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<p>An implementation of a median calculation of a sliding window along a data stream.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
<code>#include &lt;ctime&gt;</code><br />
<code>#include &lt;list&gt;</code><br />
<code>#include &lt;set&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for windowed_median.cpp:</div>
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Classes</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html">probability::windowed_median::WindowedMedian</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">A class to calculate the median of a leading sliding window at the back of a stream of integer values. <a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#details">More...</a><br /></td></tr>
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Namespaces</h2></td></tr>
<tr class="memitem:d4/ded/namespaceprobability"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/ded/namespaceprobability.html">probability</a></td></tr>
<tr class="memdesc:d4/ded/namespaceprobability"><td class="mdescLeft">&#160;</td><td class="mdescRight">Probability algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:dd/d21/namespacewindowed__median"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d21/namespacewindowed__median.html">windowed_median</a></td></tr>
<tr class="memdesc:dd/d21/namespacewindowed__median"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the Windowed Median algorithm implementation. <br /></td></tr>
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Typedefs</h2></td></tr>
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using&#160;</td><td class="memItemRight" valign="bottom"><b>probability::windowed_median::Window</b> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a>&lt; int &gt;</td></tr>
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using&#160;</td><td class="memItemRight" valign="bottom"><b>probability::windowed_median::size_type</b> = Window::size_type</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a6dc652a36ea42ba262c4e4236e3e6601"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;vals, int windowSize)</td></tr>
<tr class="memdesc:a6dc652a36ea42ba262c4e4236e3e6601"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">More...</a><br /></td></tr>
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<tr class="memitem:ac0f2228420376f4db7e1274f2b41667c"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/ded/windowed__median_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">main</a> (int argc, const char *argv[])</td></tr>
<tr class="memdesc:ac0f2228420376f4db7e1274f2b41667c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d1/ded/windowed__median_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">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 >An implementation of a median calculation of a sliding window along a data stream. </p>
<p >Given a stream of integers, the algorithm calculates the median of a fixed size window at the back of the stream. The leading time complexity of this algorithm is O(log(N), and it is inspired by the known algorithm to [find median from (infinite) data stream](<a href="https://www.tutorialcup.com/interview/algorithm/find-median-from-data-stream.htm">https://www.tutorialcup.com/interview/algorithm/find-median-from-data-stream.htm</a>), with the proper modifications to account for the finite window size for which the median is requested</p>
<h3><a class="anchor" id="autotoc_md99"></a>
Algorithm</h3>
<p >The sliding window is managed by a list, which guarantees O(1) for both pushing and popping. Each new value is pushed to the window back, while a value from the front of the window is popped. In addition, the algorithm manages a multi-value binary search tree (BST), implemented by <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset.html">std::multiset</a>. For each new value that is inserted into the window, it is also inserted to the BST. When a value is popped from the window, it is also erased from the BST. Both insertion and erasion to/from the BST are O(logN) in time, with N the size of the window. Finally, the algorithm keeps a pointer to the root of the BST, and updates its position whenever values are inserted or erased to/from BST. The root of the tree is the median! Hence, median retrieval is always O(1)</p>
<p >Time complexity: O(logN). Space complexity: O(N). N - size of window </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/YanivHollander" target="_blank">Yaniv Hollander</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ac0f2228420376f4db7e1274f2b41667c" name="ac0f2228420376f4db7e1274f2b41667c"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac0f2228420376f4db7e1274f2b41667c">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const char *&#160;</td>
<td class="paramname"><em>argv</em>[]&#160;</td>
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<td></td>
<td>)</td>
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<p>Main function. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">argc</td><td>command line argument count (ignored) </td></tr>
<tr><td class="paramname">argv</td><td>command line array of arguments (ignored) </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p >A few fixed test cases</p>
<p >Array of sorted values; odd window size</p>
<p >Array of sorted values - decreasing; odd window size</p>
<p >Even window size</p>
<p >Array with repeating values</p>
<p >Array with same values except one</p>
<p >Array that includes repeating values including negatives</p>
<p >Array with large values - sum of few pairs exceeds MAX_INT. Window size is even - testing calculation of average median between two middle values</p>
<p >Random test cases</p>
<p >Array size in the range [5, 20]</p>
<p >Window size in the range [3, 10]</p>
<p >Random array values (positive/negative)</p>
<p >Testing randomized test</p>
<div class="fragment"><div class="line"><span class="lineno"> 198</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 199</span><span class="comment"> /// A few fixed test cases</span></div>
<div class="line"><span class="lineno"> 200</span><span class="comment"></span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({1, 2, 3, 4, 5, 6, 7, 8, 9},</div>
<div class="line"><span class="lineno"> 201</span> 3); <span class="comment">/// Array of sorted values; odd window size</span></div>
<div class="line"><span class="lineno"> 202</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 3, 2, 1},</div>
<div class="line"><span class="lineno"> 203</span> 3); <span class="comment">/// Array of sorted values - decreasing; odd window size</span></div>
<div class="line"><span class="lineno"> 204</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 5, 6}, 4); <span class="comment">/// Even window size</span></div>
