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Documentation for 93a700c7e9
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realstealthninja
@@ -133,11 +133,10 @@ $(function(){initNavTree('da/dd3/karatsuba__algorithm__for__fast__multiplication
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <cstring></code><br />
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<code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for karatsuba_algorithm_for_fast_multiplication.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d2c/karatsuba__algorithm__for__fast__multiplication_8cpp__incl.svg" width="336" height="140"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d0/d2c/karatsuba__algorithm__for__fast__multiplication_8cpp__incl.svg" width="255" height="140"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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</div>
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</div>
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<p><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">Go to the source code of this file.</a></p>
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@@ -145,7 +144,7 @@ Include dependency graph for karatsuba_algorithm_for_fast_multiplication.cpp:</d
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a></td></tr>
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<tr class="memdesc:dd/dba/namespacedivide__and__conquer"><td class="mdescLeft"> </td><td class="mdescRight">for std::vector <br /></td></tr>
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<tr class="memdesc:dd/dba/namespacedivide__and__conquer"><td class="mdescLeft"> </td><td class="mdescRight">for IO operations <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a></td></tr>
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<tr class="memdesc:de/d41/namespacekaratsuba__algorithm"><td class="mdescLeft"> </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>
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@@ -206,46 +205,46 @@ Functions</h2></td></tr>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>the sum binary string </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00037">37</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
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<div class="line"><span class="lineno"> 38</span> std::string result; <span class="comment">// to store the resulting sum bits</span></div>
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<div class="line"><span class="lineno"> 39</span> </div>
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<div class="line"><span class="lineno"> 40</span> <span class="comment">// make the string lengths equal</span></div>
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<div class="line"><span class="lineno"> 41</span> int64_t len1 = first.size();</div>
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<div class="line"><span class="lineno"> 42</span> int64_t len2 = second.size();</div>
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<div class="line"><span class="lineno"> 43</span> std::string zero = <span class="stringliteral">"0"</span>;</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">if</span> (len1 < len2) {</div>
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<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len2 - len1; i++) {</div>
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<div class="line"><span class="lineno"> 46</span> zero += first;</div>
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<div class="line"><span class="lineno"> 47</span> first = zero;</div>
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<div class="line"><span class="lineno"> 48</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
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<div class="line"><span class="lineno"> 49</span> }</div>
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<div class="line"><span class="lineno"> 50</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 > len2) {</div>
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<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len1 - len2; i++) {</div>
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<div class="line"><span class="lineno"> 52</span> zero += second;</div>
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<div class="line"><span class="lineno"> 53</span> second = zero;</div>
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<div class="line"><span class="lineno"> 54</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
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<div class="line"><span class="lineno"> 55</span> }</div>
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<div class="line"><span class="lineno"> 56</span> }</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> int64_t length = std::max(len1, len2);</div>
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<div class="line"><span class="lineno"> 59</span> int64_t carry = 0;</div>
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<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i >= 0; i--) {</div>
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<div class="line"><span class="lineno"> 61</span> int64_t firstBit = first.at(i) - <span class="charliteral">'0'</span>;</div>
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<div class="line"><span class="lineno"> 62</span> int64_t secondBit = second.at(i) - <span class="charliteral">'0'</span>;</div>
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<div class="line"><span class="lineno"> 63</span> </div>
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<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">'0'</span>; <span class="comment">// sum of 3 bits</span></div>
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<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(), sum);</div>
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<div class="line"><span class="lineno"> 66</span> </div>
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<div class="line"><span class="lineno"> 67</span> carry = char((firstBit & secondBit) | (secondBit & carry) |</div>
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<div class="line"><span class="lineno"> 68</span> (firstBit & carry)); <span class="comment">// sum of 3 bits</span></div>
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<div class="line"><span class="lineno"> 69</span> }</div>
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<div class="line"><span class="lineno"> 70</span> </div>
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<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">if</span> (carry) {</div>
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<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">'1'</span>); <span class="comment">// adding 1 incase of overflow</span></div>
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<div class="line"><span class="lineno"> 73</span> }</div>
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<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>
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<div class="line"><span class="lineno"> 75</span>}</div>
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<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00036">36</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 36</span> {</div>
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<div class="line"><span class="lineno"> 37</span> std::string result; <span class="comment">// to store the resulting sum bits</span></div>
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<div class="line"><span class="lineno"> 38</span> </div>
