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@@ -123,14 +123,17 @@ Namespaces</h2></td></tr>
<tr class="memdesc:dd/dba/namespacedivide__and__conquer"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:de/d41/namespacekaratsuba__algorithm"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></td></tr>
<tr class="memdesc:de/d41/namespacekaratsuba__algorithm"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> <br /></td></tr>
<tr class="memdesc:de/d41/namespacekaratsuba__algorithm"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> implementation. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><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:a7d1dbae365c7746295d3322e6f7f80b6"><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#a7d1dbae365c7746295d3322e6f7f80b6">divide_and_conquer::karatsuba_algorithm::addStrings</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:a7d1dbae365c7746295d3322e6f7f80b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6">More...</a><br /></td></tr>
<tr class="separator:a7d1dbae365c7746295d3322e6f7f80b6"><td class="memSeparator" colspan="2">&#160;</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="separator:ad76f5cac3ef8dc034f6abb99b64c2b20"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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="separator:aad9e3edfe156b59fc06a5585403fe0d6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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="separator:a7a890d2f26855ada3b9f1d43aec70a86"><td class="memSeparator" colspan="2">&#160;</td></tr>
@@ -143,16 +146,18 @@ Functions</h2></td></tr>
</table>
<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></dl>
<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>
<a id="a7d1dbae365c7746295d3322e6f7f80b6" name="a7d1dbae365c7746295d3322e6f7f80b6"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7d1dbae365c7746295d3322e6f7f80b6">&#9670;&#160;</a></span>addStrings()</h2>
<a id="ad76f5cac3ef8dc034f6abb99b64c2b20" name="ad76f5cac3ef8dc034f6abb99b64c2b20"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad76f5cac3ef8dc034f6abb99b64c2b20">&#9670;&#160;</a></span>add_strings()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> divide_and_conquer::karatsuba_algorithm::addStrings </td>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> divide_and_conquer::karatsuba_algorithm::add_strings </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>&#160;</td>
<td class="paramname"><em>first</em>, </td>
@@ -171,66 +176,64 @@ Functions</h2></td></tr>
</table>
</div><div class="memdoc">
<p>Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. </p>
<p>Binary addition. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">first</td><td>the input string 1 </td></tr>
<tr><td class="paramname">second</td><td>the input string 2 </td></tr>
<tr><td class="paramname">first,the</td><td>input string 1 </td></tr>
<tr><td class="paramname">second,the</td><td>input string 2 </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the concatenated string </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
<div class="line"><span class="lineno"> 38</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// To store the resulting sum bits</span></div>
<dl class="section return"><dt>Returns</dt><dd>the sum binary string </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
<div class="line"><span class="lineno"> 38</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// to store the resulting sum bits</span></div>
<div class="line"><span class="lineno"> 39</span> </div>
<div class="line"><span class="lineno"> 40</span> int64_t len1 = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 41</span> int64_t len2 = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 42</span> int64_t length = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><span class="lineno"> 40</span> <span class="comment">// make the string lengths equal</span></div>
<div class="line"><span class="lineno"> 41</span> int64_t len1 = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 42</span> int64_t len2 = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">if</span> (len1 &lt; len2) <span class="comment">// make the string lengths equal</span></div>
<div class="line"><span class="lineno"> 45</span> {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><span class="lineno"> 47</span> zero += first;</div>
<div class="line"><span class="lineno"> 48</span> first = zero;</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">if</span> (len1 &lt; len2) {</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><span class="lineno"> 46</span> zero += first;</div>
<div class="line"><span class="lineno"> 47</span> first = zero;</div>
<div class="line"><span class="lineno"> 48</span> zero = <span class="stringliteral">&quot;0&quot;</span>; <span class="comment">// Prevents CI from failing</span></div>
<div class="line"><span class="lineno"> 49</span> }</div>
<div class="line"><span class="lineno"> 50</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
<div class="line"><span class="lineno"> 51</span> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><span class="lineno"> 53</span> zero += second;</div>
<div class="line"><span class="lineno"> 54</span> second = zero;</div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><span class="lineno"> 52</span> zero += second;</div>
<div class="line"><span class="lineno"> 53</span> second = zero;</div>
<div class="line"><span class="lineno"> 54</span> zero = <span class="stringliteral">&quot;0&quot;</span>; <span class="comment">// Prevents CI from failing</span></div>
