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<title>Algorithms_in_C++: machine_learning::aystar_search::AyStarSearch&lt; Puzzle &gt; Class Template Reference</title>
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@@ -141,10 +141,10 @@ using&#160;</td><td class="memItemRight" valign="bottom"><b>SetOfPuzzleInfo</b>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:abaff2ea6d309e1133fd95bbd1e39946e"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html#abaff2ea6d309e1133fd95bbd1e39946e">AyStarSearch</a> (const Puzzle &amp;initial, const Puzzle &amp;final)</td></tr>
<tr class="memdesc:abaff2ea6d309e1133fd95bbd1e39946e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Parameterized constructor for <a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html" title="A class defining A* search algorithm. for some initial state and final state.">AyStarSearch</a>. <a href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html#abaff2ea6d309e1133fd95bbd1e39946e">More...</a><br /></td></tr>
<tr class="memdesc:abaff2ea6d309e1133fd95bbd1e39946e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Parameterized constructor for <a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html" title="A class defining A* search algorithm. for some initial state and final state.">AyStarSearch</a>. <br /></td></tr>
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<tr class="memitem:a0a26aa9ad3d73707370d9fe83707aca4"><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; Puzzle &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html#a0a26aa9ad3d73707370d9fe83707aca4">Solution</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/memory/shared_ptr.html">std::shared_ptr</a>&lt; <a class="el" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html">Info</a> &gt; FinalState, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">MapOfPuzzleInfoWithPuzzleInfo</a> &amp;parent_of)</td></tr>
<tr class="memdesc:a0a26aa9ad3d73707370d9fe83707aca4"><td class="mdescLeft">&#160;</td><td class="mdescRight">A helper solution: launches when a solution for <a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html" title="A class defining A* search algorithm. for some initial state and final state.">AyStarSearch</a> is found. <a href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html#a0a26aa9ad3d73707370d9fe83707aca4">More...</a><br /></td></tr>
<tr class="memdesc:a0a26aa9ad3d73707370d9fe83707aca4"><td class="mdescLeft">&#160;</td><td class="mdescRight">A helper solution: launches when a solution for <a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html" title="A class defining A* search algorithm. for some initial state and final state.">AyStarSearch</a> is found. <br /></td></tr>
<tr class="separator:a0a26aa9ad3d73707370d9fe83707aca4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><div class="compoundTemplParams">template&lt;typename Puzzle&gt;<br />
class machine_learning::aystar_search::AyStarSearch&lt; Puzzle &gt;</div><p >A class defining <a href="https://en.wikipedia.org/wiki/A*_search_algorithm" target="_blank">A* search algorithm</a>. for some initial state and final state. </p>
<p ><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html" title="A class defining A* search algorithm. for some initial state and final state.">AyStarSearch</a> class is defined as the informed search algorithm that is formulated in terms of weighted graphs: starting from a specific starting node of a graph (initial state), it aims to find a path to the given goal node having the smallest cost (least distance travelled, shortest time, etc.) The weighted edges (or cost) is evaluated on two factors, G score (cost required from starting node or initial state to current state) and H score (cost required from current state to final state). The <code>F(state)</code>, then is evaluated as: <code>F(state) = G(state) + H(state)</code>. The best search would be the final state having minimum <code>F(state)</code> value </p><dl class="tparams"><dt>Template Parameters</dt><dd>
class machine_learning::aystar_search::AyStarSearch&lt; Puzzle &gt;</div><p>A class defining <a href="https://en.wikipedia.org/wiki/A*_search_algorithm" target="_blank">A* search algorithm</a>. for some initial state and final state. </p>
<p><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html" title="A class defining A* search algorithm. for some initial state and final state.">AyStarSearch</a> class is defined as the informed search algorithm that is formulated in terms of weighted graphs: starting from a specific starting node of a graph (initial state), it aims to find a path to the given goal node having the smallest cost (least distance travelled, shortest time, etc.) The weighted edges (or cost) is evaluated on two factors, G score (cost required from starting node or initial state to current state) and H score (cost required from current state to final state). The <code>F(state)</code>, then is evaluated as: <code>F(state) = G(state) + H(state)</code>. The best search would be the final state having minimum <code>F(state)</code> value </p><dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">Puzzle</td><td>denotes the puzzle or problem involving initial state and final state to be solved by A* search. </td></tr>
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</tr>
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<p >Main algorithm for finding <code>FinalState</code>, given the <code>InitialState</code> </p><dl class="params"><dt>Parameters</dt><dd>
<p>Main algorithm for finding <code>FinalState</code>, given the <code>InitialState</code> </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">dist</td><td>the heuristic finction, defined by the user </td></tr>
<tr><td class="paramname">permissible_depth</td><td>the depth at which the A* search discards searching for solution </td></tr>
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</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>List of moves from Final state to initial state, if evaluated, else returns an empty array </dd></dl>
<p >Stores the parent of the states</p>
<p >Stores the g_score</p>
<p >Stores the list to explore</p>
<p >Stores the list that are explored</p>
<p>Stores the parent of the states</p>
<p>Stores the g_score</p>
<p>Stores the list to explore</p>
<p>Stores the list that are explored</p>
<div class="fragment"><div class="line"><span class="lineno"> 431</span> {</div>
<div class="line"><span class="lineno"> 432</span> MapOfPuzzleInfoWithPuzzleInfo</div>
<div class="line"><span class="lineno"> 433</span> parent_of; <span class="comment">/// Stores the parent of the states</span></div>
@@ -463,7 +463,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></li><li class="navelem"><b>aystar_search</b></li><li class="navelem"><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html">AyStarSearch</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.5 </li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.6 </li>
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@@ -117,10 +117,10 @@ Collaboration diagram for operations_on_datastructures::circular_linked_list::No
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a005dc56b0c58350a13f4796b9b30b6c5"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a005dc56b0c58350a13f4796b9b30b6c5">Node</a> (int64_t _data)</td></tr>
<tr class="memdesc:a005dc56b0c58350a13f4796b9b30b6c5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Creates a new <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> with some initial data. <a href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a005dc56b0c58350a13f4796b9b30b6c5">More...</a><br /></td></tr>
<tr class="memdesc:a005dc56b0c58350a13f4796b9b30b6c5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Creates a new <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> with some initial data. <br /></td></tr>
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<tr class="memdesc:a12a06eef5ccaf667f319506eee655d95"><td class="mdescLeft">&#160;</td><td class="mdescRight">Creates a new <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> with initial data and a successor. <a href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a12a06eef5ccaf667f319506eee655d95">More...</a><br /></td></tr>
<tr class="memdesc:a12a06eef5ccaf667f319506eee655d95"><td class="mdescLeft">&#160;</td><td class="mdescRight">Creates a new <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> with initial data and a successor. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >A <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> struct that represents a single <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> in a Binary Tree. </p>
<div class="textblock"><p>A <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> struct that represents a single <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> in a Binary Tree. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a005dc56b0c58350a13f4796b9b30b6c5" name="a005dc56b0c58350a13f4796b9b30b6c5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a005dc56b0c58350a13f4796b9b30b6c5">&#9670;&#160;</a></span>Node() <span class="overload">[1/2]</span></h2>
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</table>
</dd>
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<p >&lt; Set value of <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> data</p>
<p >&lt; Initialize successor</p>
<p>&lt; Set value of <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> data</p>
<p>&lt; Initialize successor</p>
<div class="fragment"><div class="line"><span class="lineno"> 39</span> {</div>
<div class="line"><span class="lineno"> 40</span> <a class="code hl_variable" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a7461292b8b91aed86404d0ab019dfdd1">data</a> = _data; <span class="comment">///&lt; Set value of Node data</span></div>
<div class="line"><span class="lineno"> 41</span> <a class="code hl_variable" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a7c867b8e1034a6f5da490c8b8c09cb77">next</a> = <span class="keyword">nullptr</span>; <span class="comment">///&lt; Initialize successor</span></div>
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</table>
</dd>
</dl>
<p >&lt; Set value of <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> data</p>
<p >&lt; Initialize successor</p>
<p>&lt; Set value of <a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html" title="A Node struct that represents a single Node in a Binary Tree.">Node</a> data</p>
<p>&lt; Initialize successor</p>
<div class="fragment"><div class="line"><span class="lineno"> 48</span> {</div>
<div class="line"><span class="lineno"> 49</span> <a class="code hl_variable" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a7461292b8b91aed86404d0ab019dfdd1">data</a> = _data; <span class="comment">///&lt; Set value of Node data</span></div>
<div class="line"><span class="lineno"> 50</span> <a class="code hl_variable" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html#a7c867b8e1034a6f5da490c8b8c09cb77">next</a> = _next; <span class="comment">///&lt; Initialize successor</span></div>
@@ -239,7 +239,7 @@ int64_t&#160;</td><td class="memItemRight" valign="bottom"><b>data</b></td></tr>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../da/d6d/namespaceoperations__on__datastructures.html">operations_on_datastructures</a></li><li class="navelem"><b>circular_linked_list</b></li><li class="navelem"><a class="el" href="../../da/d16/structoperations__on__datastructures_1_1circular__linked__list_1_1_node.html">Node</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.5 </li>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:aa12088ba133dd0910103db0eb0ef2797"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aa12088ba133dd0910103db0eb0ef2797">geometric_distribution</a> (const float &amp;<a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>)</td></tr>
<tr class="memdesc:aa12088ba133dd0910103db0eb0ef2797"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor for the geometric distribution. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aa12088ba133dd0910103db0eb0ef2797">More...</a><br /></td></tr>
<tr class="memdesc:aa12088ba133dd0910103db0eb0ef2797"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor for the geometric distribution. <br /></td></tr>
<tr class="separator:aa12088ba133dd0910103db0eb0ef2797"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a41051365f8ac7700f2ed5880a6760413"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a41051365f8ac7700f2ed5880a6760413">expected_value</a> () const</td></tr>
