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@@ -121,7 +138,9 @@ Include dependency graph for maximum_circular_subarray.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="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></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>
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<tr class="memdesc:a5239174fa0d987f2c67edc1f2af82beb"><td class="mdescLeft">&#160;</td><td class="mdescRight">returns the maximum contiguous circular sum of an array <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>C++ program for maximum contiguous circular sum problem using <a href="https://en.wikipedia.org/wiki/Maximum_subarray_problem" target="_blank">Kadane's Algorithm</a> </p>
<p>The idea is to modify Kadane’s algorithm to find a minimum contiguous subarray sum and the maximum contiguous subarray sum, then check for the maximum value between the max_value and the value left after subtracting min_value from the total sum. For more information, check <a href="https://www.geeksforgeeks.org/maximum-contiguous-circular-sum/" target="_blank">Geeks For Geeks</a> explanation page. </p>
<p class="definition">Definition in file <a class="el" href="../../db/dfb/maximum__circular__subarray_8cpp_source.html">maximum_circular_subarray.cpp</a>.</p>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../db/dfb/maximum__circular__subarray_8cpp_source.html#l00087">87</a> of file <a class="el" href="../../db/dfb/maximum__circular__subarray_8cpp_source.html">maximum_circular_subarray.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 87</span> {</div>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="line"><span class="lineno"> 68</span> <span class="comment">// Explanation: Subarray 12, 8, -8, 9, -9, 10 gives the maximum sum, that is 22.</span></div>
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<div class="headertitle"><div class="title">maximum_circular_subarray.cpp</div></div>
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<a href="../../db/dfb/maximum__circular__subarray_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a> {</div>
<div class="foldopen" id="foldopen00026" data-start="{" data-end="}">
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"><a class="line" href="../../dd/d24/namespacedynamic__programming.html#a5239174fa0d987f2c67edc1f2af82beb"> 26</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#a5239174fa0d987f2c67edc1f2af82beb">maxCircularSum</a>(std::vector&lt;int&gt;&amp; arr)</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span>{</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// Edge Case</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordflow">if</span> (arr.size() == 1)</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">return</span> arr[0];</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// Sum variable which stores total sum of the array.</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordtype">int</span> sum = 0;</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; arr.size(); i++) {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> sum += arr[i];</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> }</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Every variable stores first value of the array.</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordtype">int</span> current_max = arr[0], max_so_far = arr[0], current_min = arr[0], min_so_far = arr[0];</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Concept of Kadane&#39;s Algorithm</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; arr.size(); i++) {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// Kadane&#39;s Algorithm to find Maximum subarray sum.</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> current_max = std::max(current_max + arr[i], arr[i]);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> max_so_far = std::max(max_so_far, current_max);</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Kadane&#39;s Algorithm to find Minimum subarray sum.</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> current_min = std::min(current_min + arr[i], arr[i]);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> min_so_far = std::min(min_so_far, current_min);</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">if</span> (min_so_far == sum)</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">return</span> max_so_far;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// Return the maximum value</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">return</span> std::max(max_so_far, sum - min_so_far);</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span>}</div>
</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>} <span class="comment">// namespace dynamic_programming</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="foldopen" id="foldopen00064" data-start="{" data-end="}">
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="../../db/dfb/maximum__circular__subarray_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 64</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../db/dfb/maximum__circular__subarray_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// Description of the test</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// Input: arr[] = {8, -8, 9, -9, 10, -11, 12}</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// Output: 22 </span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// Explanation: Subarray 12, 8, -8, 9, -9, 10 gives the maximum sum, that is 22.</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordtype">int</span> n = 7; <span class="comment">// size of the array</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> std::vector&lt;int&gt; arr = {8, -8, 9, -9, 10, -11, 12}; </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> assert(<a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#a5239174fa0d987f2c67edc1f2af82beb">dynamic_programming::maxCircularSum</a>(arr) == 22); <span class="comment">// this ensures that the algorithm works as expected</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> arr = {8, -8, 10, -9, 10, -11, 12};</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> assert(<a class="code hl_function" href="../../dd/d24/namespacedynamic__programming.html#a5239174fa0d987f2c67edc1f2af82beb">dynamic_programming::maxCircularSum</a>(arr) == 23);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> std::cout &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</span>;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span>}</div>
</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="foldopen" id="foldopen00087" data-start="{" data-end="}">
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="../../db/dfb/maximum__circular__subarray_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97"> 87</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span> *argv[]) {</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_function" href="../../db/dfb/maximum__circular__subarray_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
</div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
<div class="ttc" id="amaximum__circular__subarray_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/dfb/maximum__circular__subarray_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementation.</div><div class="ttdef"><b>Definition</b> <a href="#l00064">maximum_circular_subarray.cpp:64</a></div></div>
<div class="ttc" id="anamespacedynamic__programming_html"><div class="ttname"><a href="../../dd/d24/namespacedynamic__programming.html">dynamic_programming</a></div><div class="ttdoc">Dynamic Programming algorithms.</div></div>
<div class="ttc" id="anamespacedynamic__programming_html_a5239174fa0d987f2c67edc1f2af82beb"><div class="ttname"><a href="../../dd/d24/namespacedynamic__programming.html#a5239174fa0d987f2c67edc1f2af82beb">dynamic_programming::maxCircularSum</a></div><div class="ttdeci">int maxCircularSum(std::vector&lt; int &gt; &amp;arr)</div><div class="ttdoc">returns the maximum contiguous circular sum of an array</div><div class="ttdef"><b>Definition</b> <a href="#l00026">maximum_circular_subarray.cpp:26</a></div></div>
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