<div class="line"><span class="lineno"> 55</span> }</div>
<div class="line"><span class="lineno"> 56</span> }</div>
<div class="line"><span class="lineno"> 57</span> int64_t carry = 0;</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i &gt;= 0; i--) {</div>
<div class="line"><span class="lineno"> 59</span> int64_t firstBit = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><span class="lineno"> 60</span> int64_t secondBit = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><span class="lineno"> 61</span> </div>
<div class="line"><span class="lineno"> 62</span> int64_t <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = (firstBit ^ secondBit ^ carry) + <span class="charliteral">&#39;0&#39;</span>; <span class="comment">// sum of 3 bits</span></div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> temp;</div>
<div class="line"><span class="lineno"> 64</span> temp = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/to_string.html">std::to_string</a>(sum);</div>
<div class="line"><span class="lineno"> 65</span> temp += <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = temp;</div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> carry = (firstBit &amp; secondBit) | (secondBit &amp; carry) |</div>
<div class="line"><span class="lineno"> 69</span> (firstBit &amp; carry); <span class="comment">// sum of 3 bits</span></div>
<div class="line"><span class="lineno"> 70</span> }</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">if</span> (carry) {</div>
<div class="line"><span class="lineno"> 73</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="charliteral">&#39;1&#39;</span> + <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; <span class="comment">// adding 1 incase of overflow</span></div>
<div class="line"><span class="lineno"> 74</span> }</div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><span class="lineno"> 76</span>}</div>
<div class="line"><span class="lineno"> 57</span> </div>
<div class="line"><span class="lineno"> 58</span> int64_t length = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><span class="lineno"> 59</span> int64_t carry = 0;</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i &gt;= 0; i--) {</div>
<div class="line"><span class="lineno"> 61</span> int64_t firstBit = first.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><span class="lineno"> 62</span> int64_t secondBit = second.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">at</a>(i) - <span class="charliteral">&#39;0&#39;</span>;</div>
<div class="line"><span class="lineno"> 63</span> </div>
<div class="line"><span class="lineno"> 64</span> int64_t <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = (char(firstBit ^ secondBit ^ carry)) + <span class="charliteral">&#39;0&#39;</span>; <span class="comment">// sum of 3 bits</span></div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.insert(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.begin(), <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>);</div>
<div class="line"><span class="lineno"> 66</span> </div>
<div class="line"><span class="lineno"> 67</span> carry = char((firstBit &amp; secondBit) | (secondBit &amp; carry) |</div>
<div class="line"><span class="lineno"> 68</span> (firstBit &amp; carry)); <span class="comment">// sum of 3 bits</span></div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">if</span> (carry) {</div>
<div class="line"><span class="lineno"> 72</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.insert(<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.begin(), <span class="charliteral">&#39;1&#39;</span>); <span class="comment">// adding 1 incase of overflow</span></div>
<div class="line"><span class="lineno"> 73</span> }</div>
<div class="line"><span class="lineno"> 74</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><span class="lineno"> 75</span>}</div>
<div class="ttc" id="aat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/at.html">std::string::at</a></div><div class="ttdeci">T at(T... args)</div></div>
<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition:</b> fibonacci_sum.cpp:76</div></div>
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">std::string::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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@@ -270,56 +273,45 @@ Here is the call graph for this function:</div>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the multiplicative number value </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
<div class="line"><span class="lineno"> 85</span> int64_t len1 = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 86</span> int64_t len2 = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 87</span> int64_t n = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len1 &lt; len2) {</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len2 - len1; i++) {</div>
<div class="line"><span class="lineno"> 91</span> zero += str1;</div>
<div class="line"><span class="lineno"> 92</span> str1 = zero;</div>
<div class="line"><span class="lineno"> 93</span> }</div>
<div class="line"><span class="lineno"> 94</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 &gt; len2) {</div>
<div class="line"><span class="lineno"> 95</span> zero = <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">for</span> (int64_t i = 0; i &lt; len1 - len2; i++) {</div>
<div class="line"><span class="lineno"> 97</span> zero += str2;</div>
<div class="line"><span class="lineno"> 98</span> str2 = zero;</div>