<tr class="memdesc:a41051365f8ac7700f2ed5880a6760413"><td class="mdescLeft">&#160;</td><td class="mdescRight">The expected value of a geometrically distributed random variable X. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a41051365f8ac7700f2ed5880a6760413">More...</a><br /></td></tr>
<tr class="memdesc:a41051365f8ac7700f2ed5880a6760413"><td class="mdescLeft">&#160;</td><td class="mdescRight">The expected value of a geometrically distributed random variable X. <br /></td></tr>
<tr class="separator:a41051365f8ac7700f2ed5880a6760413"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aea8b0d649f0dc9a6f8baf3341a0b4960"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aea8b0d649f0dc9a6f8baf3341a0b4960">variance</a> () const</td></tr>
<tr class="memdesc:aea8b0d649f0dc9a6f8baf3341a0b4960"><td class="mdescLeft">&#160;</td><td class="mdescRight">The variance of a geometrically distributed random variable X. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aea8b0d649f0dc9a6f8baf3341a0b4960">More...</a><br /></td></tr>
<tr class="memdesc:aea8b0d649f0dc9a6f8baf3341a0b4960"><td class="mdescLeft">&#160;</td><td class="mdescRight">The variance of a geometrically distributed random variable X. <br /></td></tr>
<tr class="separator:aea8b0d649f0dc9a6f8baf3341a0b4960"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0a10c512e13dd3a052e1c6d7f4d6f0f2"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a0a10c512e13dd3a052e1c6d7f4d6f0f2">standard_deviation</a> () const</td></tr>
<tr class="memdesc:a0a10c512e13dd3a052e1c6d7f4d6f0f2"><td class="mdescLeft">&#160;</td><td class="mdescRight">The standard deviation of a geometrically distributed random variable X. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a0a10c512e13dd3a052e1c6d7f4d6f0f2">More...</a><br /></td></tr>
<tr class="memdesc:a0a10c512e13dd3a052e1c6d7f4d6f0f2"><td class="mdescLeft">&#160;</td><td class="mdescRight">The standard deviation of a geometrically distributed random variable X. <br /></td></tr>
<tr class="separator:a0a10c512e13dd3a052e1c6d7f4d6f0f2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aee973db9f0435e0cb4cc70f8eb3447a1"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aee973db9f0435e0cb4cc70f8eb3447a1">probability_density</a> (const uint32_t &amp;k) const</td></tr>
<tr class="memdesc:aee973db9f0435e0cb4cc70f8eb3447a1"><td class="mdescLeft">&#160;</td><td class="mdescRight">The probability density function. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aee973db9f0435e0cb4cc70f8eb3447a1">More...</a><br /></td></tr>
<tr class="memdesc:aee973db9f0435e0cb4cc70f8eb3447a1"><td class="mdescLeft">&#160;</td><td class="mdescRight">The probability density function. <br /></td></tr>
<tr class="separator:aee973db9f0435e0cb4cc70f8eb3447a1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a08328dc7d62188427111f176b56a105a"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a">cumulative_distribution</a> (const uint32_t &amp;k) const</td></tr>
<tr class="memdesc:a08328dc7d62188427111f176b56a105a"><td class="mdescLeft">&#160;</td><td class="mdescRight">The cumulative distribution function. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a">More...</a><br /></td></tr>
<tr class="memdesc:a08328dc7d62188427111f176b56a105a"><td class="mdescLeft">&#160;</td><td class="mdescRight">The cumulative distribution function. <br /></td></tr>
<tr class="separator:a08328dc7d62188427111f176b56a105a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aaf762e88c66918d7afda4234f28a7ddf"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aaf762e88c66918d7afda4234f28a7ddf">inverse_cumulative_distribution</a> (const float &amp;cdf) const</td></tr>
<tr class="memdesc:aaf762e88c66918d7afda4234f28a7ddf"><td class="mdescLeft">&#160;</td><td class="mdescRight">The inverse cumulative distribution function. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aaf762e88c66918d7afda4234f28a7ddf">More...</a><br /></td></tr>
<tr class="memdesc:aaf762e88c66918d7afda4234f28a7ddf"><td class="mdescLeft">&#160;</td><td class="mdescRight">The inverse cumulative distribution function. <br /></td></tr>
<tr class="separator:aaf762e88c66918d7afda4234f28a7ddf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8aae1cebcf42ed2332f1c7217c401aa3"><td class="memItemLeft" align="right" valign="top">uint32_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a8aae1cebcf42ed2332f1c7217c401aa3">draw_sample</a> () const</td></tr>
<tr class="memdesc:a8aae1cebcf42ed2332f1c7217c401aa3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generates a (discrete) sample according to the geometrical distribution. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a8aae1cebcf42ed2332f1c7217c401aa3">More...</a><br /></td></tr>
<tr class="memdesc:a8aae1cebcf42ed2332f1c7217c401aa3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Generates a (discrete) sample according to the geometrical distribution. <br /></td></tr>
<tr class="separator:a8aae1cebcf42ed2332f1c7217c401aa3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4620163a196709484225774d87de6d69"><td class="memItemLeft" align="right" valign="top">float&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a4620163a196709484225774d87de6d69">range_tries</a> (const uint32_t &amp;min_tries=1, const uint32_t &amp;max_tries=<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits</a>&lt; uint32_t &gt;::max()) const</td></tr>
<tr class="memdesc:a4620163a196709484225774d87de6d69"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function computes the probability to have success in a given range of tries. <a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a4620163a196709484225774d87de6d69">More...</a><br /></td></tr>
<tr class="memdesc:a4620163a196709484225774d87de6d69"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function computes the probability to have success in a given range of tries. <br /></td></tr>
<tr class="separator:a4620163a196709484225774d87de6d69"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pri-attribs" name="pri-attribs"></a>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >A class to model the geometric distribution. </p>
<div class="textblock"><p>A class to model the geometric distribution. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="aa12088ba133dd0910103db0eb0ef2797" name="aa12088ba133dd0910103db0eb0ef2797"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa12088ba133dd0910103db0eb0ef2797">&#9670;&#160;</a></span>geometric_distribution()</h2>
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</div><div class="memdoc">
<p>The cumulative distribution function. </p>
<p >The sum of all probabilities up to (and including) k trials. Basically CDF(k) = P(x &lt;= k) </p><dl class="params"><dt>Parameters</dt><dd>
<p>The sum of all probabilities up to (and including) k trials. Basically CDF(k) = P(x &lt;= k) </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>The number of trials in [1,\infty) </td></tr>
</table>
@@ -326,7 +326,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>The inverse cumulative distribution function. </p>
<p >This functions answers the question: Up to how many trials are needed to have success with a probability of cdf? The exact floating point value is reported. </p><dl class="params"><dt>Parameters</dt><dd>
<p>This functions answers the question: Up to how many trials are needed to have success with a probability of cdf? The exact floating point value is reported. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">cdf</td><td>The probability in [0,1] </td></tr>
</table>
@@ -371,7 +371,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>The probability density function. </p>
<p >As we use the first definition of the geometric series (1), we are doing k - 1 failed trials and the k-th trial is a success. </p><dl class="params"><dt>Parameters</dt><dd>
<p>As we use the first definition of the geometric series (1), we are doing k - 1 failed trials and the k-th trial is a success. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">k</td><td>The number of trials to observe the first success in [1,\infty) </td></tr>
</table>
@@ -425,7 +425,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>This function computes the probability to have success in a given range of tries. </p>
<p >Computes P(min_tries &lt;= x &lt;= max_tries). Can be used to calculate P(x &gt;= min_tries) by not passing a second argument. Can be used to calculate P(x &lt;= max_tries) by passing 1 as the first argument </p><dl class="params"><dt>Parameters</dt><dd>
<p>Computes P(min_tries &lt;= x &lt;= max_tries). Can be used to calculate P(x &gt;= min_tries) by not passing a second argument. Can be used to calculate P(x &lt;= max_tries) by passing 1 as the first argument </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">min_tries</td><td>The minimum number of tries in [1,\infty) (inclusive) </td></tr>
<tr><td class="paramname">max_tries</td><td>The maximum number of tries in [min_tries, \infty) (inclusive) </td></tr>
@@ -526,7 +526,7 @@ Here is the call graph for this function:</div>
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<li class="navelem"><a class="el" href="../../d4/ded/namespaceprobability.html">probability</a></li><li class="navelem"><b>geometric_dist</b></li><li class="navelem"><a class="el" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html">geometric_distribution</a></li>
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@@ -119,12 +119,12 @@ Functions</h2></td></tr>
<tr class="memitem:a35e4874a3e1d67eb708dc57944c8aea0"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d23/eulers__totient__function_8cpp.html#a35e4874a3e1d67eb708dc57944c8aea0">phiFunction</a> (uint64_t n)</td></tr>
<tr class="separator:a35e4874a3e1d67eb708dc57944c8aea0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d23/eulers__totient__function_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/d23/eulers__totient__function_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">More...</a><br /></td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <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 to find <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function" target="_blank">Euler's Totient</a> function. </p>
<p >Euler Totient Function is also known as phi function. </p><p class="formulaDsp">
<div class="textblock"><p>C++ Program to find <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function" target="_blank">Euler's Totient</a> function. </p>
<p>Euler Totient Function is also known as phi function. </p><p class="formulaDsp">
\[\phi(n) =
\phi\left({p_1}^{a_1}\right)\cdot\phi\left({p_2}^{a_2}\right)\ldots\]
</p>
@@ -134,7 +134,7 @@ Functions</h2></td></tr>
<li>\(\phi(n^k) = n^k - n^{k-1}\)</li>
<li>\(\phi(a,b) = \phi(a)\cdot\phi(b)\) where a and b are relative primes.</li>
</ol>
<p >Applying this 3 properties on the first equation. </p><p class="formulaDsp">
<p>Applying this 3 properties on the first equation. </p><p class="formulaDsp">
\[\phi(n) =
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<p >Function to caculate Euler's totient phi </p>
<p>Function to caculate Euler's totient phi </p>
<div class="fragment"><div class="line"><span class="lineno"> 32</span> {</div>
<div class="line"><span class="lineno"> 33</span> uint64_t <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = n;</div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Calculate the square root of any positive real number in \(O(\log
<div class="textblock"><p>Calculate the square root of any positive real number in \(O(\log
N)\) time, with precision fixed using <a href="https://en.wikipedia.org/wiki/Bisection_method" target="_blank">bisection method</a> of root-finding. </p>
<dl class="section see"><dt>See also</dt><dd>Can be implemented using faster and better algorithms like <a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html" title="Solve the equation using Newton-Raphson method for both real and complex solutions.">newton_raphson_method.cpp</a> and <a class="el" href="../../dd/d29/false__position_8cpp.html" title="Solve the equation using false position method, also known as the Secant method.">false_position.cpp</a> </dd></dl>
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<p >main function </p>
<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {</div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordtype">double</span> n{};</div>
<div class="line"><span class="lineno"> 44</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
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<p >Bisection method implemented for the function \(x^2-a=0\) whose roots are \(\pm\sqrt{a}\) and only the positive root is returned. </p>
