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<p>The <a href="https://cp-algorithms.com/string/z-function.html" target="_blank">Z function</a> for finding occurences of a pattern within a piece of text with time and space complexity O(n + m)
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;cstring&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for z_function.cpp:</div>
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<p><a href="../../d3/d80/z__function_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:ac044c4794349a8cff6256b99950d5773" id="r_ac044c4794349a8cff6256b99950d5773"><td class="memItemLeft" align="right" valign="top">std::vector&lt; uint64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ac044c4794349a8cff6256b99950d5773">Z_function</a> (const std::string &amp;pattern)</td></tr>
<tr class="memdesc:ac044c4794349a8cff6256b99950d5773"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
<tr class="memitem:ac186ca3ac3a69b5e52543bb13fe46db8" id="r_ac186ca3ac3a69b5e52543bb13fe46db8"><td class="memItemLeft" align="right" valign="top">std::vector&lt; uint64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a> (const std::string &amp;pattern, const std::string &amp;text)</td></tr>
<tr class="memdesc:ac186ca3ac3a69b5e52543bb13fe46db8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Using Z_function to find a pattern in a text. <br /></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>The <a href="https://cp-algorithms.com/string/z-function.html" target="_blank">Z function</a> for finding occurences of a pattern within a piece of text with time and space complexity O(n + m) </p>
<ol type="1">
<li>The Z-function for a string is an array of length n where the i-th element is equal to the greatest number of characters starting from the position i that coincide with the first characters of s.</li>
<li>E.g.: string: ababb then z[2]=2 as s[2]=s[0] and s[3]=s[1] and s[4]!=s[2] <dl class="section author"><dt>Author</dt><dd><a href="https://github.com/RitikaGupta8734" target="_blank">Ritika Gupta</a> </dd></dl>
</li>
</ol>
<p class="definition">Definition in file <a class="el" href="../../d3/d80/z__function_8cpp_source.html">z_function.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="ac186ca3ac3a69b5e52543bb13fe46db8" name="ac186ca3ac3a69b5e52543bb13fe46db8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac186ca3ac3a69b5e52543bb13fe46db8">&#9670;&#160;</a></span>find_pat_in_text()</h2>
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<td class="memname">std::vector&lt; uint64_t &gt; find_pat_in_text </td>
<td>(</td>
<td class="paramtype">const std::string &amp;</td> <td class="paramname"><span class="paramname"><em>pattern</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const std::string &amp;</td> <td class="paramname"><span class="paramname"><em>text</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<p>Using Z_function to find a pattern in a text. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">pattern</td><td>string pattern to search </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">text</td><td>text in which to search </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>a vector of starting indexes where pattern is found in the text </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d3/d80/z__function_8cpp_source.html#l00054">54</a> of file <a class="el" href="../../d3/d80/z__function_8cpp_source.html">z_function.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 55</span> {</div>
<div class="line"><span class="lineno"> 56</span> uint64_t text_length = text.size(), pattern_length = pattern.size();</div>
<div class="line"><span class="lineno"> 57</span> std::vector&lt;uint64_t&gt; z = <a class="code hl_function" href="#ac044c4794349a8cff6256b99950d5773">Z_function</a>(pattern + <span class="charliteral">&#39;#&#39;</span> + text);</div>
<div class="line"><span class="lineno"> 58</span> std::vector&lt;uint64_t&gt; matching_indexes;</div>
<div class="line"><span class="lineno"> 59</span> </div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; text_length; i++) {</div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">if</span> (z[i + pattern_length + 1] == pattern_length) {</div>
<div class="line"><span class="lineno"> 62</span> matching_indexes.push_back(i);</div>
<div class="line"><span class="lineno"> 63</span> }</div>
