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<div id="projectbrief">Set of algorithms implemented in C.</div>
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<p><a href="https://projecteuler.net/problem=23">Problem 23</a> solution - optimization using look-up array
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;stdlib.h&gt;</code><br />
<code>#include &lt;time.h&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for sol2.c:</div>
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Functions</h2></td></tr>
<tr class="memitem:a1aca7f530f82b27100262adba9e7556b"><td class="memItemLeft" align="right" valign="top">char&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/dbd/problem__23_2sol2_8c.html#a1aca7f530f82b27100262adba9e7556b">get_perfect_number</a> (unsigned long N)</td></tr>
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<tr class="memitem:a34f4ad85151e3a43368ae67f42347f56"><td class="memItemLeft" align="right" valign="top"><a id="a34f4ad85151e3a43368ae67f42347f56"></a>
char&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/dbd/problem__23_2sol2_8c.html#a34f4ad85151e3a43368ae67f42347f56">is_abundant</a> (unsigned long N)</td></tr>
<tr class="memdesc:a34f4ad85151e3a43368ae67f42347f56"><td class="mdescLeft">&#160;</td><td class="mdescRight">Is the given number an abundant number (1) or not (0) <br /></td></tr>
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<tr class="memitem:ac5d600bf3077f4188afc4c5cd2c40eaf"><td class="memItemLeft" align="right" valign="top"><a id="ac5d600bf3077f4188afc4c5cd2c40eaf"></a>
unsigned long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/dbd/problem__23_2sol2_8c.html#ac5d600bf3077f4188afc4c5cd2c40eaf">get_next_abundant</a> (unsigned long N)</td></tr>
<tr class="memdesc:ac5d600bf3077f4188afc4c5cd2c40eaf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find the next abundant number after N and not including N. <br /></td></tr>
<tr class="separator:ac5d600bf3077f4188afc4c5cd2c40eaf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3ab61b5a1c4f2288625d160aa0ea8478"><td class="memItemLeft" align="right" valign="top">char&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/dbd/problem__23_2sol2_8c.html#a3ab61b5a1c4f2288625d160aa0ea8478">is_sum_of_abundant</a> (unsigned long N)</td></tr>
<tr class="memdesc:a3ab61b5a1c4f2288625d160aa0ea8478"><td class="mdescLeft">&#160;</td><td class="mdescRight">check if a given number can be represented as a sum of two abundant numbers. <a href="../../d4/dbd/problem__23_2sol2_8c.html#a3ab61b5a1c4f2288625d160aa0ea8478">More...</a><br /></td></tr>
<tr class="separator:a3ab61b5a1c4f2288625d160aa0ea8478"><td class="memSeparator" colspan="2">&#160;</td></tr>
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int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/dbd/problem__23_2sol2_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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Variables</h2></td></tr>
<tr class="memitem:af920a16d6ef69dd604b283f427892e06"><td class="memItemLeft" align="right" valign="top">char *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/dbd/problem__23_2sol2_8c.html#af920a16d6ef69dd604b283f427892e06">abundant_flags</a> = NULL</td></tr>
<tr class="memdesc:af920a16d6ef69dd604b283f427892e06"><td class="mdescLeft">&#160;</td><td class="mdescRight">This is the global array to be used to store a flag to identify if a particular number is abundant (1) or not (0). <a href="../../d4/dbd/problem__23_2sol2_8c.html#af920a16d6ef69dd604b283f427892e06">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://projecteuler.net/problem=23">Problem 23</a> solution - optimization using look-up array </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
<p>Optimization applied - compute &amp; store abundant numbers once into a look-up array. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a1aca7f530f82b27100262adba9e7556b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a1aca7f530f82b27100262adba9e7556b">&#9670;&nbsp;</a></span>get_perfect_number()</h2>
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<td class="memname">char get_perfect_number </td>
<td>(</td>
<td class="paramtype">unsigned long&#160;</td>
<td class="paramname"><em>N</em></td><td>)</td>
<td></td>
</tr>
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<dl class="section return"><dt>Returns</dt><dd>-1 if N is deficient </dd>
<dd>
1 if N is abundant </dd>
<dd>
0 if N is perfect </dd></dl>
