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d2/d26/count__inversions_8cpp.html
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@@ -152,7 +152,7 @@ Functions</h2></td></tr>
<p>two elements a[i] and a[j] form an inversion if <code>a[i]</code> &gt; <code>a[j]</code> and i &lt; j</p>
<p>Time Complexity --&gt; <code>O(n.log n)</code></p>
<p>Space Complexity --&gt; <code>O(n)</code> ; additional array <code>temp[1..n]</code> </p>
<h3><a class="anchor" id="autotoc_md70"></a>
<h3><a class="anchor" id="autotoc_md71"></a>
Algorithm</h3>
<ol type="1">
<li>The idea is similar to merge sort, divide the array into two equal or almost equal halves in each step until the base case is reached.</li>

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d2/d3b/namespaceqr__algorithm.html
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@@ -438,7 +438,7 @@ template&lt;typename T &gt; </div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; tmp_vector -= col_vector2;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; }</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="keywordtype">double</span> mag = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(tmp_vector);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="keywordtype">double</span> <a class="code" href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">mag</a> = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">vector_mag</a>(tmp_vector);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160;<span class="comment">// parallelize on threads</span></div>
@@ -471,6 +471,7 @@ template&lt;typename T &gt; </div>
<div class="ttc" id="anamespaceqr__algorithm_html_a5422c76bfa322620de611083bd518d71"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">qr_algorithm::vector_proj</a></div><div class="ttdeci">std::valarray&lt; T &gt; vector_proj(const std::valarray&lt; T &gt; &amp;a, const std::valarray&lt; T &gt; &amp;b)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:104</div></div>
<div class="ttc" id="anamespaceqr__algorithm_html_ad16da2183db22378435042f26af43d5f"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">qr_algorithm::vector_mag</a></div><div class="ttdeci">double vector_mag(const std::valarray&lt; T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:92</div></div>
<div class="ttc" id="asize_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a></div></div>
<div class="ttc" id="avector__cross__product_8cpp_html_a4b2a9757a87c18e1642d72410ecfaba8"><div class="ttname"><a href="../../df/d66/vector__cross__product_8cpp.html#a4b2a9757a87c18e1642d72410ecfaba8">math::vector_cross::mag</a></div><div class="ttdeci">double mag(const std::array&lt; double, 3 &gt; &amp;vec)</div><div class="ttdoc">Calculates the magnitude of the mathematical vector from it's direction ratios.</div><div class="ttdef"><b>Definition:</b> vector_cross_product.cpp:83</div></div>
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