<div class="line"><span class="lineno"> 205</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 3, 3, 3, 3, 3}, 3); <span class="comment">/// Array with repeating values</span></div>
<div class="line"><span class="lineno"> 206</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 7, 3, 3, 3, 3}, 3); <span class="comment">/// Array with same values except one</span></div>
<div class="line"><span class="lineno"> 207</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({4, 3, 3, -5, -5, 1, 3, 4, 5},</div>
<div class="line"><span class="lineno"> 208</span> 5); <span class="comment">/// Array that includes repeating values including negatives</span></div>
<div class="line"><span class="lineno"> 209</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 210</span><span class="comment"> /// Array with large values - sum of few pairs exceeds MAX_INT. Window size</span></div>
<div class="line"><span class="lineno"> 211</span><span class="comment"> /// is even - testing calculation of average median between two middle</span></div>
<div class="line"><span class="lineno"> 212</span><span class="comment"> /// values</span></div>
<div class="line"><span class="lineno"> 213</span><span class="comment"></span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({470211272, 101027544, 1457850878, 1458777923, 2007237709, 823564440,</div>
<div class="line"><span class="lineno"> 214</span> 1115438165, 1784484492, 74243042, 114807987},</div>
<div class="line"><span class="lineno"> 215</span> 6);</div>
<div class="line"><span class="lineno"> 216</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 217</span><span class="comment"> /// Random test cases</span></div>
<div class="line"><span class="lineno"> 218</span><span class="comment"></span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<span class="keyword">static_cast&lt;</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>)));</div>
<div class="line"><span class="lineno"> 219</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> vals;</div>
<div class="line"><span class="lineno"> 220</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 8; i &lt; 100; i++) {</div>
<div class="line"><span class="lineno"> 221</span> <span class="keyword">const</span> <span class="keyword">auto</span> n =</div>
<div class="line"><span class="lineno"> 222</span> 1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() /</div>
<div class="line"><span class="lineno"> 223</span> ((RAND_MAX + 5u) / 20); <span class="comment">/// Array size in the range [5, 20]</span></div>
<div class="line"><span class="lineno"> 224</span> <span class="keyword">auto</span> windowSize =</div>
<div class="line"><span class="lineno"> 225</span> 1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() / ((RAND_MAX + 3u) /</div>
<div class="line"><span class="lineno"> 226</span> 10); <span class="comment">/// Window size in the range [3, 10]</span></div>
<div class="line"><span class="lineno"> 227</span> vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();</div>
<div class="line"><span class="lineno"> 228</span> vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">reserve</a>(n);</div>
<div class="line"><span class="lineno"> 229</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><span class="lineno"> 230</span> vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(</div>
<div class="line"><span class="lineno"> 231</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() - RAND_MAX); <span class="comment">/// Random array values (positive/negative)</span></div>
<div class="line"><span class="lineno"> 232</span> }</div>
<div class="line"><span class="lineno"> 233</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>(vals, windowSize); <span class="comment">/// Testing randomized test</span></div>
<div class="line"><span class="lineno"> 234</span> }</div>
<div class="line"><span class="lineno"> 235</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 236</span>}</div>
<div class="ttc" id="aclear_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/clear.html">std::vector::clear</a></div><div class="ttdeci">T clear(T... args)</div></div>
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<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
<div class="ttc" id="awindowed__median_8cpp_html_a6dc652a36ea42ba262c4e4236e3e6601"><div class="ttname"><a href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a></div><div class="ttdeci">static void test(const std::vector&lt; int &gt; &amp;vals, int windowSize)</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> windowed_median.cpp:182</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6dc652a36ea42ba262c4e4236e3e6601">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;&#160;</td>
<td class="paramname"><em>vals</em>, </td>
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<td class="paramtype">int&#160;</td>
<td class="paramname"><em>windowSize</em>&#160;</td>
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<p>Self-test implementations. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">vals</td><td>Stream of values </td></tr>
<tr><td class="paramname">windowSize</td><td>Size of sliding window </td></tr>
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<p >Comparing medians: efficient function vs. Naive one</p>
<div class="fragment"><div class="line"><span class="lineno"> 182</span> {</div>
<div class="line"><span class="lineno"> 183</span> <a class="code hl_class" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html">probability::windowed_median::WindowedMedian</a> windowedMedian(windowSize);</div>
<div class="line"><span class="lineno"> 184</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> val : vals) {</div>
<div class="line"><span class="lineno"> 185</span> windowedMedian.insert(val);</div>
<div class="line"><span class="lineno"> 186</span><span class="comment"></span> </div>
<div class="line"><span class="lineno"> 187</span><span class="comment"> /// Comparing medians: efficient function vs. Naive one</span></div>
<div class="line"><span class="lineno"> 188</span><span class="comment"></span> assert(windowedMedian.getMedian() == windowedMedian.getMedianNaive());</div>
<div class="line"><span class="lineno"> 189</span> }</div>
<div class="line"><span class="lineno"> 190</span>}</div>
<div class="ttc" id="aclassprobability_1_1windowed__median_1_1_windowed_median_html"><div class="ttname"><a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html">probability::windowed_median::WindowedMedian</a></div><div class="ttdoc">A class to calculate the median of a leading sliding window at the back of a stream of integer values...</div><div class="ttdef"><b>Definition:</b> windowed_median.cpp:56</div></div>
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