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<div class="line"><span class="lineno"> 39</span> <span class="comment">// make the string lengths equal</span></div>
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<div class="line"><span class="lineno"> 40</span> int64_t len1 = first.size();</div>
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<div class="line"><span class="lineno"> 41</span> int64_t len2 = second.size();</div>
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<div class="line"><span class="lineno"> 42</span> std::string zero = <span class="stringliteral">"0"</span>;</div>
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<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">if</span> (len1 < len2) {</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len2 - len1; i++) {</div>
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<div class="line"><span class="lineno"> 45</span> zero += first;</div>
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<div class="line"><span class="lineno"> 46</span> first = zero;</div>
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<div class="line"><span class="lineno"> 47</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
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<div class="line"><span class="lineno"> 48</span> }</div>
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<div class="line"><span class="lineno"> 49</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 > len2) {</div>
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<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len1 - len2; i++) {</div>
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<div class="line"><span class="lineno"> 51</span> zero += second;</div>
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<div class="line"><span class="lineno"> 52</span> second = zero;</div>
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<div class="line"><span class="lineno"> 53</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
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<div class="line"><span class="lineno"> 54</span> }</div>
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<div class="line"><span class="lineno"> 55</span> }</div>
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<div class="line"><span class="lineno"> 56</span> </div>
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<div class="line"><span class="lineno"> 57</span> int64_t length = std::max(len1, len2);</div>
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<div class="line"><span class="lineno"> 58</span> int64_t carry = 0;</div>
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<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i >= 0; i--) {</div>
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<div class="line"><span class="lineno"> 60</span> int64_t firstBit = first.at(i) - <span class="charliteral">'0'</span>;</div>
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<div class="line"><span class="lineno"> 61</span> int64_t secondBit = second.at(i) - <span class="charliteral">'0'</span>;</div>
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<div class="line"><span class="lineno"> 62</span> </div>
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<div class="line"><span class="lineno"> 63</span> int64_t <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = (char(firstBit ^ secondBit ^ carry)) + <span class="charliteral">'0'</span>; <span class="comment">// sum of 3 bits</span></div>
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<div class="line"><span class="lineno"> 64</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(), sum);</div>
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<div class="line"><span class="lineno"> 65</span> </div>
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<div class="line"><span class="lineno"> 66</span> carry = char((firstBit & secondBit) | (secondBit & carry) |</div>
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<div class="line"><span class="lineno"> 67</span> (firstBit & carry)); <span class="comment">// sum of 3 bits</span></div>
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<div class="line"><span class="lineno"> 68</span> }</div>
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<div class="line"><span class="lineno"> 69</span> </div>
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<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">if</span> (carry) {</div>
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<div class="line"><span class="lineno"> 71</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">'1'</span>); <span class="comment">// adding 1 incase of overflow</span></div>
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<div class="line"><span class="lineno"> 72</span> }</div>
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<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><span class="lineno"> 74</span>}</div>
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<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> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
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<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector< std::valarray< T > > &A)</div><div class="ttdef"><b>Definition</b> <a href="../../d8/d95/vector__ops_8hpp_source.html#l00232">vector_ops.hpp:232</a></div></div>
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</div><!-- fragment -->
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@@ -280,41 +279,41 @@ Functions</h2></td></tr>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>the product number value </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00112">112</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 112</span> {</div>
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<div class="line"><span class="lineno"> 113</span> int64_t len1 = str1.size();</div>
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<div class="line"><span class="lineno"> 114</span> int64_t len2 = str2.size();</div>
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<div class="line"><span class="lineno"> 115</span> int64_t n = std::max(len1, len2);</div>
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<div class="line"><span class="lineno"> 116</span> </div>
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<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">if</span> (n == 0) {</div>
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<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 119</span> }</div>
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<div class="line"><span class="lineno"> 120</span> <span class="keywordflow">if</span> (n == 1) {</div>
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<div class="line"><span class="lineno"> 121</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">'0'</span>) * (str2[0] - <span class="charliteral">'0'</span>);</div>
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<div class="line"><span class="lineno"> 122</span> }</div>
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<div class="line"><span class="lineno"> 123</span> </div>
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<div class="line"><span class="lineno"> 124</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
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<div class="line"><span class="lineno"> 125</span> int64_t sh = n - fh; <span class="comment">// second half of string</span></div>
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<div class="line"><span class="lineno"> 126</span> </div>