<div class="line"><span class="lineno"> 99</span> }</div>
<div class="line"><span class="lineno"> 100</span> }</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><span class="lineno"> 102</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 103</span> }</div>
<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 105</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">&#39;0&#39;</span>) * (str2[0] - <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><span class="lineno"> 106</span> }</div>
<div class="line"><span class="lineno"> 107</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
<div class="line"><span class="lineno"> 108</span> int64_t sh = (n - fh); <span class="comment">// second half of string</span></div>
<div class="line"><span class="lineno"> 109</span> </div>
<div class="line"><span class="lineno"> 110</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xl = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, fh); <span class="comment">// first half of first string</span></div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xr = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(fh, sh); <span class="comment">// second half of first string</span></div>
<div class="line"><span class="lineno"> 112</span> </div>
<div class="line"><span class="lineno"> 113</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yl = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, fh); <span class="comment">// first half of second string</span></div>
<div class="line"><span class="lineno"> 114</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yr = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(fh, sh); <span class="comment">// second half of second string</span></div>
<div class="line"><span class="lineno"> 115</span> </div>
<div class="line"><span class="lineno"> 116</span> <span class="comment">// Calculating the three products of inputs of size n/2 recursively</span></div>
<div class="line"><span class="lineno"> 117</span> int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
<div class="line"><span class="lineno"> 118</span> int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
<div class="line"><span class="lineno"> 119</span> int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
<div class="line"><span class="lineno"> 120</span> divide_and_conquer::karatsuba_algorithm::addStrings(Xl, Xr),</div>
<div class="line"><span class="lineno"> 121</span> divide_and_conquer::karatsuba_algorithm::addStrings(Yl, Yr));</div>
<div class="line"><span class="lineno"> 122</span> </div>
<div class="line"><span class="lineno"> 123</span> <span class="keywordflow">return</span> product1 * (1 &lt;&lt; (2 * sh)) +</div>
<div class="line"><span class="lineno"> 124</span> (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
<div class="line"><span class="lineno"> 125</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
<div class="line"><span class="lineno"> 126</span>}</div>
<div class="ttc" id="anamespacekaratsuba__algorithm_html"><div class="ttname"><a href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></div><div class="ttdoc">Functions for the Karatsuba algorithm for fast multiplication</div></div>
<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
<dl class="section return"><dt>Returns</dt><dd>the product number value </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 112</span> {</div>
<div class="line"><span class="lineno"> 113</span> int64_t len1 = str1.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 114</span> int64_t len2 = str2.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 115</span> int64_t n = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(len1, len2);</div>
<div class="line"><span class="lineno"> 116</span> </div>
<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 119</span> }</div>
<div class="line"><span class="lineno"> 120</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 121</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">&#39;0&#39;</span>) * (str2[0] - <span class="charliteral">&#39;0&#39;</span>);</div>
<div class="line"><span class="lineno"> 122</span> }</div>
<div class="line"><span class="lineno"> 123</span> </div>
<div class="line"><span class="lineno"> 124</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
<div class="line"><span class="lineno"> 125</span> int64_t sh = n - fh; <span class="comment">// second half of string</span></div>
<div class="line"><span class="lineno"> 126</span> </div>
<div class="line"><span class="lineno"> 127</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xl = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, 0, fh, n); <span class="comment">// first half of first string</span></div>
<div class="line"><span class="lineno"> 128</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Xr = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, fh, sh, n); <span class="comment">// second half of first string</span></div>
<div class="line"><span class="lineno"> 129</span> </div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yl = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, 0, fh, n); <span class="comment">// first half of second string</span></div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> Yr = <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, fh, sh, n); <span class="comment">// second half of second string</span></div>
<div class="line"><span class="lineno"> 132</span> </div>
<div class="line"><span class="lineno"> 133</span> <span class="comment">// calculating the three products of inputs of size n/2 recursively</span></div>
