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<div class="headertitle"><div class="title">dynamic_programming Namespace Reference</div></div>
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<p>Dynamic Programming algorithms.
<a href="../../dd/d24/namespacedynamic__programming.html#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a0a2215194e58786c34db1ccaf8031079"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html#a0a2215194e58786c34db1ccaf8031079">LIS</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; &amp;a, const uint32_t &amp;n)</td></tr>
<tr class="memdesc:a0a2215194e58786c34db1ccaf8031079"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate the longest increasing subsequence for the specified numbers. <br /></td></tr>
<tr class="separator:a0a2215194e58786c34db1ccaf8031079"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5239174fa0d987f2c67edc1f2af82beb"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d24/namespacedynamic__programming.html#a5239174fa0d987f2c67edc1f2af82beb">maxCircularSum</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt; &amp;arr)</td></tr>
<tr class="memdesc:a5239174fa0d987f2c67edc1f2af82beb"><td class="mdescLeft">&#160;</td><td class="mdescRight">returns the maximum contiguous circular sum of an array <br /></td></tr>
<tr class="separator:a5239174fa0d987f2c67edc1f2af82beb"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Dynamic Programming algorithms. </p>
<p>Dynamic programming algorithms.</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>Dynamic Programming algorithm.</p>
<p>Dynamic Programming Algorithms.</p>
<p>for <code>assert</code> for IO operations for <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></code> library for <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></code> STL library</p>
<p>for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a> for io operations</p>
<p>Dynamic Programming algorithms</p>
<p>for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a> for IO operations</p>
<p>Dynamic Programming algorithms</p>
<p>for assert for IO operations</p>
<p>Dynamic Programming algorithms</p>
<p>for std::assert for IO operations for unordered map</p>
<p>Dynamic Programming algorithms </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0a2215194e58786c34db1ccaf8031079" name="a0a2215194e58786c34db1ccaf8031079"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0a2215194e58786c34db1ccaf8031079">&#9670;&#160;</a></span>LIS()</h2>
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<td class="memname">uint64_t dynamic_programming::LIS </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint64_t &gt; &amp;&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const uint32_t &amp;&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
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<p>Calculate the longest increasing subsequence for the specified numbers. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>the array used to calculate the longest increasing subsequence </td></tr>
<tr><td class="paramname">n</td><td>the size used for the arrays </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the length of the longest increasing subsequence in the <code>a</code> array of size <code>n</code> </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 39</span> {</div>
<div class="line"><span class="lineno"> 40</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> lis(n);</div>
<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><span class="lineno"> 42</span> lis[i] = 1;</div>
<div class="line"><span class="lineno"> 43</span> }</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; i; ++j) {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">if</span> (a[i] &gt; a[j] &amp;&amp; lis[i] &lt; lis[j] + 1) {</div>
<div class="line"><span class="lineno"> 47</span> lis[i] = lis[j] + 1;</div>
<div class="line"><span class="lineno"> 48</span> }</div>
<div class="line"><span class="lineno"> 49</span> }</div>
<div class="line"><span class="lineno"> 50</span> }</div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordtype">int</span> res = 0;</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><span class="lineno"> 53</span> res = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(res, lis[i]);</div>
<div class="line"><span class="lineno"> 54</span> }</div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><span class="lineno"> 56</span>}</div>
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(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</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a5239174fa0d987f2c67edc1f2af82beb">&#9670;&#160;</a></span>maxCircularSum()</h2>
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<td class="memname">int dynamic_programming::maxCircularSum </td>
<td>(</td>
<td class="paramtype"><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>arr</em></td><td>)</td>
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<p>returns the maximum contiguous circular sum of an array </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">arr</td><td>is the array/vector </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>int which is the maximum sum </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 27</span>{</div>
<div class="line"><span class="lineno"> 28</span> <span class="comment">// Edge Case</span></div>
<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">if</span> (arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() == 1)</div>
<div class="line"><span class="lineno"> 30</span> <span class="keywordflow">return</span> arr[0];</div>
<div class="line"><span class="lineno"> 31</span> </div>
<div class="line"><span class="lineno"> 32</span> <span class="comment">// Sum variable which stores total sum of the array.</span></div>
<div class="line"><span class="lineno"> 33</span> <span class="keywordtype">int</span> sum = 0;</div>
<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
<div class="line"><span class="lineno"> 35</span> sum += arr[i];</div>
<div class="line"><span class="lineno"> 36</span> }</div>
<div class="line"><span class="lineno"> 37</span> </div>
<div class="line"><span class="lineno"> 38</span> <span class="comment">// Every variable stores first value of the array.</span></div>
<div class="line"><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"><span class="lineno"> 40</span> </div>
<div class="line"><span class="lineno"> 41</span> <span class="comment">// Concept of Kadane&#39;s Algorithm</span></div>
<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt; arr.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
<div class="line"><span class="lineno"> 43</span> <span class="comment">// Kadane&#39;s Algorithm to find Maximum subarray sum.</span></div>
<div class="line"><span class="lineno"> 44</span> current_max = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(current_max + arr[i], arr[i]);</div>
<div class="line"><span class="lineno"> 45</span> max_so_far = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(max_so_far, current_max);</div>
<div class="line"><span class="lineno"> 46</span> </div>
<div class="line"><span class="lineno"> 47</span> <span class="comment">// Kadane&#39;s Algorithm to find Minimum subarray sum.</span></div>
<div class="line"><span class="lineno"> 48</span> current_min = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(current_min + arr[i], arr[i]);</div>
<div class="line"><span class="lineno"> 49</span> min_so_far = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(min_so_far, current_min);</div>
<div class="line"><span class="lineno"> 50</span> }</div>
<div class="line"><span class="lineno"> 51</span> </div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">if</span> (min_so_far == sum)</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> max_so_far;</div>
<div class="line"><span class="lineno"> 54</span> </div>
<div class="line"><span class="lineno"> 55</span> <span class="comment">// Return the maximum value</span></div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(max_so_far, sum - min_so_far);</div>
<div class="line"><span class="lineno"> 57</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>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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