<p>Bisection method implemented for the function \(x^2-a=0\) whose roots are \(\pm\sqrt{a}\) and only the positive root is returned. </p>
<div class="fragment"><div class="line"><span class="lineno"> 16</span> {</div>
<div class="line"><span class="lineno"> 17</span> <span class="keywordflow">if</span> (a &gt; 0 &amp;&amp; a &lt; 1) {</div>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a0c8cbe7239232863f104793c08273039"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a0c8cbe7239232863f104793c08273039">query</a> (int64_t l, int64_t r)</td></tr>
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</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the computed value of the given interval. @complexity: O(1) </dd></dl>
<p >&lt; smallest power of 2 covering [l,r]</p>
<p >&lt; represents minimum value over the range [g,l]</p>
<p >&lt; represents minimum value over the range [g, r - pow(2,g) + 1]</p>
<p >&lt; represents minimum value over the whole range [l,r]</p>
<p>&lt; smallest power of 2 covering [l,r]</p>
<p>&lt; represents minimum value over the range [g,l]</p>
<p>&lt; represents minimum value over the range [g, r - pow(2,g) + 1]</p>
<p>&lt; represents minimum value over the whole range [l,r]</p>
<div class="fragment"><div class="line"><span class="lineno"> 109</span> {</div>
<div class="line"><span class="lineno"> 110</span> int64_t <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">g</a> = <a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a6cf72f93b1551f0d943c585b4f173be3">LOG</a>[r - <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">l</a> + 1]; <span class="comment">///&lt; smallest power of 2 covering [l,r]</span></div>
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<tr class="memitem:a3fe35440c27758ecc2287e08217d63a7"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a3fe35440c27758ecc2287e08217d63a7">math::cone_volume</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, double PI=3.14)</td></tr>
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<tr class="memdesc:a3fe35440c27758ecc2287e08217d63a7"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cone" target="_blank">cone</a> <br /></td></tr>
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<tr class="memdesc:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Triangular_prism" target="_blank">triangular</a> prism. <a href="../../dd/d47/namespacemath.html#a2d704a7b72a6b2db8b76c8581b577b2c">More...</a><br /></td></tr>
<tr class="memdesc:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Triangular_prism" target="_blank">triangular</a> prism. <br /></td></tr>
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<tr class="memitem:a94db02b3c9e55a69ac1696f30e2f761c"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a94db02b3c9e55a69ac1696f30e2f761c">math::pyramid_volume</a> (T length, T width, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:a94db02b3c9e55a69ac1696f30e2f761c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Pyramid_(geometry)" target="_blank">pyramid</a> <a href="../../dd/d47/namespacemath.html#a94db02b3c9e55a69ac1696f30e2f761c">More...</a><br /></td></tr>
<tr class="memdesc:a94db02b3c9e55a69ac1696f30e2f761c"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Pyramid_(geometry)" target="_blank">pyramid</a> <br /></td></tr>
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<tr class="memitem:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a34d66a77c19ce9b8b3a3d14352b34551">math::sphere_volume</a> (T radius, double PI=3.14)</td></tr>
<tr class="memdesc:a34d66a77c19ce9b8b3a3d14352b34551"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> <a href="../../dd/d47/namespacemath.html#a34d66a77c19ce9b8b3a3d14352b34551">More...</a><br /></td></tr>
<tr class="memdesc:a34d66a77c19ce9b8b3a3d14352b34551"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> <br /></td></tr>
<tr class="separator:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abde24398be43538c62e4a496968e60ca"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:abde24398be43538c62e4a496968e60ca"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abde24398be43538c62e4a496968e60ca">math::cylinder_volume</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, double PI=3.14)</td></tr>
<tr class="memdesc:abde24398be43538c62e4a496968e60ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> <a href="../../dd/d47/namespacemath.html#abde24398be43538c62e4a496968e60ca">More...</a><br /></td></tr>
<tr class="memdesc:abde24398be43538c62e4a496968e60ca"><td class="mdescLeft">&#160;</td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> <br /></td></tr>
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../da/d39/volume_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <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="../../da/d39/volume_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/d39/volume_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implmentations for the <a href="https://en.wikipedia.org/wiki/Volume" target="_blank">volume</a> of various 3D shapes. </p>
<p >The volume of a 3D shape is the amount of 3D space that the shape takes up. All shapes have a formula to get the volume of any given shape. These implementations support multiple return types.</p>
<div class="textblock"><p>Implmentations for the <a href="https://en.wikipedia.org/wiki/Volume" target="_blank">volume</a> of various 3D shapes. </p>
<p>The volume of a 3D shape is the amount of 3D space that the shape takes up. All shapes have a formula to get the volume of any given shape. These implementations support multiple return types.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Focusucof" target="_blank">Focusucof</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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@@ -138,13 +138,13 @@ Classes</h2></td></tr>
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Macros</h2></td></tr>
<tr class="memitem:acce684d03a24f9c13a9ed36de6d24a57"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d41/uint128__t_8hpp.html#acce684d03a24f9c13a9ed36de6d24a57">CIPHERS_UINT128_T_HPP_</a></td></tr>
<tr class="memdesc:acce684d03a24f9c13a9ed36de6d24a57"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></code> library <a href="../../da/d41/uint128__t_8hpp.html#acce684d03a24f9c13a9ed36de6d24a57">More...</a><br /></td></tr>
<tr class="memdesc:acce684d03a24f9c13a9ed36de6d24a57"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></code> library <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a3ff77262ffd6743df5b808d41382a6f3"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d41/uint128__t_8hpp.html#a3ff77262ffd6743df5b808d41382a6f3">add</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;first, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;second)</td></tr>
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<tr class="memdesc:a3ff77262ffd6743df5b808d41382a6f3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adding two string. <br /></td></tr>
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<tr class="memitem:aaaf018bfb929bea8e60320cfad566a04"><td class="memTemplParams" colspan="2">template&lt;typename T , typename = typename std::enable_if&lt; std::is_integral&lt;T&gt;::value, T&gt;::type&gt; </td></tr>
<tr class="memitem:aaaf018bfb929bea8e60320cfad566a04"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../db/d9a/classuint128__t.html">uint128_t</a>&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/d41/uint128__t_8hpp.html#aaaf018bfb929bea8e60320cfad566a04">operator+</a> (const T &amp;p, const <a class="el" href="../../db/d9a/classuint128__t.html">uint128_t</a> &amp;q)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of 128-bit unsigned integers. </p><dl class="section note"><dt>Note</dt><dd>The implementation can be flagged as not completed. This header is used with enough operations as a part of bigger integer types 256-bit integer. </dd></dl>
<div class="textblock"><p>Implementation of 128-bit unsigned integers. </p><dl class="section note"><dt>Note</dt><dd>The implementation can be flagged as not completed. This header is used with enough operations as a part of bigger integer types 256-bit integer. </dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AshishYUO" target="_blank">Ashish Daulatabad</a> </dd></dl>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<p>Adding two string. </p>
<p >Adds two long integer, only used for printing numbers </p><dl class="params"><dt>Parameters</dt><dd>
<p>Adds two long integer, only used for printing numbers </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">first</td><td>First integer string </td></tr>
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@@ -131,15 +131,15 @@ Namespaces</h2></td></tr>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:aadebe9c855821d6515ca5b171222ef7b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">graph::depth_first_search::addEdge</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt; &gt; *adj, size_t u, size_t v)</td></tr>
<tr class="memdesc:aadebe9c855821d6515ca5b171222ef7b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds and edge between two vertices of graph say u and v in this case. <a href="../../da/d4b/depth__first__search__with__stack_8cpp.html#aadebe9c855821d6515ca5b171222ef7b">More...</a><br /></td></tr>
<tr class="memdesc:aadebe9c855821d6515ca5b171222ef7b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds and edge between two vertices of graph say u and v in this case. <br /></td></tr>
<tr class="separator:aadebe9c855821d6515ca5b171222ef7b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5738da9f508f6a9e87f123c9fb6f2ea9"><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; size_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a5738da9f508f6a9e87f123c9fb6f2ea9">graph::depth_first_search::dfs</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt; &gt; &amp;graph, size_t start)</td></tr>
<tr class="memdesc:a5738da9f508f6a9e87f123c9fb6f2ea9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Explores the given vertex, exploring a vertex means traversing over all the vertices which are connected to the vertex that is currently being explored and push it onto the stack. <a href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a5738da9f508f6a9e87f123c9fb6f2ea9">More...</a><br /></td></tr>
<tr class="memdesc:a5738da9f508f6a9e87f123c9fb6f2ea9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Explores the given vertex, exploring a vertex means traversing over all the vertices which are connected to the vertex that is currently being explored and push it onto the stack. <br /></td></tr>
<tr class="separator:a5738da9f508f6a9e87f123c9fb6f2ea9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="separator:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/d4b/depth__first__search__with__stack_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
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<tr class="separator:a330a2b0a904f01802ada1f8f3b28e76c"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Depth-first_search" target="_blank">Depth First Search Algorithm using Stack (Depth First Search Algorithm)</a> </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Depth-first_search" target="_blank">Depth First Search Algorithm using Stack (Depth First Search Algorithm)</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="http://github.com/ayaankhan98" target="_blank">Ayaan Khan</a> </dd>
<dd>
<a href="https://github.com/sauravUppoor" target="_blank">Saurav Uppoor</a></dd></dl>
<p>Depth First Search also quoted as DFS is a <a class="el" href="../../da/d9a/class_graph.html">Graph</a> Traversal Algorithm. Time Complexity O(|V| + |E|) where V is number of vertices and E is number of edges in graph.</p>
<p >Application of Depth First Search are</p>
<p>Application of Depth First Search are</p>
<ol type="1">
<li>Finding connected components</li>
<li>Finding 2-(edge or vertex)-connected components.</li>
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</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>vector with nodes stored in the order of DFS traversal </dd></dl>
<p >checked[i] stores the status of each node</p>
<p >while stack is not empty we keep exploring the node on top of stack</p>
<p >push the node to the final result vector</p>
<p >exploring the neighbours of the current node</p>
<p ><a class="el" href="../../db/d8b/struct_node.html">Node</a> has been explored</p>
<p>checked[i] stores the status of each node</p>
<p>while stack is not empty we keep exploring the node on top of stack</p>