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<div class="line"><span class="lineno"> 127</span> std::string Xl = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, 0, fh, n); <span class="comment">// first half of first string</span></div>
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<div class="line"><span class="lineno"> 128</span> std::string Xr = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str1, fh, sh, n); <span class="comment">// second half of first string</span></div>
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<div class="line"><span class="lineno"> 129</span> </div>
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<div class="line"><span class="lineno"> 130</span> std::string Yl = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, 0, fh, n); <span class="comment">// first half of second string</span></div>
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<div class="line"><span class="lineno"> 131</span> std::string Yr = <a class="code hl_function" href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a>(str2, fh, sh, n); <span class="comment">// second half of second string</span></div>
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<div class="line"><span class="lineno"> 132</span> </div>
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<div class="line"><span class="lineno"> 133</span> <span class="comment">// calculating the three products of inputs of size n/2 recursively</span></div>
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<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>
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<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>
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<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>
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<div class="line"><span class="lineno"> 137</span> <a class="code hl_function" href="#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Xl, Xr),</div>
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<div class="line"><span class="lineno"> 138</span> <a class="code hl_function" href="#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Yl, Yr));</div>
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<div class="line"><span class="lineno"> 139</span> </div>
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<div class="line"><span class="lineno"> 140</span> <span class="keywordflow">return</span> product1 * (1 << (2 * sh)) +</div>
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<div class="line"><span class="lineno"> 141</span> (product3 - product1 - product2) * (1 << sh) +</div>
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<div class="line"><span class="lineno"> 142</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
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<div class="line"><span class="lineno"> 143</span>}</div>
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<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aad9e3edfe156b59fc06a5585403fe0d6"><div class="ttname"><a href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a></div><div class="ttdeci">std::string safe_substr(const std::string &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> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00086">karatsuba_algorithm_for_fast_multiplication.cpp:86</a></div></div>
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<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ad76f5cac3ef8dc034f6abb99b64c2b20"><div class="ttname"><a href="#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a></div><div class="ttdeci">std::string add_strings(std::string first, std::string second)</div><div class="ttdoc">Binary addition.</div><div class="ttdef"><b>Definition</b> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00037">karatsuba_algorithm_for_fast_multiplication.cpp:37</a></div></div>
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<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00111">111</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 111</span> {</div>
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<div class="line"><span class="lineno"> 112</span> int64_t len1 = str1.size();</div>
|
||||
<div class="line"><span class="lineno"> 113</span> int64_t len2 = str2.size();</div>
|
||||
<div class="line"><span class="lineno"> 114</span> int64_t n = std::max(len1, len2);</div>
|
||||
<div class="line"><span class="lineno"> 115</span> </div>
|
||||
<div class="line"><span class="lineno"> 116</span> <span class="keywordflow">if</span> (n == 0) {</div>
|
||||
<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 118</span> }</div>
|
||||
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">if</span> (n == 1) {</div>
|
||||
<div class="line"><span class="lineno"> 120</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">'0'</span>) * (str2[0] - <span class="charliteral">'0'</span>);</div>
|
||||
<div class="line"><span class="lineno"> 121</span> }</div>
|
||||
<div class="line"><span class="lineno"> 122</span> </div>
|
||||
<div class="line"><span class="lineno"> 123</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
|
||||
<div class="line"><span class="lineno"> 124</span> int64_t sh = n - fh; <span class="comment">// second half of string</span></div>
|
||||
<div class="line"><span class="lineno"> 125</span> </div>
|
||||
<div class="line"><span class="lineno"> 126</span> std::string Xl = <a class="code hl_function" href="#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"> 127</span> std::string Xr = <a class="code hl_function" href="#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"> 128</span> </div>
|
||||
<div class="line"><span class="lineno"> 129</span> std::string Yl = <a class="code hl_function" href="#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"> 130</span> std::string Yr = <a class="code hl_function" href="#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"> 131</span> </div>
|
||||
<div class="line"><span class="lineno"> 132</span> <span class="comment">// calculating the three products of inputs of size n/2 recursively</span></div>
|
||||
<div class="line"><span class="lineno"> 133</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"> 134</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"> 135</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"> 136</span> <a class="code hl_function" href="#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Xl, Xr),</div>
|
||||
<div class="line"><span class="lineno"> 137</span> <a class="code hl_function" href="#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Yl, Yr));</div>
|
||||
<div class="line"><span class="lineno"> 138</span> </div>
|
||||
<div class="line"><span class="lineno"> 139</span> <span class="keywordflow">return</span> product1 * (1 << (2 * sh)) +</div>
|
||||
<div class="line"><span class="lineno"> 140</span> (product3 - product1 - product2) * (1 << sh) +</div>
|
||||
<div class="line"><span class="lineno"> 141</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
|
||||
<div class="line"><span class="lineno"> 142</span>}</div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aad9e3edfe156b59fc06a5585403fe0d6"><div class="ttname"><a href="#aad9e3edfe156b59fc06a5585403fe0d6">divide_and_conquer::karatsuba_algorithm::safe_substr</a></div><div class="ttdeci">std::string safe_substr(const std::string &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> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00085">karatsuba_algorithm_for_fast_multiplication.cpp:85</a></div></div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ad76f5cac3ef8dc034f6abb99b64c2b20"><div class="ttname"><a href="#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a></div><div class="ttdeci">std::string add_strings(std::string first, std::string second)</div><div class="ttdoc">Binary addition.</div><div class="ttdef"><b>Definition</b> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00036">karatsuba_algorithm_for_fast_multiplication.cpp:36</a></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>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
