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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Lyndon_word" target="_blank">Duval's algorithm</a>.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstddef&gt;</code><br />
<code>#include &lt;deque&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;string&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for duval.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/dd6/namespacestring.html">string</a></td></tr>
<tr class="memdesc:d6/dd6/namespacestring"><td class="mdescLeft">&#160;</td><td class="mdescRight">string manipulation algorithms <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ac2a35302e6bed93c4b2c6f55a21a5632" id="r_ac2a35302e6bed93c4b2c6f55a21a5632"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ac2a35302e6bed93c4b2c6f55a21a5632"><td class="memTemplItemLeft" align="right" valign="top">size_t&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">string::duval</a> (const T &amp;s)</td></tr>
<tr class="memdesc:ac2a35302e6bed93c4b2c6f55a21a5632"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find the lexicographically smallest cyclic shift of a sequence. <br /></td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">self test implementation returns void <br /></td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">main function <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Lyndon_word" target="_blank">Duval's algorithm</a>. </p>
<p>Duval's algorithm is an algorithm to find the lexicographically smallest rotation of a string. It is based on the concept of Lyndon words. Lyndon words are defined as the lexicographically smallest string in a rotation equivalence class. A rotation equivalence class is a set of strings that can be obtained by rotating a string. For example, the rotation equivalence class of "abc" is {"abc", "bca", "cab"}. The lexicographically smallest string in this class is "abc".</p>
<p>Duval's algorithm works by iterating over the string and finding the smallest rotation of the string that is a Lyndon word. This is done by comparing the string with its suffixes and finding the smallest suffix that is lexicographically smaller than the string. This suffix is then added to the result and the process is repeated with the remaining string. The algorithm has a time complexity of O(n) where n is the length of the string.</p>
<dl class="section note"><dt>Note</dt><dd>While Lyndon words are described in the context of strings, Duval's algorithm can be used to find the lexicographically smallest cyclic shift of any sequence of comparable elements.</dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/aminegh20" target="_blank">Amine Ghoussaini</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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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"> 115</span> {</div>
<div class="line"><span class="lineno"> 116</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self test implementations</span></div>
<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 118</span>}</div>
<div class="ttc" id="aduval_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">self test implementation returns void</div><div class="ttdef"><b>Definition</b> duval.cpp:77</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<p>self test implementation returns void </p>
<div class="fragment"><div class="line"><span class="lineno"> 77</span> {</div>
<div class="line"><span class="lineno"> 78</span> <span class="keyword">using namespace </span><a class="code hl_namespace" href="../../d6/dd6/namespacestring.html">string</a>;</div>
<div class="line"><span class="lineno"> 79</span> </div>
<div class="line"><span class="lineno"> 80</span> <span class="comment">// Test 1</span></div>
<div class="line"><span class="lineno"> 81</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s1 = <span class="stringliteral">&quot;abcab&quot;</span>;</div>
<div class="line"><span class="lineno"> 82</span> assert(<a class="code hl_function" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">duval</a>(s1) == 3);</div>
<div class="line"><span class="lineno"> 83</span> </div>
<div class="line"><span class="lineno"> 84</span> <span class="comment">// Test 2</span></div>
<div class="line"><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s2 = <span class="stringliteral">&quot;011100&quot;</span>;</div>
<div class="line"><span class="lineno"> 86</span> assert(<a class="code hl_function" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">duval</a>(s2) == 4);</div>
<div class="line"><span class="lineno"> 87</span> </div>
<div class="line"><span class="lineno"> 88</span> <span class="comment">// Test 3</span></div>
<div class="line"><span class="lineno"> 89</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> v = {5, 2, 1, 3, 4};</div>
<div class="line"><span class="lineno"> 90</span> assert(<a class="code hl_function" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">duval</a>(v) == 2);</div>
<div class="line"><span class="lineno"> 91</span> </div>
<div class="line"><span class="lineno"> 92</span> <span class="comment">// Test 4</span></div>
<div class="line"><span class="lineno"> 93</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;int, 5&gt;</a> a = {1, 2, 3, 4, 5};</div>
<div class="line"><span class="lineno"> 94</span> assert(<a class="code hl_function" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">duval</a>(a) == 0);</div>
<div class="line"><span class="lineno"> 95</span> </div>
<div class="line"><span class="lineno"> 96</span> <span class="comment">// Test 5</span></div>
<div class="line"><span class="lineno"> 97</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/deque.html">std::deque&lt;char&gt;</a> d = {<span class="charliteral">&#39;a&#39;</span>, <span class="charliteral">&#39;z&#39;</span>, <span class="charliteral">&#39;c&#39;</span>, <span class="charliteral">&#39;a&#39;</span>, <span class="charliteral">&#39;b&#39;</span>};</div>
<div class="line"><span class="lineno"> 98</span> assert(<a class="code hl_function" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">duval</a>(d) == 3);</div>
<div class="line"><span class="lineno"> 99</span> </div>
<div class="line"><span class="lineno"> 100</span> <span class="comment">// Test 6</span></div>
<div class="line"><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s3;</div>
<div class="line"><span class="lineno"> 102</span> assert(<a class="code hl_function" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">duval</a>(s3) == 0);</div>
<div class="line"><span class="lineno"> 103</span> </div>
<div class="line"><span class="lineno"> 104</span> <span class="comment">// Test 7</span></div>
<div class="line"><span class="lineno"> 105</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> v2 = {5, 2, 1, 3, -4};</div>
<div class="line"><span class="lineno"> 106</span> assert(<a class="code hl_function" href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">duval</a>(v2) == 4);</div>
<div class="line"><span class="lineno"> 107</span> </div>
<div class="line"><span class="lineno"> 108</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;All tests passed!&quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 109</span>}</div>
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
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<div class="ttc" id="anamespacestring_html"><div class="ttname"><a href="../../d6/dd6/namespacestring.html">string</a></div><div class="ttdoc">string manipulation algorithms</div><div class="ttdef"><b>Definition</b> duval.cpp:41</div></div>
<div class="ttc" id="anamespacestring_html_ac2a35302e6bed93c4b2c6f55a21a5632"><div class="ttname"><a href="../../d6/dd6/namespacestring.html#ac2a35302e6bed93c4b2c6f55a21a5632">string::duval</a></div><div class="ttdeci">size_t duval(const T &amp;s)</div><div class="ttdoc">Find the lexicographically smallest cyclic shift of a sequence.</div><div class="ttdef"><b>Definition</b> duval.cpp:49</div></div>
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