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<p>Algorithm of <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for radix_sort2.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:d5/d91/namespacesorting"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d91/namespacesorting.html">sorting</a></td></tr>
<tr class="memdesc:d5/d91/namespacesorting"><td class="mdescLeft">&#160;</td><td class="mdescRight">for working with vectors <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:da/dda/namespaceradix__sort"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dda/namespaceradix__sort.html">radix_sort</a></td></tr>
<tr class="memdesc:da/dda/namespaceradix__sort"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a> algorithm. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a98ead7d43b11505398daf9a894f122f9"><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; uint64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d61/radix__sort2_8cpp.html#a98ead7d43b11505398daf9a894f122f9">sorting::radix_sort::step_ith</a> (uint16_t cur_digit, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; &amp;ar)</td></tr>
<tr class="memdesc:a98ead7d43b11505398daf9a894f122f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to sort vector according to current digit using stable sorting. <a href="../../d8/d61/radix__sort2_8cpp.html#a98ead7d43b11505398daf9a894f122f9">More...</a><br /></td></tr>
<tr class="separator:a98ead7d43b11505398daf9a894f122f9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae0cfd94fa3765b53d4ec7893ffaee5f8"><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; uint64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d61/radix__sort2_8cpp.html#ae0cfd94fa3765b53d4ec7893ffaee5f8">sorting::radix_sort::radix</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; &amp;ar)</td></tr>
<tr class="memdesc:ae0cfd94fa3765b53d4ec7893ffaee5f8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to sort vector digit by digit. <a href="../../d8/d61/radix__sort2_8cpp.html#ae0cfd94fa3765b53d4ec7893ffaee5f8">More...</a><br /></td></tr>
<tr class="separator:ae0cfd94fa3765b53d4ec7893ffaee5f8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to test the above algorithm. <a href="../../d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">More...</a><br /></td></tr>
<tr class="separator:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d61/radix__sort2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d8/d61/radix__sort2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Algorithm of <a href="https://en.wikipedia.org/wiki/Radix_sort" target="_blank">Radix sort</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Suyashjaiswal" target="_blank">Suyash Jaiswal</a></dd></dl>
<p>Sort the vector of unsigned integers using radix sort i.e. sorting digit by digit using <a href="https://en.wikipedia.org/wiki/Counting_sort" target="_blank">Counting Sort</a> as subroutine. Running time of radix sort is O(d*(n+b)) where b is the base for representing numbers and d in the max digits in input integers and n is number of unsigned integers. consider example for n = 5, aray elements = 432,234,143,332,123 sorting digit by digit sorting according to 1) 1st digit place =&gt; 432, 332, 143, 123, 234</p>
<p >2) 2nd digit place =&gt; 123, 432, 332, 234, 143</p>
<p >3) 3rd digit place =&gt; 123, 143, 234, 332, 432</p>
<p >using count sort at each step, which is stable. stable =&gt; already sorted according to previous digits. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 117</span> {</div>
<div class="line"><span class="lineno"> 118</span> <a class="code hl_function" href="../../d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 120</span>}</div>
<div class="ttc" id="aradix__sort2_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../d8/d61/radix__sort2_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Function to test the above algorithm.</div><div class="ttdef"><b>Definition:</b> radix_sort2.cpp:102</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae0cfd94fa3765b53d4ec7893ffaee5f8">&#9670;&#160;</a></span>radix()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; sorting::radix_sort::radix </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; uint64_t &gt; &amp;&#160;</td>
<td class="paramname"><em>ar</em></td><td>)</td>
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<p>Function to sort vector digit by digit. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">ar</td><td>- vector to be sorted </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>sorted vector </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 80</span> {</div>
<div class="line"><span class="lineno"> 81</span> uint64_t max_ele =</div>
<div class="line"><span class="lineno"> 82</span> *<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max_element.html">max_element</a>(ar.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()); <span class="comment">// returns the max element.</span></div>
<div class="line"><span class="lineno"> 83</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> temp = ar;</div>
<div class="line"><span class="lineno"> 84</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; max_ele / i &gt; 0;</div>
<div class="line"><span class="lineno"> 85</span> i *= 10) { <span class="comment">// loop breaks when i &gt; max_ele because no further digits</span></div>
<div class="line"><span class="lineno"> 86</span> <span class="comment">// left to makes changes in aray.</span></div>
<div class="line"><span class="lineno"> 87</span> temp = <a class="code hl_function" href="../../d8/d61/radix__sort2_8cpp.html#a98ead7d43b11505398daf9a894f122f9">step_ith</a>(i, temp);</div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">for</span> (uint64_t i : temp) {</div>
<div class="line"><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><span class="lineno"> 91</span> }</div>
<div class="line"><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">return</span> temp;</div>
<div class="line"><span class="lineno"> 94</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::begin</a></div><div class="ttdeci">T begin(T... args)</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::end</a></div><div class="ttdeci">T end(T... args)</div></div>