@@ -337,12 +336,12 @@ Functions</h2></td></tr>
|
||||
<p>Main function. </p>
|
||||
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00181">181</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
|
||||
<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="#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="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00151">karatsuba_algorithm_for_fast_multiplication.cpp:151</a></div></div>
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00180">180</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 180</span> {</div>
|
||||
<div class="line"><span class="lineno"> 181</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
|
||||
<div class="line"><span class="lineno"> 182</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 183</span>}</div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00150">karatsuba_algorithm_for_fast_multiplication.cpp:150</a></div></div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -389,25 +388,25 @@ Functions</h2></td></tr>
|
||||
<dd>
|
||||
"0" if substring spans to leading zeros only </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00086">86</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
|
||||
<div class="line"><span class="lineno"> 87</span> int64_t len = str.size();</div>
|
||||
<div class="line"><span class="lineno"> 88</span> </div>
|
||||
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len >= n) {</div>
|
||||
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">return</span> str.substr(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 "whole" 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 "whole" 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 < 0) {</div>
|
||||
<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">return</span> <span class="stringliteral">"0"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 98</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (y1 < 0) {</div>
|
||||
<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> str.substr(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.substr(y1, x2);</div>
|
||||
<div class="line"><span class="lineno"> 102</span> }</div>
|
||||
<div class="line"><span class="lineno"> 103</span>}</div>
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00085">85</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 85</span> {</div>
|
||||
<div class="line"><span class="lineno"> 86</span> int64_t len = str.size();</div>
|
||||
<div class="line"><span class="lineno"> 87</span> </div>
|
||||
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">if</span> (len >= n) {</div>
|
||||
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> str.substr(x1, x2);</div>
|
||||
<div class="line"><span class="lineno"> 90</span> }</div>
|
||||
<div class="line"><span class="lineno"> 91</span> </div>
|
||||
<div class="line"><span class="lineno"> 92</span> int64_t y1 = x1 - (n - len); <span class="comment">// index in str of first char of substring of "whole" string</span></div>
|
||||
<div class="line"><span class="lineno"> 93</span> int64_t y2 = (x1 + x2 - 1) - (n - len); <span class="comment">// index in str of last char of substring of "whole" string</span></div>
|
||||
<div class="line"><span class="lineno"> 94</span> </div>
|
||||
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">if</span> (y2 < 0) {</div>
|
||||
<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">return</span> <span class="stringliteral">"0"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 97</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (y1 < 0) {</div>
|
||||
<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">return</span> str.substr(0, y2 + 1);</div>
|
||||
<div class="line"><span class="lineno"> 99</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><span class="lineno"> 100</span> <span class="keywordflow">return</span> str.substr(y1, x2);</div>
|
||||
<div class="line"><span class="lineno"> 101</span> }</div>
|
||||
<div class="line"><span class="lineno"> 102</span>}</div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -437,33 +436,33 @@ Functions</h2></td></tr>
|
||||
<p>Self-test implementations. </p>
|
||||
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00151">151</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
|
||||
<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> std::string s11 = <span class="stringliteral">"1"</span>; <span class="comment">// 1</span></div>
|
||||
<div class="line"><span class="lineno"> 154</span> std::string s12 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><span class="lineno"> 155</span> std::cout << <span class="stringliteral">"1st test... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 156</span> assert(<a class="code hl_function" href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><span class="lineno"> 157</span> s11, s12) == 10);</div>
|
||||
<div class="line"><span class="lineno"> 158</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</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> std::string s21 = <span class="stringliteral">"11"</span>; <span class="comment">// 3</span></div>
|
||||
<div class="line"><span class="lineno"> 162</span> std::string s22 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><span class="lineno"> 163</span> std::cout << <span class="stringliteral">"2nd test... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 164</span> assert(<a class="code hl_function" href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><span class="lineno"> 165</span> s21, s22) == 30);</div>
|
||||
<div class="line"><span class="lineno"> 166</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</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> std::string s31 = <span class="stringliteral">"110"</span>; <span class="comment">// 6</span></div>
|
||||
<div class="line"><span class="lineno"> 170</span> std::string s32 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><span class="lineno"> 171</span> std::cout << <span class="stringliteral">"3rd test... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 172</span> assert(<a class="code hl_function" href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><span class="lineno"> 173</span> s31, s32) == 60);</div>
|
||||
<div class="line"><span class="lineno"> 174</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 175</span>}</div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_a7a890d2f26855ada3b9f1d43aec70a86"><div class="ttname"><a href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a></div><div class="ttdeci">int64_t karatsuba_algorithm(std::string str1, std::string str2)</div><div class="ttdoc">The main function implements Karatsuba's algorithm for fast multiplication.</div><div class="ttdef"><b>Definition</b> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00112">karatsuba_algorithm_for_fast_multiplication.cpp:112</a></div></div>
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00150">150</a> of file <a class="el" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html">karatsuba_algorithm_for_fast_multiplication.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 150</span> {</div>
|
||||