<p>push the node to the final result vector</p>
<p>exploring the neighbours of the current node</p>
<p><a class="el" href="../../db/d8b/struct_node.html">Node</a> has been explored</p>
<div class="fragment"><div class="line"><span class="lineno"> 87</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 88</span><span class="comment"> /// checked[i] stores the status of each node</span></div>
<div class="line"><span class="lineno"> 89</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;size_t&gt;</a> checked(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.size(), <a class="code hl_variable" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#afb80b42b42381658a12a57a975ecd0c7">WHITE</a>), traversed_path;</div>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p >creating a graph</p>
<p >taking input for the edges</p>
<p >taking input for the starting position</p>
<p >Printing the order of traversal</p>
<p>creating a graph</p>
<p>taking input for the edges</p>
<p>taking input for the starting position</p>
<p>Printing the order of traversal</p>
<div class="fragment"><div class="line"><span class="lineno"> 173</span> {</div>
<div class="line"><span class="lineno"> 174</span> <a class="code hl_function" href="../../da/d4b/depth__first__search__with__stack_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><span class="lineno"> 175</span> </div>
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<p >Self-test implementations </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
<p >Test 1</p>
<p >for the above sample data, this is the expected output</p>
<p >Test 2</p>
<p >for the above sample data, this is the expected output</p>
<p >Test 3</p>
<p >for the above sample data, this is the expected output</p>
<p>Self-test implementations </p><dl class="section return"><dt>Returns</dt><dd>none </dd></dl>
<p>Test 1</p>
<p>for the above sample data, this is the expected output</p>
<p>Test 2</p>
<p>for the above sample data, this is the expected output</p>
<p>Test 3</p>
<p>for the above sample data, this is the expected output</p>
<div class="fragment"><div class="line"><span class="lineno"> 123</span> {</div>
<div class="line"><span class="lineno"> 124</span> <span class="keywordtype">size_t</span> start_pos;</div>
<div class="line"><span class="lineno"> 125</span><span class="comment"></span> </div>
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<p >for IO operations header for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a> header for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> header for preprocessor macro assert() header for limits of integral types </p>
<p>for IO operations header for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/stack.html">std::stack</a> header for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> header for preprocessor macro assert() header for limits of integral types </p>
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@@ -127,19 +127,19 @@ Namespaces</h2></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a0d5e1d651d0d30bd682f176d8f2b83d0"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">bit_manipulation::count_of_trailing_ciphers_in_factorial_n::numberOfCiphersInFactorialN</a> (uint64_t n)</td></tr>
<tr class="memdesc:a0d5e1d651d0d30bd682f176d8f2b83d0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to count the number of the trailing ciphers. <a href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">More...</a><br /></td></tr>
<tr class="memdesc:a0d5e1d651d0d30bd682f176d8f2b83d0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to count the number of the trailing ciphers. <br /></td></tr>
<tr class="separator:a0d5e1d651d0d30bd682f176d8f2b83d0"><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="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <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="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><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 ><a href="https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus" target="_blank">Count the number of ciphers</a> in <code>n!</code> implementation </p>
<p >Given an integer number as input. The goal is to find the number of trailing zeroes in the factorial calculated for that number. A factorial of a number N is a product of all numbers in the range [1, N].</p>
<p >We know that we get a trailing zero only if the number is multiple of 10 or has a factor pair (2,5). In all factorials of any number greater than 5, we have many 2s more than 5s in the prime factorization of that number. Dividing a number by powers of 5 will give us the count of 5s in its factors. So, the number of 5s will tell us the number of trailing zeroes. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd></dl>
<div class="textblock"><p><a href="https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus" target="_blank">Count the number of ciphers</a> in <code>n!</code> implementation </p>
<p>Given an integer number as input. The goal is to find the number of trailing zeroes in the factorial calculated for that number. A factorial of a number N is a product of all numbers in the range [1, N].</p>
<p>We know that we get a trailing zero only if the number is multiple of 10 or has a factor pair (2,5). In all factorials of any number greater than 5, we have many 2s more than 5s in the prime factorization of that number. Dividing a number by powers of 5 will give us the count of 5s in its factors. So, the number of 5s will tell us the number of trailing zeroes. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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@@ -128,24 +128,24 @@ Namespaces</h2></td></tr>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a0138c226bd79ffe6d839c787cfc60347"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347">dynamic_programming::minimum_edit_distance::min</a> (uint64_t x, uint64_t y, uint64_t z)</td></tr>
<tr class="memdesc:a0138c226bd79ffe6d839c787cfc60347"><td class="mdescLeft">&#160;</td><td class="mdescRight">Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost among them. <a href="../../da/d52/minimum__edit__distance_8cpp.html#a0138c226bd79ffe6d839c787cfc60347">More...</a><br /></td></tr>
<tr class="memdesc:a0138c226bd79ffe6d839c787cfc60347"><td class="mdescLeft">&#160;</td><td class="mdescRight">Takes input of the cost of three operations: Insert, Replace and Delete and return the minimum cost among them. <br /></td></tr>
<tr class="separator:a0138c226bd79ffe6d839c787cfc60347"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ade2fcfe0359f3c7691bfaa04b14943e2"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#ade2fcfe0359f3c7691bfaa04b14943e2">dynamic_programming::minimum_edit_distance::editDistDP</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str1, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str2, uint64_t m, uint64_t n)</td></tr>
<tr class="memdesc:ade2fcfe0359f3c7691bfaa04b14943e2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates and stores the result of all the sub-problems, so that we don't have to recur to compute the minimum cost of a particular operation if it is already computed and stored in the <code>dp</code> vector. <a href="../../da/d52/minimum__edit__distance_8cpp.html#ade2fcfe0359f3c7691bfaa04b14943e2">More...</a><br /></td></tr>
<tr class="memdesc:ade2fcfe0359f3c7691bfaa04b14943e2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculates and stores the result of all the sub-problems, so that we don't have to recur to compute the minimum cost of a particular operation if it is already computed and stored in the <code>dp</code> vector. <br /></td></tr>
<tr class="separator:ade2fcfe0359f3c7691bfaa04b14943e2"><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="../../da/d52/minimum__edit__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../da/d52/minimum__edit__distance_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d52/minimum__edit__distance_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">main function <a href="../../da/d52/minimum__edit__distance_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">More...</a><br /></td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">main function <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Edit_distance" target="_blank">Minimum Edit Distance</a> using Dynamic Programing. </p>
<p >Given two strings str1 &amp; str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.</p>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Edit_distance" target="_blank">Minimum Edit Distance</a> using Dynamic Programing. </p>
<p>Given two strings str1 &amp; str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.</p>
<h3><a class="anchor" id="autotoc_md73"></a>
Algorithm</h3>
<p >We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.</p><ol type="1">
<p>We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.</p><ol type="1">
<li>If the last characters of two strings are the same, Ignore the characters and get the count for the remaining string. So, we get the solution for lengths m-1 and n-1 in a DP array.</li>
<li>Else, (If last characters are not the same), we will consider all three operations (Insert, Remove, Replace) on the last character of the first string and compute the minimum cost for all three operations and take the minimum of three values in the DP array. For Insert: Recur for m and n-1 For Remove: Recur for for m-1 and n For Replace: Recur for for m-1 and n-1</li>
</ol>
@@ -201,16 +201,16 @@ Algorithm</h3>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>dp[m][n] the minimum cost of operations needed to convert str1 to str2 </dd></dl>
<p >Create a table to store results of subproblems</p>
<p >creasting 2D vector dp to store the results of subproblems</p>
<p >Fill d[][] in bottom up manner</p>
<p >If first string is empty, only option is to insert all characters of second string</p>
<p ><a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> operations = j</p>
<p >If second string is empty, only option is to remove all characters of second string</p>
<p ><a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> operations = i</p>
<p >If last characters are same, ignore last char and recur for remaining string</p>
<p >If the last character is different, consider all possibilities and find the minimum</p>
<p >returning the minimum cost of operations needed to convert str1 to str2</p>
<p>Create a table to store results of subproblems</p>
<p>creasting 2D vector dp to store the results of subproblems</p>
<p>Fill d[][] in bottom up manner</p>
<p>If first string is empty, only option is to insert all characters of second string</p>
<p><a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> operations = j</p>
<p>If second string is empty, only option is to remove all characters of second string</p>
<p><a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> operations = i</p>
<p>If last characters are same, ignore last char and recur for remaining string</p>
<p>If the last character is different, consider all possibilities and find the minimum</p>
<p>returning the minimum cost of operations needed to convert str1 to str2</p>
<div class="fragment"><div class="line"><span class="lineno"> 88</span> {<span class="comment"></span></div>
<div class="line"><span class="lineno"> 89</span><span class="comment"> /// Create a table to store results of subproblems</span></div>
<div class="line"><span class="lineno"> 90</span><span class="comment"></span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;uint64_t&gt;</a>&gt;<a class="code hl_namespace" href="../../df/d88/namespacedp.html">dp</a>(m+1, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a>(n+1)); <span class="comment">/// creasting 2D vector dp to store the results of subproblems</span></div>
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y if <code>y</code> is the minimum value </dd>
<dd>
z if <code>z</code> is the minimum value </dd></dl>
<p >returns x, if x is the minimum value</p>
<p >returns y, if y is the minimum value</p>
<p >returns z if z is the minimum value</p>
<p>returns x, if x is the minimum value</p>
<p>returns y, if y is the minimum value</p>
<p>returns z if z is the minimum value</p>
<div class="fragment"><div class="line"><span class="lineno"> 63</span> {</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">if</span> (x &lt;= y &amp;&amp; x &lt;= z) {</div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">return</span> x; <span class="comment">/// returns x, if x is the minimum value</span></div>
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<tr class="memdesc:a3cfc522c782726f49ee20af17b77f867"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> Constructor which initialises our complex number. <br /></td></tr>