<div class="ttc" id="amax_element_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max_element.html">std::max_element</a></div><div class="ttdeci">T max_element(T... args)</div></div>
<div class="ttc" id="aradix__sort2_8cpp_html_a98ead7d43b11505398daf9a894f122f9"><div class="ttname"><a href="../../d8/d61/radix__sort2_8cpp.html#a98ead7d43b11505398daf9a894f122f9">sorting::radix_sort::step_ith</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; step_ith(uint16_t cur_digit, const std::vector&lt; uint64_t &gt; &amp;ar)</div><div class="ttdoc">Function to sort vector according to current digit using stable sorting.</div><div class="ttdef"><b>Definition:</b> radix_sort2.cpp:49</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a98ead7d43b11505398daf9a894f122f9">&#9670;&#160;</a></span>step_ith()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; sorting::radix_sort::step_ith </td>
<td>(</td>
<td class="paramtype">uint16_t&#160;</td>
<td class="paramname"><em>cur_digit</em>, </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; uint64_t &gt; &amp;&#160;</td>
<td class="paramname"><em>ar</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>Function to sort vector according to current digit using stable sorting. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">cur_digit</td><td>- sort according to the cur_digit </td></tr>
<tr><td class="paramname">ar</td><td>- vector to be sorted </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> sorted till ith digit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 51</span> { <span class="comment">// sorting according to current digit.</span></div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordtype">int</span> n = ar.<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"> 53</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint32_t&gt;</a> position(10, 0);</div>
<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><span class="lineno"> 55</span> position[(ar[i] / cur_digit) %</div>
<div class="line"><span class="lineno"> 56</span> 10]++; <span class="comment">// counting frequency of 0-9 at cur_digit.</span></div>
<div class="line"><span class="lineno"> 57</span> }</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordtype">int</span> cur = 0;</div>
<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 10; ++i) {</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">int</span> a = position[i];</div>
<div class="line"><span class="lineno"> 61</span> position[i] = cur; <span class="comment">// assingning starting position of 0-9.</span></div>
<div class="line"><span class="lineno"> 62</span> cur += a;</div>
<div class="line"><span class="lineno"> 63</span> }</div>
<div class="line"><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> temp(n);</div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><span class="lineno"> 66</span> temp[position[(ar[i] / cur_digit) % 10]] =</div>
<div class="line"><span class="lineno"> 67</span> ar[i]; <span class="comment">// storing ar[i] in ar[i]&#39;s cur_digit expected position of</span></div>
<div class="line"><span class="lineno"> 68</span> <span class="comment">// this step.</span></div>
<div class="line"><span class="lineno"> 69</span> position[(ar[i] / cur_digit) %</div>
<div class="line"><span class="lineno"> 70</span> 10]++; <span class="comment">// incrementing ar[i]&#39;s cur_digit position by 1, as</span></div>
<div class="line"><span class="lineno"> 71</span> <span class="comment">// current place used by ar[i].</span></div>
<div class="line"><span class="lineno"> 72</span> }</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">return</span> temp;</div>
<div class="line"><span class="lineno"> 74</span>}</div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">static void tests </td>
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<p>Function to test the above algorithm. </p>
<dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
<p >Test 1</p>
<p >Test 2</p>
<div class="fragment"><div class="line"><span class="lineno"> 102</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 103</span><span class="comment"> /// Test 1</span></div>
<div class="line"><span class="lineno"> 104</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> ar1 = {432, 234, 143, 332, 123};</div>
<div class="line"><span class="lineno"> 105</span> ar1 = <a class="code hl_function" href="../../d8/d61/radix__sort2_8cpp.html#ae0cfd94fa3765b53d4ec7893ffaee5f8">sorting::radix_sort::radix</a>(ar1);</div>
<div class="line"><span class="lineno"> 106</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(ar1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()));<span class="comment"></span></div>
<div class="line"><span class="lineno"> 107</span><span class="comment"> /// Test 2</span></div>
<div class="line"><span class="lineno"> 108</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> ar2 = {213, 3214, 123, 111, 112, 142,</div>
<div class="line"><span class="lineno"> 109</span> 133, 132, 32, 12, 113};</div>
<div class="line"><span class="lineno"> 110</span> ar2 = <a class="code hl_function" href="../../d8/d61/radix__sort2_8cpp.html#ae0cfd94fa3765b53d4ec7893ffaee5f8">sorting::radix_sort::radix</a>(ar2);</div>
<div class="line"><span class="lineno"> 111</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(ar2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/begin.html">begin</a>(), ar2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/end.html">end</a>()));</div>
<div class="line"><span class="lineno"> 112</span>}</div>
<div class="ttc" id="ais_sorted_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a></div><div class="ttdeci">T is_sorted(T... args)</div></div>
<div class="ttc" id="aradix__sort2_8cpp_html_ae0cfd94fa3765b53d4ec7893ffaee5f8"><div class="ttname"><a href="../../d8/d61/radix__sort2_8cpp.html#ae0cfd94fa3765b53d4ec7893ffaee5f8">sorting::radix_sort::radix</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; radix(const std::vector&lt; uint64_t &gt; &amp;ar)</div><div class="ttdoc">Function to sort vector digit by digit.</div><div class="ttdef"><b>Definition:</b> radix_sort2.cpp:80</div></div>
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