><dt>Note</dt><dd>This doesn't work on negative preferences. the preferences should be continuous integers starting from 0 to number of preferences - 1. </dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">primary_preferences</td><td>the preferences of the primary set should be a 2D vector </td></tr>
<tr><td class="paramname">secondary_preferences</td><td>the preferences of the secondary set should be a 2D vector </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>matches the stable matching between the two sets </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {</div>
<div class="line"><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> num_elements = secondary_preferences.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 44</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::uint32_t&gt;</a> matches(num_elements, -1);</div>
<div class="line"><span class="lineno"> 45</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> is_free_primary(num_elements, <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 46</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::uint32_t&gt;</a> proposal_index(num_elements, 0); <span class="comment">// Tracks the next secondary to propose for each primary</span></div>
<div class="line"><span class="lineno"> 47</span> </div>
<div class="line"><span class="lineno"> 48</span> <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordtype">int</span> free_primary_index = -1;</div>
<div class="line"><span class="lineno"> 50</span> </div>
<div class="line"><span class="lineno"> 51</span> <span class="comment">// Find the next free primary</span></div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> i = 0; i &lt; num_elements; i++) {</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">if</span> (is_free_primary[i]) {</div>
<div class="line"><span class="lineno"> 54</span> free_primary_index = i;</div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">break</span>;</div>
<div class="line"><span class="lineno"> 56</span> }</div>
<div class="line"><span class="lineno"> 57</span> }</div>
<div class="line"><span class="lineno"> 58</span> </div>
<div class="line"><span class="lineno"> 59</span> <span class="comment">// If no free primary is found, break the loop</span></div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">if</span> (free_primary_index == -1) <span class="keywordflow">break</span>;</div>
<div class="line"><span class="lineno"> 61</span> </div>
<div class="line"><span class="lineno"> 62</span> <span class="comment">// Get the next secondary to propose</span></div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> secondary_to_propose = primary_preferences[free_primary_index][proposal_index[free_primary_index]];</div>
<div class="line"><span class="lineno"> 64</span> proposal_index[free_primary_index]++;</div>
<div class="line"><span class="lineno"> 65</span> </div>
<div class="line"><span class="lineno"> 66</span> <span class="comment">// Get the current match of the secondary</span></div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a> current_match = matches[secondary_to_propose];</div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> <span class="comment">// If the secondary is free, match them</span></div>
<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">if</span> (current_match == -1) {</div>
<div class="line"><span class="lineno"> 71</span> matches[secondary_to_propose] = free_primary_index;</div>
<div class="line"><span class="lineno"> 72</span> is_free_primary[free_primary_index] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 73</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 74</span> <span class="comment">// Determine if the current match should be replaced</span></div>
<div class="line"><span class="lineno"> 75</span> <span class="keyword">auto</span> new_proposer_rank = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find</a>(secondary_preferences[secondary_to_propose].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(),</div>
<div class="line"><span class="lineno"> 76</span> secondary_preferences[secondary_to_propose].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>(),</div>
<div class="line"><span class="lineno"> 77</span> free_primary_index);</div>
<div class="line"><span class="lineno"> 78</span> <span class="keyword">auto</span> current_match_rank = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/find.html">std::find</a>(secondary_preferences[secondary_to_propose].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">begin</a>(),</div>
<div class="line"><span class="lineno"> 79</span> secondary_preferences[secondary_to_propose].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>(),</div>
<div class="line"><span class="lineno"> 80</span> current_match);</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> <span class="comment">// If the new proposer is preferred over the current match</span></div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">if</span> (new_proposer_rank &lt; current_match_rank) {</div>
<div class="line"><span class="lineno"> 84</span> matches[secondary_to_propose] = free_primary_index;</div>
<div class="line"><span class="lineno"> 85</span> is_free_primary[free_primary_index] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 86</span> is_free_primary[current_match] = <span class="keyword">true</span>; <span class="comment">// Current match is now free</span></div>
<div class="line"><span class="lineno"> 87</span> }</div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> }</div>
<div class="line"><span class="lineno"> 90</span> </div>
<div class="line"><span class="lineno"> 91</span> <span class="keywordflow">return</span> matches;</div>
<div class="line"><span class="lineno"> 92</span>}</div>
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