<div class="fragment"><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;{</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> sum = 1;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="keywordtype">char</span> ret = 0;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> i = 2; i * i &lt;= N; i++)</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordflow">if</span> (N % i == 0)</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; sum += i;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> tmp = N / i;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">if</span> (tmp != i)</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; sum += tmp;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; }</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; }</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; ret = sum == N ? 0 : (sum &gt; N ? 1 : -1);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160;<span class="preprocessor">#ifdef DEBUG</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; printf(<span class="stringliteral">&quot;%5lu: %5lu : %d\n&quot;</span>, N, sum, ret);</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;}</div>
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<a id="a3ab61b5a1c4f2288625d160aa0ea8478"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3ab61b5a1c4f2288625d160aa0ea8478">&#9670;&nbsp;</a></span>is_sum_of_abundant()</h2>
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<td class="memname">char is_sum_of_abundant </td>
<td>(</td>
<td class="paramtype">unsigned long&#160;</td>
<td class="paramname"><em>N</em></td><td>)</td>
<td></td>
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<p>check if a given number can be represented as a sum of two abundant numbers. </p>
<dl class="section return"><dt>Returns</dt><dd>1 - if yes </dd>
<dd>
0 - if not </dd></dl>
<div class="fragment"><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;{</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="comment">/* optimized logic:</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;<span class="comment"> * i + j = N where both i and j should be abundant</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;<span class="comment"> * hence we can simply check for j = N - i as we loop through i</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> i = <a class="code" href="../../d4/dbd/problem__23_2sol2_8c.html#ac5d600bf3077f4188afc4c5cd2c40eaf">get_next_abundant</a>(1); i &lt;= (N &gt;&gt; 1);</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; i = <a class="code" href="../../d4/dbd/problem__23_2sol2_8c.html#ac5d600bf3077f4188afc4c5cd2c40eaf">get_next_abundant</a>(i))</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d4/dbd/problem__23_2sol2_8c.html#a34f4ad85151e3a43368ae67f42347f56">is_abundant</a>(N - i))</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;<span class="preprocessor">#ifdef DEBUG</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; printf(<span class="stringliteral">&quot;\t%4lu + %4lu = %4lu\n&quot;</span>, i, N - i, N);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">return</span> 1;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; }</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160;}</div>
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Here is the call graph for this function:</div>
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<h2 class="groupheader">Variable Documentation</h2>
<a id="af920a16d6ef69dd604b283f427892e06"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af920a16d6ef69dd604b283f427892e06">&#9670;&nbsp;</a></span>abundant_flags</h2>
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<td class="memname">char* abundant_flags = NULL</td>
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<p>This is the global array to be used to store a flag to identify if a particular number is abundant (1) or not (0). </p>
<p>Using a whole byte to store a binary info would be redundant. We will use each byte to represent 8 numbers by relying on bits. This saves memory required by 1/8 </p>
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<div class="ttc" id="aproblem__23_2sol2_8c_html_ac5d600bf3077f4188afc4c5cd2c40eaf"><div class="ttname"><a href="../../d4/dbd/problem__23_2sol2_8c.html#ac5d600bf3077f4188afc4c5cd2c40eaf">get_next_abundant</a></div><div class="ttdeci">unsigned long get_next_abundant(unsigned long N)</div><div class="ttdoc">Find the next abundant number after N and not including N.</div><div class="ttdef"><b>Definition:</b> sol2.c:70</div></div>
<div class="ttc" id="aproblem__23_2sol2_8c_html_a34f4ad85151e3a43368ae67f42347f56"><div class="ttname"><a href="../../d4/dbd/problem__23_2sol2_8c.html#a34f4ad85151e3a43368ae67f42347f56">is_abundant</a></div><div class="ttdeci">char is_abundant(unsigned long N)</div><div class="ttdoc">Is the given number an abundant number (1) or not (0)</div><div class="ttdef"><b>Definition:</b> sol2.c:59</div></div>
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