<div class="line"><span class="lineno"> 64</span> }</div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">return</span> matching_indexes;</div>
<div class="line"><span class="lineno"> 66</span>}</div>
<div class="ttc" id="az__function_8cpp_html_ac044c4794349a8cff6256b99950d5773"><div class="ttname"><a href="#ac044c4794349a8cff6256b99950d5773">Z_function</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; Z_function(const std::string &amp;pattern)</div><div class="ttdoc">for IO operations</div><div class="ttdef"><b>Definition</b> <a href="../../d3/d80/z__function_8cpp_source.html#l00029">z_function.cpp:29</a></div></div>
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<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</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d3/d80/z__function_8cpp_source.html#l00110">110</a> of file <a class="el" href="../../d3/d80/z__function_8cpp_source.html">z_function.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 110</span> {</div>
<div class="line"><span class="lineno"> 111</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"> 112</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 113</span>}</div>
<div class="ttc" id="az__function_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../d3/d80/z__function_8cpp_source.html#l00072">z_function.cpp:72</a></div></div>
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<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="mlabels-left">
<table class="memname">
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<td class="memname">void test </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d3/d80/z__function_8cpp_source.html#l00072">72</a> of file <a class="el" href="../../d3/d80/z__function_8cpp_source.html">z_function.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 72</span> {</div>
<div class="line"><span class="lineno"> 73</span> <span class="comment">// usual case</span></div>
<div class="line"><span class="lineno"> 74</span> std::string text1 = <span class="stringliteral">&quot;alskfjaldsabc1abc1abcbksbcdnsdabcabc&quot;</span>;</div>
<div class="line"><span class="lineno"> 75</span> std::string pattern1 = <span class="stringliteral">&quot;abc&quot;</span>;</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> <span class="comment">// matching_indexes1 gets the indexes where pattern1 exists in text1</span></div>
<div class="line"><span class="lineno"> 78</span> std::vector&lt;uint64_t&gt; matching_indexes1 = <a class="code hl_function" href="#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a>(pattern1, text1);</div>
<div class="line"><span class="lineno"> 79</span> assert((matching_indexes1 == std::vector&lt;uint64_t&gt;{10, 14, 18, 30, 33}));</div>
<div class="line"><span class="lineno"> 80</span> </div>
<div class="line"><span class="lineno"> 81</span> <span class="comment">// corner case</span></div>
<div class="line"><span class="lineno"> 82</span> std::string text2 = <span class="stringliteral">&quot;greengrass&quot;</span>;</div>
<div class="line"><span class="lineno"> 83</span> std::string pattern2 = <span class="stringliteral">&quot;abc&quot;</span>;</div>
<div class="line"><span class="lineno"> 84</span> </div>
<div class="line"><span class="lineno"> 85</span> <span class="comment">// matching_indexes2 gets the indexes where pattern2 exists in text2</span></div>
<div class="line"><span class="lineno"> 86</span> std::vector&lt;uint64_t&gt; matching_indexes2 = <a class="code hl_function" href="#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a>(pattern2, text2);</div>
<div class="line"><span class="lineno"> 87</span> assert((matching_indexes2 == std::vector&lt;uint64_t&gt;{}));</div>
<div class="line"><span class="lineno"> 88</span> </div>
<div class="line"><span class="lineno"> 89</span> <span class="comment">// corner case - empty text</span></div>
<div class="line"><span class="lineno"> 90</span> std::string text3 = <span class="stringliteral">&quot;&quot;</span>;</div>
<div class="line"><span class="lineno"> 91</span> std::string pattern3 = <span class="stringliteral">&quot;abc&quot;</span>;</div>
<div class="line"><span class="lineno"> 92</span> </div>
<div class="line"><span class="lineno"> 93</span> <span class="comment">// matching_indexes3 gets the indexes where pattern3 exists in text3</span></div>
