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<div id="projectbrief">Set of algorithms implemented in C++.</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
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@@ -116,7 +133,9 @@ Include dependency graph for least_common_multiple.cpp:</div>
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<p><a href="../../d4/d21/least__common__multiple_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a8ba1fc66e4134ab25b2602b323150563" id="r_a8ba1fc66e4134ab25b2602b323150563"><td class="memItemLeft" align="right" valign="top">unsigned int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a> (unsigned int x, unsigned int y)</td></tr>
@@ -131,6 +150,8 @@ Functions</h2></td></tr>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Copyright 2020 </p><dl class="section author"><dt>Author</dt><dd>tjgurwara99</dd></dl>
<p>A basic implementation of LCM function </p>
<p class="definition">Definition in file <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html">least_common_multiple.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a8ba1fc66e4134ab25b2602b323150563" name="a8ba1fc66e4134ab25b2602b323150563"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a8ba1fc66e4134ab25b2602b323150563">&#9670;&#160;</a></span>gcd()</h2>
@@ -151,6 +172,8 @@ Functions</h2></td></tr>
</table>
</div><div class="memdoc">
<p>Function for finding greatest common divisor of two numbers. @params two integers x and y whose gcd we want to find. </p><dl class="section return"><dt>Returns</dt><dd>greatest common divisor of x and y. </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html#l00016">16</a> of file <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html">least_common_multiple.cpp</a>.</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> (x == 0) {</div>
<div class="line"><span class="lineno"> 18</span> <span class="keywordflow">return</span> y;</div>
@@ -172,13 +195,8 @@ Functions</h2></td></tr>
<div class="line"><span class="lineno"> 34</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = y / x;</div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y - temp * x);</div>
<div class="line"><span class="lineno"> 36</span>}</div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a8ba1fc66e4134ab25b2602b323150563"><div class="ttname"><a href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a></div><div class="ttdeci">unsigned int gcd(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition</b> least_common_multiple.cpp:16</div></div>
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<p>Function for finding the least common multiple of two numbers. @params integer x and y whose lcm we want to find. </p><dl class="section return"><dt>Returns</dt><dd>lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y) </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html#l00043">43</a> of file <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html">least_common_multiple.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 43</span> {</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> x / <a class="code hl_function" href="#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y) * y;</div>
<div class="line"><span class="lineno"> 45</span>}</div>
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<p>Main function </p>
<p class="definition">Definition at line <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html#l00078">78</a> of file <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html">least_common_multiple.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 78</span> {</div>
<div class="line"><span class="lineno"> 79</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 81</span>}</div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition</b> least_common_multiple.cpp:50</div></div>
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<p>Function for testing the <a class="el" href="#aa8d0e241db517813725e721a152e3a25">lcm()</a> functions with some assert statements. </p>
<p class="definition">Definition at line <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html#l00050">50</a> of file <a class="el" href="../../d4/d21/least__common__multiple_8cpp_source.html">least_common_multiple.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 50</span> {</div>
<div class="line"><span class="lineno"> 51</span> <span class="comment">// First test on lcm(5,10) == 10</span></div>
<div class="line"><span class="lineno"> 52</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 5 and 10 is 10 but lcm function gives a different &quot;</span></div>
<div class="line"><span class="lineno"> 53</span> <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><span class="lineno"> 54</span> <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10) == 10));</div>
<div class="line"><span class="lineno"> 55</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;First assertion passes: LCM of 5 and 10 is &quot;</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</div>
<div class="line"><span class="lineno"> 56</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 55</span> std::cout &lt;&lt; <span class="stringliteral">&quot;First assertion passes: LCM of 5 and 10 is &quot;</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</div>
<div class="line"><span class="lineno"> 56</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 57</span> </div>
<div class="line"><span class="lineno"> 58</span> <span class="comment">// Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)</span></div>
<div class="line"><span class="lineno"> 59</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 2 and 3 is 6 but lcm function gives a different &quot;</span></div>
<div class="line"><span class="lineno"> 60</span> <span class="stringliteral">&quot;result.\n&quot;</span>,</div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3) == 6));</div>
<div class="line"><span class="lineno"> 62</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;Second assertion passes: LCM of 2 and 3 is &quot;</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3)</div>
<div class="line"><span class="lineno"> 63</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 62</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Second assertion passes: LCM of 2 and 3 is &quot;</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3)</div>
<div class="line"><span class="lineno"> 63</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 65</span> <span class="comment">// Testing an integer overflow.</span></div>
<div class="line"><span class="lineno"> 66</span> <span class="comment">// The algorithm should work as long as the result fits into integer.</span></div>
<div class="line"><span class="lineno"> 67</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">&quot;LCM of 987654321 and 987654321 is 987654321 but lcm function&quot;</span></div>
<div class="line"><span class="lineno"> 68</span> <span class="stringliteral">&quot; gives a different result.\n&quot;</span>,</div>
<div class="line"><span class="lineno"> 69</span> <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321) == 987654321));</div>
<div class="line"><span class="lineno"> 70</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;Third assertion passes: LCM of 987654321 and 987654321 is &quot;</span></div>
<div class="line"><span class="lineno"> 70</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Third assertion passes: LCM of 987654321 and 987654321 is &quot;</span></div>
<div class="line"><span class="lineno"> 71</span> &lt;&lt; <a class="code hl_function" href="#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321)</div>
<div class="line"><span class="lineno"> 72</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 72</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 73</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_aa8d0e241db517813725e721a152e3a25"><div class="ttname"><a href="#aa8d0e241db517813725e721a152e3a25">lcm</a></div><div class="ttdeci">unsigned int lcm(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition</b> least_common_multiple.cpp:43</div></div>
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<div class="ttc" id="aleast__common__multiple_8cpp_html_aa8d0e241db517813725e721a152e3a25"><div class="ttname"><a href="#aa8d0e241db517813725e721a152e3a25">lcm</a></div><div class="ttdeci">unsigned int lcm(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d21/least__common__multiple_8cpp_source.html#l00043">least_common_multiple.cpp:43</a></div></div>
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