<div class="line"><span class="lineno"> 134</span> int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
<div class="line"><span class="lineno"> 135</span> int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
<div class="line"><span class="lineno"> 136</span> int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
<div class="line"><span class="lineno"> 137</span> divide_and_conquer::karatsuba_algorithm::add_strings(Xl, Xr),</div>
<div class="line"><span class="lineno"> 138</span> divide_and_conquer::karatsuba_algorithm::add_strings(Yl, Yr));</div>
<div class="line"><span class="lineno"> 139</span> </div>
<div class="line"><span class="lineno"> 140</span> <span class="keywordflow">return</span> product1 * (1 &lt;&lt; (2 * sh)) +</div>
<div class="line"><span class="lineno"> 141</span> (product3 - product1 - product2) * (1 &lt;&lt; sh) +</div>
<div class="line"><span class="lineno"> 142</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
<div class="line"><span class="lineno"> 143</span>}</div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aad9e3edfe156b59fc06a5585403fe0d6"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a></div><div class="ttdeci">std::string safe_substr(const std::string &amp;str, int64_t x1, int64_t x2, int64_t n)</div><div class="ttdoc">Wrapper function for substr that considers leading zeros.</div><div class="ttdef"><b>Definition:</b> karatsuba_algorithm_for_fast_multiplication.cpp:86</div></div>
<div class="ttc" id="anamespacekaratsuba__algorithm_html"><div class="ttname"><a href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></div><div class="ttdoc">Functions for the Karatsuba algorithm for fast multiplication implementation.</div></div>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 164</span> {</div>
<div class="line"><span class="lineno"> 165</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 166</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 167</span>}</div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> karatsuba_algorithm_for_fast_multiplication.cpp:134</div></div>
<div class="fragment"><div class="line"><span class="lineno"> 181</span> {</div>
<div class="line"><span class="lineno"> 182</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 183</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 184</span>}</div>
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> karatsuba_algorithm_for_fast_multiplication.cpp:151</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aad9e3edfe156b59fc06a5585403fe0d6">&#9670;&#160;</a></span>safe_substr()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> divide_and_conquer::karatsuba_algorithm::safe_substr </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> &amp;&#160;</td>
<td class="paramname"><em>str</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>x1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>x2</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>n</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>Wrapper function for substr that considers leading zeros. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">str,the</td><td>binary input string. </td></tr>
<tr><td class="paramname">x1,the</td><td>substr parameter integer 1 </td></tr>
<tr><td class="paramname">x2,the</td><td>substr parameter integer 2 </td></tr>
<tr><td class="paramname">n,is</td><td>the length of the "whole" string: leading zeros + str </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the "safe" substring for the algorithm <em>without</em> leading zeros </dd>
<dd>
"0" if substring spans to leading zeros only </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
<div class="line"><span class="lineno"> 87</span> int64_t len = str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 88</span> </div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len &gt;= n) {</div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">return</span> str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(x1, x2);</div>
<div class="line"><span class="lineno"> 91</span> }</div>
<div class="line"><span class="lineno"> 92</span> </div>
<div class="line"><span class="lineno"> 93</span> int64_t y1 = x1 - (n - len); <span class="comment">// index in str of first char of substring of &quot;whole&quot; string</span></div>
<div class="line"><span class="lineno"> 94</span> int64_t y2 = (x1 + x2 - 1) - (n - len); <span class="comment">// index in str of last char of substring of &quot;whole&quot; string</span></div>
<div class="line"><span class="lineno"> 95</span> </div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">if</span> (y2 &lt; 0) {</div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">return</span> <span class="stringliteral">&quot;0&quot;</span>;</div>
<div class="line"><span class="lineno"> 98</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (y1 &lt; 0) {</div>
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(0, y2 + 1);</div>
<div class="line"><span class="lineno"> 100</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 101</span> <span class="keywordflow">return</span> str.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">substr</a>(y1, x2);</div>
<div class="line"><span class="lineno"> 102</span> }</div>
<div class="line"><span class="lineno"> 103</span>}</div>
<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 134</span> {</div>
<div class="line"><span class="lineno"> 135</span> <span class="comment">// 1st test</span></div>