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<tr class="memdesc:af8aacf982e2e6c142921bc850f6dc974"><td class="mdescLeft">&#160;</td><td class="mdescRight">Member function to get imaginary value of our complex number. Member function (getter) to access the class' im value. <br /></td></tr>
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<tr class="memdesc:ae5b51b749ea4964104b9527af9d8f556"><td class="mdescLeft">&#160;</td><td class="mdescRight">Member function to give the modulus of our complex number. Member function to which gives the absolute value (modulus) of our complex number. <br /></td></tr>
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<tr class="memdesc:ae1e03712837450549e0c9b4017533a41"><td class="mdescLeft">&#160;</td><td class="mdescRight">Member function to give the argument of our complex number. <br /></td></tr>
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<tr class="memitem:a820afcbb330df716577459d7a3aa3a1c"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../da/d5a/class_complex.html">Complex</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d5a/class_complex.html#a820afcbb330df716577459d7a3aa3a1c">operator+</a> (const <a class="el" href="../../da/d5a/class_complex.html">Complex</a> &amp;other)</td></tr>
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<tr class="memdesc:a820afcbb330df716577459d7a3aa3a1c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '+' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to add two complex numbers. <br /></td></tr>
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<tr class="memitem:a36739619a07b5478bcd8a28ad2f8b7da"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../da/d5a/class_complex.html">Complex</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d5a/class_complex.html#a36739619a07b5478bcd8a28ad2f8b7da">operator-</a> (const <a class="el" href="../../da/d5a/class_complex.html">Complex</a> &amp;other)</td></tr>
<tr class="memdesc:a36739619a07b5478bcd8a28ad2f8b7da"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '-' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to subtract two complex numbers. <a href="../../da/d5a/class_complex.html#a36739619a07b5478bcd8a28ad2f8b7da">More...</a><br /></td></tr>
<tr class="memdesc:a36739619a07b5478bcd8a28ad2f8b7da"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '-' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to subtract two complex numbers. <br /></td></tr>
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<tr class="memdesc:aa9b4a7d6083ca7040ddd4fe93db5c19d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '*' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to multiple two complex numbers. <a href="../../da/d5a/class_complex.html#aa9b4a7d6083ca7040ddd4fe93db5c19d">More...</a><br /></td></tr>
<tr class="memdesc:aa9b4a7d6083ca7040ddd4fe93db5c19d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '*' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to multiple two complex numbers. <br /></td></tr>
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<tr class="memdesc:a8d5427f6c42c15283031d73e1418c59d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '~' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload of the BITWISE NOT which gives us the conjugate of our complex number. NOTE: This is overloading the BITWISE operator but its not a BITWISE operation in this definition. <a href="../../da/d5a/class_complex.html#a8d5427f6c42c15283031d73e1418c59d">More...</a><br /></td></tr>
<tr class="memdesc:a8d5427f6c42c15283031d73e1418c59d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '~' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload of the BITWISE NOT which gives us the conjugate of our complex number. NOTE: This is overloading the BITWISE operator but its not a BITWISE operation in this definition. <br /></td></tr>
<tr class="separator:a8d5427f6c42c15283031d73e1418c59d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac38437c10eb798f176c384a695171b90"><td class="memItemLeft" align="right" valign="top"><a class="el" href="../../da/d5a/class_complex.html">Complex</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d5a/class_complex.html#ac38437c10eb798f176c384a695171b90">operator/</a> (const <a class="el" href="../../da/d5a/class_complex.html">Complex</a> &amp;other)</td></tr>
<tr class="memdesc:ac38437c10eb798f176c384a695171b90"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '/' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to divide two complex numbers. This function would throw an exception if the other number is zero. <a href="../../da/d5a/class_complex.html#ac38437c10eb798f176c384a695171b90">More...</a><br /></td></tr>
<tr class="memdesc:ac38437c10eb798f176c384a695171b90"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '/' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to divide two complex numbers. This function would throw an exception if the other number is zero. <br /></td></tr>
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<tr class="memitem:a4ac9f529d54cacf2969f2c7179b4c4ac"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="../../da/d5a/class_complex.html">Complex</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d5a/class_complex.html#a4ac9f529d54cacf2969f2c7179b4c4ac">operator=</a> (const <a class="el" href="../../da/d5a/class_complex.html">Complex</a> &amp;other)</td></tr>
<tr class="memdesc:a4ac9f529d54cacf2969f2c7179b4c4ac"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '=' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to copy RHS instance of <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> to LHS instance of <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a>. <a href="../../da/d5a/class_complex.html#a4ac9f529d54cacf2969f2c7179b4c4ac">More...</a><br /></td></tr>
<tr class="memdesc:a4ac9f529d54cacf2969f2c7179b4c4ac"><td class="mdescLeft">&#160;</td><td class="mdescRight">Operator overload of '=' on <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> class. Operator overload to be able to copy RHS instance of <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> to LHS instance of <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a>. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Class <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> to represent complex numbers as a field. </p>
<div class="textblock"><p>Class <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> to represent complex numbers as a field. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="a3cfc522c782726f49ee20af17b77f867" name="a3cfc522c782726f49ee20af17b77f867"></a>
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<p><a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> Constructor which initialises our complex number. </p>
<p ><a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> Constructor which initialises the complex number which takes three arguments. </p><dl class="params"><dt>Parameters</dt><dd>
<p><a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> Constructor which initialises the complex number which takes three arguments. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>If the third parameter is 'true' then this x is the absolute value of the complex number, if the third parameter is 'false' then this x is the real value of the complex number (optional). </td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >A <a class="el" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html" title="A Node structure representing a single link Node in a linked list.">Node</a> structure representing a single link <a class="el" href="../../da/d61/structsearch_1_1sublist__search_1_1_node.html" title="A Node structure representing a single link Node in a linked list.">Node</a> in a linked list. </p>
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Functions</h2></td></tr>
<tr class="memitem:a6109193567a5b7e36a27f2b4865fce20"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d6d/namespaceoperations__on__datastructures.html#a6109193567a5b7e36a27f2b4865fce20">print</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;array)</td></tr>
<tr class="memdesc:a6109193567a5b7e36a27f2b4865fce20"><td class="mdescLeft">&#160;</td><td class="mdescRight">Prints the values of a vector sequentially, ending with a newline character. <a href="../../da/d6d/namespaceoperations__on__datastructures.html#a6109193567a5b7e36a27f2b4865fce20">More...</a><br /></td></tr>
<tr class="memdesc:a6109193567a5b7e36a27f2b4865fce20"><td class="mdescLeft">&#160;</td><td class="mdescRight">Prints the values of a vector sequentially, ending with a newline character. <br /></td></tr>
<tr class="separator:a6109193567a5b7e36a27f2b4865fce20"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afce39cf843989a39811a49ebe29dd6d8"><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; int32_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">shift_left</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;array, size_t shift)</td></tr>
<tr class="memdesc:afce39cf843989a39811a49ebe29dd6d8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shifts the given vector to the left by the shift amount and returns a new vector with the result. The original vector is not mutated. <a href="../../da/d6d/namespaceoperations__on__datastructures.html#afce39cf843989a39811a49ebe29dd6d8">More...</a><br /></td></tr>
<tr class="memdesc:afce39cf843989a39811a49ebe29dd6d8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shifts the given vector to the left by the shift amount and returns a new vector with the result. The original vector is not mutated. <br /></td></tr>
<tr class="separator:afce39cf843989a39811a49ebe29dd6d8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1bfb8711f49e591eb168ccaa3df6fb86"><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; int32_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d6d/namespaceoperations__on__datastructures.html#a1bfb8711f49e591eb168ccaa3df6fb86">shift_right</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;array, size_t shift)</td></tr>
<tr class="memdesc:a1bfb8711f49e591eb168ccaa3df6fb86"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shifts the given vector to the right by the shift amount and returns a new vector with the result. The original vector is not mutated. <a href="../../da/d6d/namespaceoperations__on__datastructures.html#a1bfb8711f49e591eb168ccaa3df6fb86">More...</a><br /></td></tr>
<tr class="memdesc:a1bfb8711f49e591eb168ccaa3df6fb86"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shifts the given vector to the right by the shift amount and returns a new vector with the result. The original vector is not mutated. <br /></td></tr>
<tr class="separator:a1bfb8711f49e591eb168ccaa3df6fb86"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:adaf9a06f0c236c2d95c97e441ea2d12e"><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; int32_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d6d/namespaceoperations__on__datastructures.html#adaf9a06f0c236c2d95c97e441ea2d12e">get_intersection</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;first, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;second)</td></tr>
<tr class="memdesc:adaf9a06f0c236c2d95c97e441ea2d12e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Gets the intersection of two sorted arrays, and returns them in a vector. <a href="../../da/d6d/namespaceoperations__on__datastructures.html#adaf9a06f0c236c2d95c97e441ea2d12e">More...</a><br /></td></tr>
<tr class="memdesc:adaf9a06f0c236c2d95c97e441ea2d12e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Gets the intersection of two sorted arrays, and returns them in a vector. <br /></td></tr>
<tr class="separator:adaf9a06f0c236c2d95c97e441ea2d12e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2b8ff06a84b041457873840bf82e2d74"><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; int32_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d6d/namespaceoperations__on__datastructures.html#a2b8ff06a84b041457873840bf82e2d74">get_union</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;first, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int32_t &gt; &amp;second)</td></tr>
<tr class="memdesc:a2b8ff06a84b041457873840bf82e2d74"><td class="mdescLeft">&#160;</td><td class="mdescRight">Gets the union of two sorted arrays, and returns them in a vector. <a href="../../da/d6d/namespaceoperations__on__datastructures.html#a2b8ff06a84b041457873840bf82e2d74">More...</a><br /></td></tr>
