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<title>Algorithms_in_C++: math/least_common_multiple.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -145,27 +145,27 @@ Functions</h2></td></tr>
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<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>
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<div class="fragment"><div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> {</div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> <span class="keywordflow">if</span> (x == 0) {</div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> <span class="keywordflow">return</span> y;</div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> }</div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordflow">if</span> (y == 0) {</div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> }</div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">if</span> (x == y) {</div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> }</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> <span class="keywordflow">if</span> (x > y) {</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// The following is valid because we have checked whether y == 0</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = x / y;</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(y, x - temp * y);</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> }</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// Again the following is valid because we have checked whether x == 0</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = y / x;</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y - temp * x);</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 16</span> {</div>
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<div class="line"><span class="lineno"> 17</span> <span class="keywordflow">if</span> (x == 0) {</div>
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<div class="line"><span class="lineno"> 18</span> <span class="keywordflow">return</span> y;</div>
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<div class="line"><span class="lineno"> 19</span> }</div>
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<div class="line"><span class="lineno"> 20</span> <span class="keywordflow">if</span> (y == 0) {</div>
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<div class="line"><span class="lineno"> 21</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><span class="lineno"> 22</span> }</div>
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<div class="line"><span class="lineno"> 23</span> <span class="keywordflow">if</span> (x == y) {</div>
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<div class="line"><span class="lineno"> 24</span> <span class="keywordflow">return</span> x;</div>
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<div class="line"><span class="lineno"> 25</span> }</div>
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<div class="line"><span class="lineno"> 26</span> <span class="keywordflow">if</span> (x > y) {</div>
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<div class="line"><span class="lineno"> 27</span> <span class="comment">// The following is valid because we have checked whether y == 0</span></div>
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<div class="line"><span class="lineno"> 28</span> </div>
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<div class="line"><span class="lineno"> 29</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = x / y;</div>
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||||
<div class="line"><span class="lineno"> 30</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(y, x - temp * y);</div>
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||||
<div class="line"><span class="lineno"> 31</span> }</div>
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<div class="line"><span class="lineno"> 32</span> <span class="comment">// Again the following is valid because we have checked whether x == 0</span></div>
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<div class="line"><span class="lineno"> 33</span> </div>
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<div class="line"><span class="lineno"> 34</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> temp = y / x;</div>
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<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y - temp * x);</div>
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<div class="line"><span class="lineno"> 36</span>}</div>
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<div class="ttc" id="aleast__common__multiple_8cpp_html_a8ba1fc66e4134ab25b2602b323150563"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#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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@@ -202,9 +202,9 @@ Here is the call graph for this function:</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>
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<div class="fragment"><div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> {</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">return</span> x / <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y) * y;</div>
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||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 43</span> {</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> x / <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a>(x, y) * y;</div>
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<div class="line"><span class="lineno"> 45</span>}</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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@@ -230,10 +230,10 @@ Here is the call graph for this function:</div>
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</table>
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<p >Main function </p>
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<div class="fragment"><div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> {</div>
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||||
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
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||||
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>}</div>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 78</span> {</div>
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||||
<div class="line"><span class="lineno"> 79</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
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||||
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 81</span>}</div>
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||||
<div class="ttc" id="aleast__common__multiple_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#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="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a> functions with some assert statements. </p>
|
||||
<div class="fragment"><div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> {</div>
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||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// First test on lcm(5,10) == 10</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">"LCM of 5 and 10 is 10 but lcm function gives a different "</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="stringliteral">"result.\n"</span>,</div>
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||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10) == 10));</div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><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> << <span class="stringliteral">"First assertion passes: LCM of 5 and 10 is "</span> << <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
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<div class="line"><a id="l00058" name="l00058"></a><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>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">"LCM of 2 and 3 is 6 but lcm function gives a different "</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="stringliteral">"result.\n"</span>,</div>
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||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3) == 6));</div>
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||||
<div class="line"><a id="l00062" name="l00062"></a><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> << <span class="stringliteral">"Second assertion passes: LCM of 2 and 3 is "</span> << <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3)</div>
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||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// Testing an integer overflow.</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// The algorithm should work as long as the result fits into integer.</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">"LCM of 987654321 and 987654321 is 987654321 but lcm function"</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="stringliteral">" gives a different result.\n"</span>,</div>
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||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321) == 987654321));</div>
|
||||
<div class="line"><a id="l00070" name="l00070"></a><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> << <span class="stringliteral">"Third assertion passes: LCM of 987654321 and 987654321 is "</span></div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> << <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321)</div>
|
||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 50</span> {</div>
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<div class="line"><span class="lineno"> 51</span> <span class="comment">// First test on lcm(5,10) == 10</span></div>
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<div class="line"><span class="lineno"> 52</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">"LCM of 5 and 10 is 10 but lcm function gives a different "</span></div>
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<div class="line"><span class="lineno"> 53</span> <span class="stringliteral">"result.\n"</span>,</div>
|
||||
<div class="line"><span class="lineno"> 54</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#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> << <span class="stringliteral">"First assertion passes: LCM of 5 and 10 is "</span> << <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(5, 10)</div>
|
||||
<div class="line"><span class="lineno"> 56</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><span class="lineno"> 57</span> </div>
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<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>
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<div class="line"><span class="lineno"> 59</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">"LCM of 2 and 3 is 6 but lcm function gives a different "</span></div>
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<div class="line"><span class="lineno"> 60</span> <span class="stringliteral">"result.\n"</span>,</div>
|
||||
<div class="line"><span class="lineno"> 61</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#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> << <span class="stringliteral">"Second assertion passes: LCM of 2 and 3 is "</span> << <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(2, 3)</div>
|
||||
<div class="line"><span class="lineno"> 63</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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||||
<div class="line"><span class="lineno"> 64</span> </div>
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<div class="line"><span class="lineno"> 65</span> <span class="comment">// Testing an integer overflow.</span></div>
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<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>
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<div class="line"><span class="lineno"> 67</span> assert(((<span class="keywordtype">void</span>)<span class="stringliteral">"LCM of 987654321 and 987654321 is 987654321 but lcm function"</span></div>
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<div class="line"><span class="lineno"> 68</span> <span class="stringliteral">" gives a different result.\n"</span>,</div>
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||||
<div class="line"><span class="lineno"> 69</span> <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#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> << <span class="stringliteral">"Third assertion passes: LCM of 987654321 and 987654321 is "</span></div>
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<div class="line"><span class="lineno"> 71</span> << <a class="code hl_function" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a>(987654321, 987654321)</div>
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<div class="line"><span class="lineno"> 72</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 73</span>}</div>
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<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>
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<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>
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<div class="ttc" id="aleast__common__multiple_8cpp_html_aa8d0e241db517813725e721a152e3a25"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#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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@@ -301,7 +301,7 @@ Here is the call graph for this function:</div>
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