<div class="line"><span class="lineno"> 151</span> <span class="comment">// 1st test</span></div>
|
||||
<div class="line"><span class="lineno"> 152</span> std::string s11 = <span class="stringliteral">"1"</span>; <span class="comment">// 1</span></div>
|
||||
<div class="line"><span class="lineno"> 153</span> std::string s12 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><span class="lineno"> 154</span> std::cout << <span class="stringliteral">"1st test... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 155</span> assert(<a class="code hl_function" href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><span class="lineno"> 156</span> s11, s12) == 10);</div>
|
||||
<div class="line"><span class="lineno"> 157</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 158</span> </div>
|
||||
<div class="line"><span class="lineno"> 159</span> <span class="comment">// 2nd test</span></div>
|
||||
<div class="line"><span class="lineno"> 160</span> std::string s21 = <span class="stringliteral">"11"</span>; <span class="comment">// 3</span></div>
|
||||
<div class="line"><span class="lineno"> 161</span> std::string s22 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><span class="lineno"> 162</span> std::cout << <span class="stringliteral">"2nd test... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 163</span> assert(<a class="code hl_function" href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><span class="lineno"> 164</span> s21, s22) == 30);</div>
|
||||
<div class="line"><span class="lineno"> 165</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 166</span> </div>
|
||||
<div class="line"><span class="lineno"> 167</span> <span class="comment">// 3rd test</span></div>
|
||||
<div class="line"><span class="lineno"> 168</span> std::string s31 = <span class="stringliteral">"110"</span>; <span class="comment">// 6</span></div>
|
||||
<div class="line"><span class="lineno"> 169</span> std::string s32 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><span class="lineno"> 170</span> std::cout << <span class="stringliteral">"3rd test... "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 171</span> assert(<a class="code hl_function" href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><span class="lineno"> 172</span> s31, s32) == 60);</div>
|
||||
<div class="line"><span class="lineno"> 173</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 174</span>}</div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_a7a890d2f26855ada3b9f1d43aec70a86"><div class="ttname"><a href="#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a></div><div class="ttdeci">int64_t karatsuba_algorithm(std::string str1, std::string str2)</div><div class="ttdoc">The main function implements Karatsuba's algorithm for fast multiplication.</div><div class="ttdef"><b>Definition</b> <a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp_source.html#l00111">karatsuba_algorithm_for_fast_multiplication.cpp:111</a></div></div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -129,150 +129,149 @@ $(function(){initNavTree('da/dd3/karatsuba__algorithm__for__fast__multiplication
|
||||
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include <cassert></span> </div>
|
||||
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <cstring></span> </div>
|
||||
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <iostream></span> </div>
|
||||
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <vector></span> </div>
|
||||
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span></div>
|
||||
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a> {</div>
|
||||
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a> {</div>
|
||||
<div class="foldopen" id="foldopen00037" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20"> 37</a></span>std::string <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">add_strings</a>(std::string first, std::string second) {</div>
|
||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> std::string result; <span class="comment">// to store the resulting sum bits</span></div>
|
||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
|
||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// make the string lengths equal</span></div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> int64_t len1 = first.size();</div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> int64_t len2 = second.size();</div>
|
||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> std::string zero = <span class="stringliteral">"0"</span>;</div>
|
||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">if</span> (len1 < len2) {</div>
|
||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len2 - len1; i++) {</div>
|
||||
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> zero += first;</div>
|
||||
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> first = zero;</div>
|
||||
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
|
||||
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
|
||||
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 > len2) {</div>
|
||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len1 - len2; i++) {</div>
|
||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> zero += second;</div>
|
||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> second = zero;</div>
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> }</div>
|
||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
|
||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> int64_t length = std::max(len1, len2);</div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> int64_t carry = 0;</div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i >= 0; i--) {</div>
|
||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> int64_t firstBit = first.at(i) - <span class="charliteral">'0'</span>;</div>
|
||||
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> int64_t secondBit = second.at(i) - <span class="charliteral">'0'</span>;</div>
|
||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
|
||||
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> int64_t sum = (char(firstBit ^ secondBit ^ carry)) + <span class="charliteral">'0'</span>; <span class="comment">// sum of 3 bits</span></div>
|
||||
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> result.insert(result.begin(), sum);</div>
|
||||
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
|
||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> carry = char((firstBit & secondBit) | (secondBit & carry) |</div>
|
||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> (firstBit & carry)); <span class="comment">// sum of 3 bits</span></div>
|
||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> }</div>
|
||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">if</span> (carry) {</div>
|
||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> result.insert(result.begin(), <span class="charliteral">'1'</span>); <span class="comment">// adding 1 incase of overflow</span></div>
|
||||
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
|
||||
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">return</span> result;</div>
|
||||
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>}</div>
|
||||
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span></div>
|
||||
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a> {</div>
|
||||
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a> {</div>
|
||||
<div class="foldopen" id="foldopen00036" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20"> 36</a></span>std::string <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">add_strings</a>(std::string first, std::string second) {</div>