<tr class="memdesc:a2b8ff06a84b041457873840bf82e2d74"><td class="mdescLeft">&#160;</td><td class="mdescRight">Gets the union of two sorted arrays, and returns them in a vector. <br /></td></tr>
<tr class="separator:a2b8ff06a84b041457873840bf82e2d74"><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 >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue</a></p>
<p >For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>.</p>
<p >for assert for IO operations</p>
<p >Operations on Data Structures</p>
<p >for assert for IO Operations</p>
<p >Operations on data structures</p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a> for assert for IO operations</p>
<p >Operations on Data Structures</p>
<p >For assert For IO operations For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></p>
<p >Operations on Data Structures</p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/count.html">std::count</a> for assert for tolower for string operations for IO Operations</p>
<p >Operations on data structures </p>
<div class="textblock"><p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/priority_queue.html">std::priority_queue</a></p>
<p>For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>.</p>
<p>for assert for IO operations</p>
<p>Operations on Data Structures</p>
<p>for assert for IO Operations</p>
<p>Operations on data structures</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/sort.html">std::sort</a> for assert for IO operations</p>
<p>Operations on Data Structures</p>
<p>For assert For IO operations For <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/queue.html">std::queue</a></p>
<p>Operations on Data Structures</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/count.html">std::count</a> for assert for tolower for string operations for IO Operations</p>
<p>Operations on data structures </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="adaf9a06f0c236c2d95c97e441ea2d12e" name="adaf9a06f0c236c2d95c97e441ea2d12e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#adaf9a06f0c236c2d95c97e441ea2d12e">&#9670;&#160;</a></span>get_intersection()</h2>
@@ -166,7 +166,7 @@ Functions</h2></td></tr>
</div><div class="memdoc">
<p>Gets the intersection of two sorted arrays, and returns them in a vector. </p>
<p >An algorithm is used that compares the elements of the two vectors, incrementing the index of the smaller of the two. If the elements are the same, the element is appended to the result array to be returned. </p><dl class="params"><dt>Parameters</dt><dd>
<p>An algorithm is used that compares the elements of the two vectors, incrementing the index of the smaller of the two. If the elements are the same, the element is appended to the result array to be returned. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">first</td><td>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of sorted integer values </td></tr>
<tr><td class="paramname">second</td><td>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of sorted integer values </td></tr>
@@ -174,16 +174,16 @@ Functions</h2></td></tr>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of the intersection of the two arrays, in ascending order </dd></dl>
<p >&lt; Vector to hold the intersection</p>
<p >&lt; Index for the first array</p>
<p >&lt; Index for the second array</p>
<p >&lt; Length of first array</p>
<p >&lt; Length of second array</p>
<p >&lt; Increment index of second array</p>
<p >&lt; Increment index of second array</p>
<p >&lt; Add the element if it is unique</p>
<p >&lt; Increment index of first array</p>
<p >&lt; Increment index of second array too</p>
<p>&lt; Vector to hold the intersection</p>
<p>&lt; Index for the first array</p>
<p>&lt; Index for the second array</p>
<p>&lt; Length of first array</p>
<p>&lt; Length of second array</p>
<p>&lt; Increment index of second array</p>
<p>&lt; Increment index of second array</p>
<p>&lt; Add the element if it is unique</p>
<p>&lt; Increment index of first array</p>
<p>&lt; Increment index of second array too</p>
<div class="fragment"><div class="line"><span class="lineno"> 50</span> {</div>
<div class="line"><span class="lineno"> 51</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res; <span class="comment">///&lt; Vector to hold the intersection</span></div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordtype">size_t</span> f_index = 0; <span class="comment">///&lt; Index for the first array</span></div>
@@ -247,7 +247,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>Gets the union of two sorted arrays, and returns them in a vector. </p>
<p >An algorithm is used that compares the elements of the two vectors, appending the one that has a lower value, and incrementing the index for that array. If one of the arrays reaches its end, all the elements of the other are appended to the resultant vector. </p><dl class="params"><dt>Parameters</dt><dd>
<p>An algorithm is used that compares the elements of the two vectors, appending the one that has a lower value, and incrementing the index for that array. If one of the arrays reaches its end, all the elements of the other are appended to the resultant vector. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">first</td><td>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of sorted integer values </td></tr>
<tr><td class="paramname">second</td><td>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of sorted integer values </td></tr>
@@ -255,24 +255,24 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> of the union of the two arrays, in ascending order </dd></dl>
<p >&lt; Vector to hold the union</p>
<p >&lt; Index for the first array</p>
<p >&lt; Index for the second array</p>
<p >&lt; Length of first array</p>
<p >&lt; Length of second array</p>
<p >&lt; Integer to store value of the next element</p>
<p >&lt; Append from first array</p>
<p >&lt; Increment index of second array</p>
<p >&lt; Append from second array</p>
<p >&lt; Increment index of second array</p>
<p >&lt; Element is the same in both</p>
<p >&lt; Increment index of first array</p>
<p >&lt; Increment index of second array too</p>
<p >&lt; Add the element if it is unique</p>
<p >&lt; Add remaining elements</p>
<p >&lt; Add the element if it is unique</p>
<p >&lt; Add remaining elements</p>
<p >&lt; Add the element if it is unique</p>
<p>&lt; Vector to hold the union</p>
<p>&lt; Index for the first array</p>
<p>&lt; Index for the second array</p>
<p>&lt; Length of first array</p>
<p>&lt; Length of second array</p>
<p>&lt; Integer to store value of the next element</p>
<p>&lt; Append from first array</p>
<p>&lt; Increment index of second array</p>
<p>&lt; Append from second array</p>
<p>&lt; Increment index of second array</p>
<p>&lt; Element is the same in both</p>
<p>&lt; Increment index of first array</p>
<p>&lt; Increment index of second array too</p>
<p>&lt; Add the element if it is unique</p>
<p>&lt; Add remaining elements</p>
<p>&lt; Add the element if it is unique</p>
<p>&lt; Add remaining elements</p>
<p>&lt; Add the element if it is unique</p>
<div class="fragment"><div class="line"><span class="lineno"> 50</span> {</div>
<div class="line"><span class="lineno"> 51</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int32_t&gt;</a> res; <span class="comment">///&lt; Vector to hold the union</span></div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordtype">size_t</span> f_index = 0; <span class="comment">///&lt; Index for the first array</span></div>
@@ -347,20 +347,20 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p >Print each value in the array</p>
<p >Print newline</p>
<p >Print each value in the array</p>
<p >Print newline</p>
<p >Print each value in the array</p>
<p >Print newline</p>
<p >Print each value in the array</p>
<p >Print newline</p>
<p >Print each value in the array</p>
<p >Print newline</p>
<p >Print each value in the array</p>
<p >Print newline</p>
<p >Print each value in the array</p>
<p >Print newline</p>
<p>Print each value in the array</p>
<p>Print newline</p>
<p>Print each value in the array</p>
<p>Print newline</p>
<p>Print each value in the array</p>
<p>Print newline</p>
<p>Print each value in the array</p>
<p>Print newline</p>
<p>Print each value in the array</p>
<p>Print newline</p>
<p>Print each value in the array</p>
<p>Print newline</p>
<p>Print each value in the array</p>
<p>Print newline</p>
<div class="fragment"><div class="line"><span class="lineno"> 29</span> {</div>
<div class="line"><span class="lineno"> 30</span> <span class="keywordflow">for</span> (int32_t i : array) {</div>
<div class="line"><span class="lineno"> 31</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; &quot;</span>; <span class="comment">/// Print each value in the array</span></div>
@@ -398,7 +398,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>Shifts the given vector to the left by the shift amount and returns a new vector with the result. The original vector is not mutated. </p>
<p >Shifts the values of the vector, by creating a new vector and adding values from the shift index to the end, then appending the rest of the elements from the start of the vector. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Shifts the values of the vector, by creating a new vector and adding values from the shift index to the end, then appending the rest of the elements from the start of the vector. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">array</td><td>A reference to the input <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
<tr><td class="paramname">shift</td><td>The amount to be shifted to the left </td></tr>
@@ -406,10 +406,10 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> with the shifted values </dd></dl>
<p >&lt; We got an invalid shift, return empty array</p>
<p >&lt; Result array</p>
<p >&lt; Add values after the shift index</p>
<p >&lt; Add the values from the start</p>
<p>&lt; We got an invalid shift, return empty array</p>
<p>&lt; Result array</p>
<p>&lt; Add values after the shift index</p>
<p>&lt; Add the values from the start</p>
<div class="fragment"><div class="line"><span class="lineno"> 47</span> {</div>
<div class="line"><span class="lineno"> 48</span> <span class="keywordflow">if</span> (array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;= shift) {</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">return</span> {}; <span class="comment">///&lt; We got an invalid shift, return empty array</span></div>
@@ -460,7 +460,7 @@ Here is the call graph for this function:</div>
</div><div class="memdoc">
<p>Shifts the given vector to the right by the shift amount and returns a new vector with the result. The original vector is not mutated. </p>
<p >Shifts the values of the vector, by creating a new vector and adding values from the shift index to the end, then appending the rest of the elements to the start of the vector. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Shifts the values of the vector, by creating a new vector and adding values from the shift index to the end, then appending the rest of the elements to the start of the vector. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">array</td><td>A reference to the input <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> </td></tr>
<tr><td class="paramname">shift</td><td>The amount to be shifted to the right </td></tr>
@@ -468,10 +468,10 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> with the shifted values </dd></dl>
<p >&lt; We got an invalid shift, return empty array</p>
<p >&lt; Result array</p>
<p >&lt; Add values after the shift index</p>
<p >&lt; Add the values from the start</p>
<p>&lt; We got an invalid shift, return empty array</p>
<p>&lt; Result array</p>
<p>&lt; Add values after the shift index</p>
<p>&lt; Add the values from the start</p>
<div class="fragment"><div class="line"><span class="lineno"> 48</span> {</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">if</span> (array.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>() &lt;= shift) {</div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">return</span> {}; <span class="comment">///&lt; We got an invalid shift, return empty array</span></div>
@@ -501,7 +501,7 @@ Here is the call graph for this function:</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:aaa7ea27346659f0abe2df82ca57fc5a7"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#aaa7ea27346659f0abe2df82ca57fc5a7">Info</a> ()=default</td></tr>
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<tr class="memdesc:a695e4314ebc3ab58e13004dc63599fe8"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructor having Puzzle as parameter <a href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a695e4314ebc3ab58e13004dc63599fe8">More...</a><br /></td></tr>
