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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;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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Functions</h2></td></tr>
<tr class="memitem:ac044c4794349a8cff6256b99950d5773"><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="../../d3/d80/z__function_8cpp.html#ac044c4794349a8cff6256b99950d5773">Z_function</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern)</td></tr>
<tr class="memdesc:ac044c4794349a8cff6256b99950d5773"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <a href="../../d3/d80/z__function_8cpp.html#ac044c4794349a8cff6256b99950d5773">More...</a><br /></td></tr>
<tr class="separator:ac044c4794349a8cff6256b99950d5773"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac186ca3ac3a69b5e52543bb13fe46db8"><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="../../d3/d80/z__function_8cpp.html#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;pattern, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &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. <a href="../../d3/d80/z__function_8cpp.html#ac186ca3ac3a69b5e52543bb13fe46db8">More...</a><br /></td></tr>
<tr class="separator:ac186ca3ac3a69b5e52543bb13fe46db8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d80/z__function_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../d3/d80/z__function_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d3/d80/z__function_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d3/d80/z__function_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 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>
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</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ac186ca3ac3a69b5e52543bb13fe46db8">&#9670;&nbsp;</a></span>find_pat_in_text()</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; find_pat_in_text </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
<td class="paramname"><em>text</em>&#160;</td>
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<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>
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</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>a vector of starting indexes where pattern is found in the text </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 54</span> {</div>
<div class="line"><span class="lineno"> 55</span> uint64_t text_length = text.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>(), pattern_length = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 56</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> z = <a class="code hl_function" href="../../d3/d80/z__function_8cpp.html#ac044c4794349a8cff6256b99950d5773">Z_function</a>(pattern + <span class="charliteral">&#39;#&#39;</span> + text);</div>
<div class="line"><span class="lineno"> 57</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> matching_indexes;</div>
<div class="line"><span class="lineno"> 58</span> </div>
<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; text_length; i++) {</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">if</span> (z[i + pattern_length + 1] == pattern_length) {</div>
<div class="line"><span class="lineno"> 61</span> matching_indexes.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(i);</div>
<div class="line"><span class="lineno"> 62</span> }</div>
<div class="line"><span class="lineno"> 63</span> }</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> matching_indexes;</div>
<div class="line"><span class="lineno"> 65</span>}</div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; uint64_t &gt;</a></div></div>
<div class="ttc" id="az__function_8cpp_html_ac044c4794349a8cff6256b99950d5773"><div class="ttname"><a href="../../d3/d80/z__function_8cpp.html#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> z_function.cpp:28</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </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"> 93</span> {</div>
<div class="line"><span class="lineno"> 94</span> <a class="code hl_function" href="../../d3/d80/z__function_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 96</span>}</div>
<div class="ttc" id="az__function_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d3/d80/z__function_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> z_function.cpp:71</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 71</span> {</div>
<div class="line"><span class="lineno"> 72</span> <span class="comment">// usual case</span></div>
<div class="line"><span class="lineno"> 73</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> text1 = <span class="stringliteral">&quot;alskfjaldsabc1abc1abcbksbcdnsdabcabc&quot;</span>;</div>
<div class="line"><span class="lineno"> 74</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern1 = <span class="stringliteral">&quot;abc&quot;</span>;</div>
<div class="line"><span class="lineno"> 75</span> </div>
<div class="line"><span class="lineno"> 76</span> <span class="comment">// matching_indexes1 gets the indexes where pattern1 exists in text1</span></div>
<div class="line"><span class="lineno"> 77</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> matching_indexes1 = <a class="code hl_function" href="../../d3/d80/z__function_8cpp.html#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a>(pattern1, text1);</div>
<div class="line"><span class="lineno"> 78</span> assert((matching_indexes1 == <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>{10, 14, 18, 30, 33}));</div>
<div class="line"><span class="lineno"> 79</span> </div>
<div class="line"><span class="lineno"> 80</span> <span class="comment">// corner case</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> text2 = <span class="stringliteral">&quot;greengrass&quot;</span>;</div>
<div class="line"><span class="lineno"> 82</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> pattern2 = <span class="stringliteral">&quot;abc&quot;</span>;</div>
<div class="line"><span class="lineno"> 83</span> </div>
<div class="line"><span class="lineno"> 84</span> <span class="comment">// matching_indexes2 gets the indexes where pattern2 exists in text2</span></div>
<div class="line"><span class="lineno"> 85</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> matching_indexes2 = <a class="code hl_function" href="../../d3/d80/z__function_8cpp.html#ac186ca3ac3a69b5e52543bb13fe46db8">find_pat_in_text</a>(pattern2, text2);</div>
<div class="line"><span class="lineno"> 86</span> assert((matching_indexes2 == <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>{}));</div>
<div class="line"><span class="lineno"> 87</span>}</div>
<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
<div class="ttc" id="az__function_8cpp_html_ac186ca3ac3a69b5e52543bb13fe46db8"><div class="ttname"><a href="../../d3/d80/z__function_8cpp.html#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> z_function.cpp:53</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac044c4794349a8cff6256b99950d5773">&#9670;&nbsp;</a></span>Z_function()</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; Z_function </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
<td class="paramname"><em>pattern</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>for IO operations </p>
<p >for string for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></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>
<div class="fragment"><div class="line"><span class="lineno"> 28</span> {</div>
<div class="line"><span class="lineno"> 29</span> uint64_t pattern_length = pattern.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 30</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> z(pattern_length, 0);</div>
<div class="line"><span class="lineno"> 31</span> </div>
<div class="line"><span class="lineno"> 32</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"> 33</span> <span class="keywordflow">if</span> (i &lt;= r) {</div>
<div class="line"><span class="lineno"> 34</span> z[i] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(r - i + 1, z[i - l]);</div>
<div class="line"><span class="lineno"> 35</span> }</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">while</span> (i + z[i] &lt; pattern_length &amp;&amp;</div>
<div class="line"><span class="lineno"> 37</span> pattern[z[i]] == pattern[i + z[i]]) {</div>
<div class="line"><span class="lineno"> 38</span> z[i]++;</div>
<div class="line"><span class="lineno"> 39</span> }</div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">if</span> (i + z[i] - 1 &gt; r) {</div>
<div class="line"><span class="lineno"> 41</span> r = i + z[i] - 1;</div>
<div class="line"><span class="lineno"> 42</span> }</div>
<div class="line"><span class="lineno"> 43</span> }</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> z;</div>
<div class="line"><span class="lineno"> 45</span>}</div>
<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
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