<div class="line"><span class="lineno"> 136</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">&quot;1&quot;</span>;</div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><span class="lineno"> 138</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;1st test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 139</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 140</span> s11, s12) == 10); <span class="comment">// here the multiplication is 10</span></div>
<div class="line"><span class="lineno"> 141</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;passed&quot;</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"> 142</span> </div>
<div class="line"><span class="lineno"> 143</span> <span class="comment">// 2nd test</span></div>
<div class="line"><span class="lineno"> 144</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">&quot;11&quot;</span>;</div>
<div class="line"><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><span class="lineno"> 146</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;2nd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 147</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 148</span> s21, s22) == 30); <span class="comment">// here the multiplication is 30</span></div>
<div class="line"><span class="lineno"> 149</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;passed&quot;</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"> 150</span> </div>
<div class="line"><span class="lineno"> 151</span> <span class="comment">// 3rd test</span></div>
<div class="line"><span class="lineno"> 152</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">&quot;110&quot;</span>;</div>
<div class="line"><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">&quot;1010&quot;</span>;</div>
<div class="line"><span class="lineno"> 154</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;3rd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 155</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 156</span> s31, s32) == 60); <span class="comment">// here the multiplication is 60</span></div>
<div class="line"><span class="lineno"> 157</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;passed&quot;</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"> 158</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 151</span> {</div>
<div class="line"><span class="lineno"> 152</span> <span class="comment">// 1st test</span></div>
<div class="line"><span class="lineno"> 153</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s11 = <span class="stringliteral">&quot;1&quot;</span>; <span class="comment">// 1</span></div>
<div class="line"><span class="lineno"> 154</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s12 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 155</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;1st test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 156</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 157</span> s11, s12) == 10);</div>
<div class="line"><span class="lineno"> 158</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;passed&quot;</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"> 159</span> </div>
<div class="line"><span class="lineno"> 160</span> <span class="comment">// 2nd test</span></div>
<div class="line"><span class="lineno"> 161</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s21 = <span class="stringliteral">&quot;11&quot;</span>; <span class="comment">// 3</span></div>
<div class="line"><span class="lineno"> 162</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s22 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 163</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;2nd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 164</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 165</span> s21, s22) == 30);</div>
<div class="line"><span class="lineno"> 166</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;passed&quot;</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"> 167</span> </div>
<div class="line"><span class="lineno"> 168</span> <span class="comment">// 3rd test</span></div>
<div class="line"><span class="lineno"> 169</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s31 = <span class="stringliteral">&quot;110&quot;</span>; <span class="comment">// 6</span></div>
<div class="line"><span class="lineno"> 170</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a> s32 = <span class="stringliteral">&quot;1010&quot;</span>; <span class="comment">// 10</span></div>
<div class="line"><span class="lineno"> 171</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;3rd test... &quot;</span>;</div>
<div class="line"><span class="lineno"> 172</span> assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(</div>
<div class="line"><span class="lineno"> 173</span> s31, s32) == 60);</div>
<div class="line"><span class="lineno"> 174</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;passed&quot;</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>
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<p>Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a>
<p>Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> implementation.
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<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> </p>
<div class="textblock"><p >Functions for the <a href="https://en.wikipedia.org/wiki/Karatsuba_algorithm" target="_blank">Karatsuba algorithm for fast multiplication</a> implementation. </p>
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