<tr class="memdesc:a695e4314ebc3ab58e13004dc63599fe8"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructor having Puzzle as parameter <br /></td></tr>
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<tr class="memdesc:ad3950824936488f66408313b1f8a8ca8"><td class="mdescLeft">&#160;</td><td class="mdescRight">constructor having three parameters <br /></td></tr>
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<tr class="memdesc:a572de12115e39e34dde6e68b707d59f5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Copy constructor. <a href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#a572de12115e39e34dde6e68b707d59f5">More...</a><br /></td></tr>
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<tr class="memdesc:a6abc89925ae7055a63b428e61525ad7a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Move constructor. <br /></td></tr>
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<tr class="memdesc:ac77d992953fa0de10a755e5a9aa06317"><td class="mdescLeft">&#160;</td><td class="mdescRight">copy assignment operator <a href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#ac77d992953fa0de10a755e5a9aa06317">More...</a><br /></td></tr>
<tr class="memdesc:ac77d992953fa0de10a755e5a9aa06317"><td class="mdescLeft">&#160;</td><td class="mdescRight">copy assignment operator <br /></td></tr>
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<tr class="memdesc:ad3993dbca9c5b3ef9ac361dc7f62ce57"><td class="mdescLeft">&#160;</td><td class="mdescRight">move assignment operator <a href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html#ad3993dbca9c5b3ef9ac361dc7f62ce57">More...</a><br /></td></tr>
<tr class="memdesc:ad3993dbca9c5b3ef9ac361dc7f62ce57"><td class="mdescLeft">&#160;</td><td class="mdescRight">move assignment operator <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><div class="compoundTemplParams">template&lt;typename Puzzle&gt;<br />
struct machine_learning::aystar_search::AyStarSearch&lt; Puzzle &gt;::Info</div><p >Struct that handles all the information related to the current state. </p>
struct machine_learning::aystar_search::AyStarSearch&lt; Puzzle &gt;::Info</div><p>Struct that handles all the information related to the current state. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="aaa7ea27346659f0abe2df82ca57fc5a7" name="aaa7ea27346659f0abe2df82ca57fc5a7"></a>
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</div><div class="memdoc">
<p>stores g score </p>
<p >Default constructor </p>
<p>Default constructor </p>
</div>
</div>
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<li class="navelem"><a class="el" href="../../d8/d77/namespacemachine__learning.html">machine_learning</a></li><li class="navelem"><b>aystar_search</b></li><li class="navelem"><a class="el" href="../../da/d02/classmachine__learning_1_1aystar__search_1_1_ay_star_search.html">AyStarSearch</a></li><li class="navelem"><a class="el" href="../../da/d70/structmachine__learning_1_1aystar__search_1_1_ay_star_search_1_1_info.html">Info</a></li>
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<tr class="memdesc:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to save resulting points to a CSV file. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of <a href="https://en.wikipedia.org/wiki/Spirograph" target="_blank">Spirograph</a> </p>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Spirograph" target="_blank">Spirograph</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<p>Implementation of the program is based on the geometry shown in the figure below:</p>
<p ><a href="https://commons.wikimedia.org/wiki/File:Resonance_Cascade.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/3/39/Resonance_Cascade.svg" alt="Spirograph geometry from Wikipedia" style="pointer-events: none; width: 250px" class="inline"/></a> </p>
<p><a href="https://commons.wikimedia.org/wiki/File:Resonance_Cascade.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/3/39/Resonance_Cascade.svg" alt="Spirograph geometry from Wikipedia" style="pointer-events: none; width: 250px" class="inline"/></a> </p>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a525335710b53cb064ca56b936120431e">&#9670;&#160;</a></span>_USE_MATH_DEFINES</h2>
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<p >required for MSVC compiler </p>
<p>required for MSVC compiler </p>
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<p >Main function </p>
<p>Main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 268</span> {</div>
<div class="line"><span class="lineno"> 269</span> <a class="code hl_function" href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">spirograph::test</a>();</div>
<div class="line"><span class="lineno"> 270</span> </div>
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<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Primality_test" target="_blank">Primality test</a> implementation. </p>
<p >A simple and efficient implementation of a function to test if a number is prime, based on the fact that </p><blockquote class="doxtable">
<p >&zwj;Every Prime number, except 2 and 3, are of the form \(6k\pm1\) for integer values of k. </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Primality_test" target="_blank">Primality test</a> implementation. </p>
<p>A simple and efficient implementation of a function to test if a number is prime, based on the fact that </p><blockquote class="doxtable">
<p>&zwj;Every Prime number, except 2 and 3, are of the form \(6k\pm1\) for integer values of k. </p>
</blockquote>
<p>This gives a 3x speed improvement. </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<p >Check if a number is prime </p><dl class="params"><dt>Parameters</dt><dd>
<p>Check if a number is prime </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">number</td><td>number to check </td></tr>
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<p >main function </p>
<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 31</span> {</div>
<div class="line"><span class="lineno"> 32</span> <span class="comment">// Main Function</span></div>
<div class="line"><span class="lineno"> 33</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the value of n to check if Prime\n&quot;</span>;</div>
@@ -211,7 +211,7 @@ Here is the call graph for this function:</div>
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_9510827d0b234b3cc54b29892f217477.html">others</a></li><li class="navelem"><a class="el" href="../../da/d7b/primality__test_8cpp.html">primality_test.cpp</a></li>
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<p>Functions for the <a href="https://en.wikipedia.org/wiki/Cycle_detection" target="_blank">Floyd's Cycle Detection</a> algorithm.
<a href="../../da/d82/namespacecycle__detection.html#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Cycle_detection" target="_blank">Floyd's Cycle Detection</a> algorithm. </p>
<div class="textblock"><p>Functions for the <a href="https://en.wikipedia.org/wiki/Cycle_detection" target="_blank">Floyd's Cycle Detection</a> algorithm. </p>
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<tr class="memitem:ad4016cfc80485a43748895a2c26c7d08"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#ad4016cfc80485a43748895a2c26c7d08">graph::addEdge</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt; &gt; *adj, size_t u, size_t v)</td></tr>
<tr class="memdesc:ad4016cfc80485a43748895a2c26c7d08"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds and edge between two vertices of graph say u and v in this case. <a href="../../df/dce/namespacegraph.html#ad4016cfc80485a43748895a2c26c7d08">More...</a><br /></td></tr>
<tr class="memdesc:ad4016cfc80485a43748895a2c26c7d08"><td class="mdescLeft">&#160;</td><td class="mdescRight">Adds and edge between two vertices of graph say u and v in this case. <br /></td></tr>
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<tr class="memitem:a64c1db5aad7502c6f08e4652f6edd463"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">graph::explore</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt; &gt; &amp;adj, size_t v, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; *visited)</td></tr>
<tr class="memdesc:a64c1db5aad7502c6f08e4652f6edd463"><td class="mdescLeft">&#160;</td><td class="mdescRight">Explores the given vertex, exploring a vertex means traversing over all the vertices which are connected to the vertex that is currently being explored. <a href="../../df/dce/namespacegraph.html#a64c1db5aad7502c6f08e4652f6edd463">More...</a><br /></td></tr>
<tr class="memdesc:a64c1db5aad7502c6f08e4652f6edd463"><td class="mdescLeft">&#160;</td><td class="mdescRight">Explores the given vertex, exploring a vertex means traversing over all the vertices which are connected to the vertex that is currently being explored. <br /></td></tr>
<tr class="separator:a64c1db5aad7502c6f08e4652f6edd463"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab5428a3519267a28bba4b4310cfbb6ae"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#ab5428a3519267a28bba4b4310cfbb6ae">graph::depth_first_search</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; size_t &gt; &gt; &amp;adj, size_t start)</td></tr>
<tr class="memdesc:ab5428a3519267a28bba4b4310cfbb6ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">initiates depth first search algorithm. <a href="../../df/dce/namespacegraph.html#ab5428a3519267a28bba4b4310cfbb6ae">More...</a><br /></td></tr>
<tr class="memdesc:ab5428a3519267a28bba4b4310cfbb6ae"><td class="mdescLeft">&#160;</td><td class="mdescRight">initiates depth first search algorithm. <br /></td></tr>
<tr class="separator:ab5428a3519267a28bba4b4310cfbb6ae"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d8d/depth__first__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Depth-first_search" target="_blank">Depth First Search Algorithm (Depth First Search)</a> </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Depth-first_search" target="_blank">Depth First Search Algorithm (Depth First Search)</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="http://github.com/ayaankhan98" target="_blank">Ayaan Khan</a></dd></dl>
<p>Depth First Search also quoted as DFS is a <a class="el" href="../../da/d9a/class_graph.html">Graph</a> Traversal Algorithm. Time Complexity O(|V| + |E|) where V is number of vertices and E is number of edges in graph.</p>
<p >Application of Depth First Search are</p>
<p>Application of Depth First Search are</p>
<ol type="1">
<li>Finding connected components</li>
<li>Finding 2-(edge or vertex)-connected components.</li>
@@ -149,7 +149,7 @@ Functions</h2></td></tr>
<li>Generating words in order to plot the limit set of a group.</li>
<li>Finding strongly connected components.</li>
</ol>
<p >And there are many more...</p>
<p>And there are many more...</p>
<h4>Working</h4>
<ol type="1">
<li>Mark all vertices as unvisited first</li>
@@ -173,10 +173,10 @@ Functions</h2></td></tr>
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<p >Main function </p>
<p >creating graph</p>
<p >taking input for edges</p>
<p >running depth first search over graph</p>
<p>Main function </p>
<p>creating graph</p>
<p>taking input for edges</p>
<p>running depth first search over graph</p>
<div class="fragment"><div class="line"><span class="lineno"> 109</span> {</div>
<div class="line"><span class="lineno"> 110</span> <span class="keywordtype">size_t</span> vertices = 0, edges = 0;</div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Enter the Vertices : &quot;</span>;</div>
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<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of graph class.</p>
<p >The graph will be represented using Adjacency List representation. This class contains 2 data members "m_vertices" &amp; "m_adjList" used to represent the number of vertices and adjacency list of the graph respectively. The vertices are labelled 0 - (m_vertices - 1). </p>
<div class="textblock"><p>Implementation of graph class.</p>
<p>The graph will be represented using Adjacency List representation. This class contains 2 data members "m_vertices" &amp; "m_adjList" used to represent the number of vertices and adjacency list of the graph respectively. The vertices are labelled 0 - (m_vertices - 1). </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="ad3b98f95ee53f91afad11b8eaddc35e0" name="ad3b98f95ee53f91afad11b8eaddc35e0"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad3b98f95ee53f91afad11b8eaddc35e0">&#9670;&#160;</a></span>Graph() <span class="overload">[1/7]</span></h2>