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> std::string result; <span class="comment">// to store the resulting sum bits</span></div>
|
||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
|
||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// make the string lengths equal</span></div>
|
||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> int64_t len1 = first.size();</div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> int64_t len2 = second.size();</div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> std::string zero = <span class="stringliteral">"0"</span>;</div>
|
||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (len1 < len2) {</div>
|
||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len2 - len1; i++) {</div>
|
||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> zero += first;</div>
|
||||
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> first = zero;</div>
|
||||
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
|
||||
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> }</div>
|
||||
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len1 > len2) {</div>
|
||||
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">for</span> (int64_t i = 0; i < len1 - len2; i++) {</div>
|
||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> zero += second;</div>
|
||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> second = zero;</div>
|
||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> zero = <span class="stringliteral">"0"</span>; <span class="comment">// Prevents CI from failing</span></div>
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
|
||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> int64_t length = std::max(len1, len2);</div>
|
||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> int64_t carry = 0;</div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">for</span> (int64_t i = length - 1; i >= 0; i--) {</div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> int64_t firstBit = first.at(i) - <span class="charliteral">'0'</span>;</div>
|
||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> int64_t secondBit = second.at(i) - <span class="charliteral">'0'</span>;</div>
|
||||
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
|
||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> int64_t sum = (char(firstBit ^ secondBit ^ carry)) + <span class="charliteral">'0'</span>; <span class="comment">// sum of 3 bits</span></div>
|
||||
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> result.insert(result.begin(), sum);</div>
|
||||
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
|
||||
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> carry = char((firstBit & secondBit) | (secondBit & carry) |</div>
|
||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> (firstBit & carry)); <span class="comment">// sum of 3 bits</span></div>
|
||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> }</div>
|
||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
|
||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">if</span> (carry) {</div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> result.insert(result.begin(), <span class="charliteral">'1'</span>); <span class="comment">// adding 1 incase of overflow</span></div>
|
||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> }</div>
|
||||
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">return</span> result;</div>
|
||||
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span></div>
|
||||
<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6"> 86</a></span>std::string <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">safe_substr</a>(<span class="keyword">const</span> std::string &str, int64_t x1, int64_t x2, int64_t n) {</div>
|
||||
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> int64_t len = str.size();</div>
|
||||
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">if</span> (len >= n) {</div>
|
||||
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">return</span> str.substr(x1, x2);</div>
|
||||
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> }</div>
|
||||
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
|
||||
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> int64_t y1 = x1 - (n - len); <span class="comment">// index in str of first char of substring of "whole" string</span></div>
|
||||
<div class="line"><a id="l00094" name="l00094"></a><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 "whole" string</span></div>
|
||||
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> </div>
|
||||
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">if</span> (y2 < 0) {</div>
|
||||
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">return</span> <span class="stringliteral">"0"</span>;</div>
|
||||
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (y1 < 0) {</div>
|
||||
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordflow">return</span> str.substr(0, y2 + 1);</div>
|
||||
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordflow">return</span> str.substr(y1, x2);</div>
|
||||
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> }</div>
|
||||
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span>}</div>
|
||||
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span></div>
|
||||
<div class="foldopen" id="foldopen00085" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6"> 85</a></span>std::string <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aad9e3edfe156b59fc06a5585403fe0d6">safe_substr</a>(<span class="keyword">const</span> std::string &str, int64_t x1, int64_t x2, int64_t n) {</div>
|
||||
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> int64_t len = str.size();</div>
|
||||
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
|
||||
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">if</span> (len >= n) {</div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">return</span> str.substr(x1, x2);</div>
|
||||
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> }</div>
|
||||
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
|
||||
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> int64_t y1 = x1 - (n - len); <span class="comment">// index in str of first char of substring of "whole" string</span></div>
|
||||
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> int64_t y2 = (x1 + x2 - 1) - (n - len); <span class="comment">// index in str of last char of substring of "whole" string</span></div>
|
||||
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
|
||||
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">if</span> (y2 < 0) {</div>
|
||||
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">return</span> <span class="stringliteral">"0"</span>;</div>
|
||||
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (y1 < 0) {</div>
|
||||
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">return</span> str.substr(0, y2 + 1);</div>
|
||||
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">return</span> str.substr(y1, x2);</div>
|
||||
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> }</div>
|
||||
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span></div>
|
||||
<div class="foldopen" id="foldopen00112" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86"> 112</a></span>int64_t <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(std::string str1, std::string str2) {</div>
|
||||
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> int64_t len1 = str1.size();</div>
|
||||
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> int64_t len2 = str2.size();</div>
|
||||
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> int64_t n = std::max(len1, len2);</div>
|