<div class="line"><span class="lineno"> 94</span> std::vector&lt;uint64_t&gt; matching_indexes3 = <a class="code hl_function" href="#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a>(pattern3, text3);</div>
<div class="line"><span class="lineno"> 95</span> assert((matching_indexes3 == std::vector&lt;uint64_t&gt;{}));</div>
<div class="line"><span class="lineno"> 96</span> </div>
<div class="line"><span class="lineno"> 97</span> <span class="comment">// corner case - empty pattern</span></div>
<div class="line"><span class="lineno"> 98</span> std::string text4 = <span class="stringliteral">&quot;redsand&quot;</span>;</div>
<div class="line"><span class="lineno"> 99</span> std::string pattern4 = <span class="stringliteral">&quot;&quot;</span>;</div>
<div class="line"><span class="lineno"> 100</span> </div>
<div class="line"><span class="lineno"> 101</span> <span class="comment">// matching_indexes4 gets the indexes where pattern4 exists in text4</span></div>
<div class="line"><span class="lineno"> 102</span> std::vector&lt;uint64_t&gt; matching_indexes4 = <a class="code hl_function" href="#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a>(pattern4, text4);</div>
<div class="line"><span class="lineno"> 103</span> assert((matching_indexes4 == std::vector&lt;uint64_t&gt;{0, 1, 2, 3, 4, 5, 6}));</div>
<div class="line"><span class="lineno"> 104</span>}</div>
<div class="ttc" id="az__function_8cpp_html_ac186ca3ac3a69b5e52543bb13fe46db8"><div class="ttname"><a href="#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a></div><div class="ttdeci">std::vector&lt; uint64_t &gt; find_pat_in_text(const std::string &amp;pattern, const std::string &amp;text)</div><div class="ttdoc">Using Z_function to find a pattern in a text.</div><div class="ttdef"><b>Definition</b> <a href="../../d3/d80/z__function_8cpp_source.html#l00054">z_function.cpp:54</a></div></div>
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<a id="ac044c4794349a8cff6256b99950d5773" name="ac044c4794349a8cff6256b99950d5773"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac044c4794349a8cff6256b99950d5773">&#9670;&#160;</a></span>Z_function()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">std::vector&lt; uint64_t &gt; Z_function </td>
<td>(</td>
<td class="paramtype">const std::string &amp;</td> <td class="paramname"><span class="paramname"><em>pattern</em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>for IO operations </p>
<p>for string for assert for std::vector</p>
<p>Generate the Z-function for the inputted string. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">pattern</td><td>text on which to apply the Z-function </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the Z-function output as a vector array </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d3/d80/z__function_8cpp_source.html#l00029">29</a> of file <a class="el" href="../../d3/d80/z__function_8cpp_source.html">z_function.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 29</span> {</div>
<div class="line"><span class="lineno"> 30</span> uint64_t pattern_length = pattern.size();</div>
<div class="line"><span class="lineno"> 31</span> std::vector&lt;uint64_t&gt; z(pattern_length, 0);</div>
<div class="line"><span class="lineno"> 32</span> </div>
<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">for</span> (uint64_t i = 1, l = 0, r = 0; i &lt; pattern_length; i++) {</div>
<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">if</span> (i &lt;= r) {</div>
<div class="line"><span class="lineno"> 35</span> z[i] = std::min(r - i + 1, z[i - l]);</div>
<div class="line"><span class="lineno"> 36</span> }</div>
<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">while</span> (i + z[i] &lt; pattern_length &amp;&amp;</div>
<div class="line"><span class="lineno"> 38</span> pattern[z[i]] == pattern[i + z[i]]) {</div>
<div class="line"><span class="lineno"> 39</span> z[i]++;</div>
<div class="line"><span class="lineno"> 40</span> }</div>
<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">if</span> (i + z[i] - 1 &gt; r) {</div>
<div class="line"><span class="lineno"> 42</span> r = i + z[i] - 1;</div>
<div class="line"><span class="lineno"> 43</span> }</div>
<div class="line"><span class="lineno"> 44</span> }</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">return</span> z;</div>
<div class="line"><span class="lineno"> 46</span>}</div>
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