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<p >Create a graph from vertices and adjacency list.</p>
<p>Create a graph from vertices and adjacency list.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">vertices</td><td>specify the number of vertices the graph would contain. </td></tr>
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<p >Create a graph from vertices and adjacency list.</p>
<p>Create a graph from vertices and adjacency list.</p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">vertices</td><td>specify the number of vertices the graph would contain. </td></tr>
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<p >Create a graph from vertices and a set of edges.</p>
<p >Adjacency list of the graph would be created from the set of edges. If the source or destination of any edge has a value greater or equal to number of vertices, then it would throw a range_error.</p>
<p>Create a graph from vertices and a set of edges.</p>
<p>Adjacency list of the graph would be created from the set of edges. If the source or destination of any edge has a value greater or equal to number of vertices, then it would throw a range_error.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">vertices</td><td>specify the number of vertices the graph would contain. </td></tr>
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<p >Add an edge in the graph.</p>
<p>Add an edge in the graph.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">edge</td><td>that needs to be added. </td></tr>
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<p >Add an <a class="el" href="../../d7/d77/class_edge.html">Edge</a> in the graph</p>
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<div class="textblock"><p >Check if a number is <a href="https://en.wikipedia.org/wiki/Palindrome" target="_blank">palindrome</a> or not. </p>
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<div class="textblock"><p >Implementation of 256-bit unsigned integers. </p><dl class="section note"><dt>Note</dt><dd>The implementation can be flagged as not completed. This header is used with enough operations to demonstrate the usage of ECDH (Elliptic Curve Diffie-Hellman) Key exchange. </dd></dl>
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<div class="textblock"><p ><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">N queens</a> all optimized </p>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" target="_blank">N queens</a> all optimized </p>
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<p >Check if a queen can be placed on matrix </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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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="../../da/db8/count__of__set__bits_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/db8/count__of__set__bits_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation to [count number of set bits of a number] (<a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/">https://www.geeksforgeeks.org/count-set-bits-in-an-integer/</a>) in an integer. </p>
<p >We are given an integer number. We need to calculate the number of set bits in it.</p>
<p >A binary number consists of two digits. They are 0 &amp; 1. Digit 1 is known as set bit in computer terms. Worst Case Time Complexity: O(log n) Space complexity: O(1) </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd>
<div class="textblock"><p>Implementation to [count number of set bits of a number] (<a href="https://www.geeksforgeeks.org/count-set-bits-in-an-integer/">https://www.geeksforgeeks.org/count-set-bits-in-an-integer/</a>) in an integer. </p>
<p>We are given an integer number. We need to calculate the number of set bits in it.</p>
<p>A binary number consists of two digits. They are 0 &amp; 1. Digit 1 is known as set bit in computer terms. Worst Case Time Complexity: O(log n) Space complexity: O(1) </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd>
<dd>
<a href="https://github.com/prashant-th18" target="_blank">Prashant Thakur</a> </dd></dl>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of singly linked list algorithm. </p>
<p >The linked list is a data structure used for holding a sequence of values, which can be added, removed and displayed. </p>
<div class="textblock"><p>Implementation of singly linked list algorithm. </p>
<p>The linked list is a data structure used for holding a sequence of values, which can be added, removed and displayed. </p>
<h3><a class="anchor" id="autotoc_md40"></a>
Algorithm</h3>
<p >Values can be added by iterating to the end of a <a class="el" href="../../d8/d10/structlist.html">list(by following
<p>Values can be added by iterating to the end of a <a class="el" href="../../d8/d10/structlist.html">list(by following
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<p >Values can be removed by also iterating through the list. When the node containing the value is found, the node pointing to the current node is made to point to the node that the current node is pointing to, and then returning the current node to heap store. </p>
<p>Values can be removed by also iterating through the list. When the node containing the value is found, the node pointing to the current node is made to point to the node that the current node is pointing to, and then returning the current node to heap store. </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<p >This function checks if the string passed consists of only digits. </p><dl class="params"><dt>Parameters</dt><dd>
<p>This function checks if the string passed consists of only digits. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
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<p >Main function: Allows the user add and delete values from the list. Also allows user to search for and display values in the list. </p><dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p>Main function: Allows the user add and delete values from the list. Also allows user to search for and display values in the list. </p><dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 222</span> {</div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >This program computes the N^th Fibonacci number in modulo mod input argument . </p>
<p >Takes O(logn) time to compute nth Fibonacci number</p>
<div class="textblock"><p>This program computes the N^th Fibonacci number in modulo mod input argument . </p>
<p>Takes O(logn) time to compute nth Fibonacci number</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/villayatali123" target="_blank">villayatali123</a> </dd>
<dd>
[unknown author]() </dd></dl>
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<p >This function finds nth fibonacci number in a given modulus </p><dl class="params"><dt>Parameters</dt><dd>
<p>This function finds nth fibonacci number in a given modulus </p><dl class="params"><dt>Parameters</dt><dd>
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<p >Main function </p>
<p>Main function </p>
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<p >Function to test above algorithm </p>
<p>Function to test above algorithm </p>
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<div class="textblock"><p ><a class="el" href="../../db/d8b/struct_node.html">Node</a> that holds key </p>
<div class="textblock"><p><a class="el" href="../../db/d8b/struct_node.html">Node</a> that holds key </p>
</div><hr/>The documentation for this struct was generated from the following file:<ul>
<li>hashing/<a class="el" href="../../db/d71/quadratic__probing__hash__table_8cpp.html">quadratic_probing_hash_table.cpp</a></li>
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Functions</h2></td></tr>
<tr class="memitem:ad76f5cac3ef8dc034f6abb99b64c2b20"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> first, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> second)</td></tr>
<tr class="memdesc:ad76f5cac3ef8dc034f6abb99b64c2b20"><td class="mdescLeft">&#160;</td><td class="mdescRight">Binary addition. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">More...</a><br /></td></tr>
<tr class="memdesc:ad76f5cac3ef8dc034f6abb99b64c2b20"><td class="mdescLeft">&#160;</td><td class="mdescRight">Binary addition. <br /></td></tr>
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<tr class="memitem:aad9e3edfe156b59fc06a5585403fe0d6"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;str, int64_t x1, int64_t x2, int64_t n)</td></tr>
<tr class="memdesc:aad9e3edfe156b59fc06a5585403fe0d6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Wrapper function for substr that considers leading zeros. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">More...</a><br /></td></tr>
<tr class="memdesc:aad9e3edfe156b59fc06a5585403fe0d6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Wrapper function for substr that considers leading zeros. <br /></td></tr>
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<tr class="memitem:a7a890d2f26855ada3b9f1d43aec70a86"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str1, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> str2)</td></tr>
<tr class="memdesc:a7a890d2f26855ada3b9f1d43aec70a86"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements Karatsuba's algorithm for fast multiplication. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">More...</a><br /></td></tr>
<tr class="memdesc:a7a890d2f26855ada3b9f1d43aec70a86"><td class="mdescLeft">&#160;</td><td class="mdescRight">The main function implements Karatsuba's algorithm for fast multiplication. <br /></td></tr>
<tr class="separator:a7a890d2f26855ada3b9f1d43aec70a86"><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="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Implementation of the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> </p>
<p >Given two strings in binary notation we want to multiply them and return the value. Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba algorithm to find the product which will solve the problem O(nlogn) of time. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd>
<div class="textblock"><p>Implementation of the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> </p>
<p>Given two strings in binary notation we want to multiply them and return the value. Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba algorithm to find the product which will solve the problem O(nlogn) of time. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy" target="_blank">Swastika Gupta</a> </dd>
<dd>
<a href="https://github.com/poypoyan" target="_blank">Ameer Carlo Lubang</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
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<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/dd3/namespacespirograph.html#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; double, double &gt;, N &gt; *points, double l, double k, double rot)</td></tr>
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<tr class="memdesc:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to save resulting points to a CSV file. <a href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">More...</a><br /></td></tr>
<tr class="memdesc:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to save resulting points to a CSV file. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Functions related to <a class="el" href="../../da/d77/spirograph_8cpp.html" title="Implementation of Spirograph">spirograph.cpp</a> </p>
<div class="textblock"><p>Functions related to <a class="el" href="../../da/d77/spirograph_8cpp.html" title="Implementation of Spirograph">spirograph.cpp</a> </p>
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<p >Generate spirograph curve into arrays <code>x</code> and <code>y</code> such that the i^th point in 2D is represented by <code>(x[i],y[i])</code>. The generating function is given by: </p><p class="formulaDsp">
<p>Generate spirograph curve into arrays <code>x</code> and <code>y</code> such that the i^th point in 2D is represented by <code>(x[i],y[i])</code>. The generating function is given by: </p><p class="formulaDsp">
\begin{eqnarray*}
x &amp;=&amp; R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right)
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<li>\(t\) is the angle of rotation of the point i.e., represents the time parameter</li>
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<p >Since we are considering ratios, the actual values of \(r\) and \(R\) are immaterial.</p>
<p>Since we are considering ratios, the actual values of \(r\) and \(R\) are immaterial.</p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
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