||||
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
|
||||
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">if</span> (n == 0) {</div>
|
||||
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> }</div>
|
||||
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">if</span> (n == 1) {</div>
|
||||
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">'0'</span>) * (str2[0] - <span class="charliteral">'0'</span>);</div>
|
||||
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div>
|
||||
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> </div>
|
||||
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
|
||||
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> int64_t sh = n - fh; <span class="comment">// second half of string</span></div>
|
||||
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
|
||||
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> std::string 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"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> std::string 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"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
|
||||
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> std::string 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"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> std::string 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"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
|
||||
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="comment">// calculating the three products of inputs of size n/2 recursively</span></div>
|
||||
<div class="line"><a id="l00134" name="l00134"></a><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"><a id="l00135" name="l00135"></a><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"><a id="l00136" name="l00136"></a><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"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Xl, Xr),</div>
|
||||
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Yl, Yr));</div>
|
||||
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> </div>
|
||||
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">return</span> product1 * (1 << (2 * sh)) +</div>
|
||||
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> (product3 - product1 - product2) * (1 << sh) +</div>
|
||||
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
|
||||
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span>}</div>
|
||||
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span></div>
|
||||
<div class="foldopen" id="foldopen00111" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86"> 111</a></span>int64_t <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(std::string str1, std::string str2) {</div>
|
||||
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> int64_t len1 = str1.size();</div>
|
||||
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> int64_t len2 = str2.size();</div>
|
||||
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> int64_t n = std::max(len1, len2);</div>
|
||||
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> </div>
|
||||
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">if</span> (n == 0) {</div>
|
||||
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> }</div>
|
||||
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">if</span> (n == 1) {</div>
|
||||
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keywordflow">return</span> (str1[0] - <span class="charliteral">'0'</span>) * (str2[0] - <span class="charliteral">'0'</span>);</div>
|
||||
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> }</div>
|
||||
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
|
||||
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> int64_t fh = n / 2; <span class="comment">// first half of string</span></div>
|
||||
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> int64_t sh = n - fh; <span class="comment">// second half of string</span></div>
|
||||
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
|
||||
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> std::string 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"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> std::string 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"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
|
||||
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> std::string 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"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> std::string 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"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
|
||||
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// calculating the three products of inputs of size n/2 recursively</span></div>
|
||||
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> int64_t product1 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xl, Yl);</div>
|
||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> int64_t product2 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(Xr, Yr);</div>
|
||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> int64_t product3 = <a class="code hl_namespace" href="../../de/d41/namespacekaratsuba__algorithm.html">karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Xl, Xr),</div>
|
||||
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a>(Yl, Yr));</div>
|
||||
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
|
||||
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">return</span> product1 * (1 << (2 * sh)) +</div>
|
||||
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> (product3 - product1 - product2) * (1 << sh) +</div>
|
||||
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> product2; <span class="comment">// combining the three products to get the final result.</span></div>
|
||||
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span>} <span class="comment">// namespace karatsuba_algorithm</span></div>
|
||||
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span>} <span class="comment">// namespace divide_and_conquer</span></div>
|
||||
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span></div>
|
||||
<div class="foldopen" id="foldopen00151" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 151</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
|
||||
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="comment">// 1st test</span></div>
|
||||
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> std::string s11 = <span class="stringliteral">"1"</span>; <span class="comment">// 1</span></div>
|
||||
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> std::string s12 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> std::cout << <span class="stringliteral">"1st test... "</span>;</div>
|
||||
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> assert(<a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> s11, s12) == 10);</div>
|
||||
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> </div>
|
||||
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// 2nd test</span></div>
|
||||
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> std::string s21 = <span class="stringliteral">"11"</span>; <span class="comment">// 3</span></div>
|
||||
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> std::string s22 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> std::cout << <span class="stringliteral">"2nd test... "</span>;</div>
|
||||
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> assert(<a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> s21, s22) == 30);</div>
|
||||
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> </div>
|
||||
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// 3rd test</span></div>
|
||||
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> std::string s31 = <span class="stringliteral">"110"</span>; <span class="comment">// 6</span></div>
|
||||
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> std::string s32 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> std::cout << <span class="stringliteral">"3rd test... "</span>;</div>
|
||||
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> assert(<a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> s31, s32) == 60);</div>
|
||||
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span>}</div>
|
||||
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span>} <span class="comment">// namespace karatsuba_algorithm</span></div>
|
||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span>} <span class="comment">// namespace divide_and_conquer</span></div>
|
||||
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span></div>
|
||||
<div class="foldopen" id="foldopen00150" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 150</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
|
||||
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="comment">// 1st test</span></div>
|
||||
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> std::string s11 = <span class="stringliteral">"1"</span>; <span class="comment">// 1</span></div>
|
||||
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> std::string s12 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> std::cout << <span class="stringliteral">"1st test... "</span>;</div>
|
||||
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> assert(<a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> s11, s12) == 10);</div>
|
||||
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
|
||||
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// 2nd test</span></div>
|
||||
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> std::string s21 = <span class="stringliteral">"11"</span>; <span class="comment">// 3</span></div>
|
||||
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> std::string s22 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> std::cout << <span class="stringliteral">"2nd test... "</span>;</div>
|
||||
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> assert(<a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> s21, s22) == 30);</div>
|
||||
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
|
||||
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// 3rd test</span></div>
|
||||
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> std::string s31 = <span class="stringliteral">"110"</span>; <span class="comment">// 6</span></div>
|
||||
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> std::string s32 = <span class="stringliteral">"1010"</span>; <span class="comment">// 10</span></div>
|
||||
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> std::cout << <span class="stringliteral">"3rd test... "</span>;</div>
|
||||
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> assert(<a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a>(</div>
|
||||
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> s31, s32) == 60);</div>
|
||||
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> std::cout << <span class="stringliteral">"passed"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span></div>
|
||||
<div class="foldopen" id="foldopen00181" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 181</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
|
||||
<div class="line"><a id="l00182" name="l00182"></a><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"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span>}</div>
|
||||
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span></div>
|
||||
<div class="foldopen" id="foldopen00180" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"><a class="line" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 180</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
|
||||
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</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"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span>}</div>
|
||||
</div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_a7a890d2f26855ada3b9f1d43aec70a86"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a></div><div class="ttdeci">int64_t karatsuba_algorithm(std::string str1, std::string str2)</div><div class="ttdoc">The main function implements Karatsuba's algorithm for fast multiplication.</div><div class="ttdef"><b>Definition</b> <a href="#l00112">karatsuba_algorithm_for_fast_multiplication.cpp:112</a></div></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> <a href="#l00151">karatsuba_algorithm_for_fast_multiplication.cpp:151</a></div></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 &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> <a href="#l00086">karatsuba_algorithm_for_fast_multiplication.cpp:86</a></div></div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ad76f5cac3ef8dc034f6abb99b64c2b20"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a></div><div class="ttdeci">std::string add_strings(std::string first, std::string second)</div><div class="ttdoc">Binary addition.</div><div class="ttdef"><b>Definition</b> <a href="#l00037">karatsuba_algorithm_for_fast_multiplication.cpp:37</a></div></div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00181">karatsuba_algorithm_for_fast_multiplication.cpp:181</a></div></div>
|
||||
<div class="ttc" id="anamespacedivide__and__conquer_html"><div class="ttname"><a href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a></div><div class="ttdoc">for std::vector</div></div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_a7a890d2f26855ada3b9f1d43aec70a86"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86">divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm</a></div><div class="ttdeci">int64_t karatsuba_algorithm(std::string str1, std::string str2)</div><div class="ttdoc">The main function implements Karatsuba's algorithm for fast multiplication.</div><div class="ttdef"><b>Definition</b> <a href="#l00111">karatsuba_algorithm_for_fast_multiplication.cpp:111</a></div></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> <a href="#l00150">karatsuba_algorithm_for_fast_multiplication.cpp:150</a></div></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 &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> <a href="#l00085">karatsuba_algorithm_for_fast_multiplication.cpp:85</a></div></div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ad76f5cac3ef8dc034f6abb99b64c2b20"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ad76f5cac3ef8dc034f6abb99b64c2b20">divide_and_conquer::karatsuba_algorithm::add_strings</a></div><div class="ttdeci">std::string add_strings(std::string first, std::string second)</div><div class="ttdoc">Binary addition.</div><div class="ttdef"><b>Definition</b> <a href="#l00036">karatsuba_algorithm_for_fast_multiplication.cpp:36</a></div></div>
|
||||
<div class="ttc" id="akaratsuba__algorithm__for__fast__multiplication_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00180">karatsuba_algorithm_for_fast_multiplication.cpp:180</a></div></div>
|
||||
<div class="ttc" id="anamespacedivide__and__conquer_html"><div class="ttname"><a href="../../dd/dba/namespacedivide__and__conquer.html">divide_and_conquer</a></div><div class="ttdoc">for IO operations</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>
|
||||
</div><!-- fragment --></div><!-- contents -->
|
||||
</div><!-- doc-content -->
|
||||
|
||||
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