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    <p>By the way, if you have large sorted sets std::set_intersection is not the fastest algorithm. std::set_intersection takes up to 2*(m+n)-1 comparisons but algorithms like the one from Baeza-Yates can be faster. For small m, Baeza-Yates is O(m * log(n)), while for n = alpha * m it is O(n). The basic idea is to do a kind of 2 way binary search.</p> <p><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.91.7899&amp;rep=rep1&amp;type=pdf" rel="nofollow noreferrer">http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.91.7899&amp;rep=rep1&amp;type=pdf</a></p> <p>Experimental Analysis of a Fast Intersection Algorithm for Sorted Sequences Ricardo Baeza-Yates and Alejandro Salinger</p> <p>OR</p> <p>R. Baeza-Yates. A Fast Set Intersection Algorithm for Sorted Sequences. In Proceedings of the 15th Annual Symposium on Combinatorial Pattern Matching (CPM 2004), Springer LNCS 3109, pp 400-408, Istanbul, Turkey, July 2004.</p> <p>Below is an explanation and an implementation by Erik Frey where he shows significantly faster results than std::set_intersection with a binary probe. I have not tried his code yet. <br> <a href="http://fawx.com/" rel="nofollow noreferrer">http://fawx.com/</a> <br></p> <ol> <li>Pick the median element, A, in the smaller set. </li> <li>Search for its insertion-position element, B, in the larger set. </li> <li>If A and B are equal, append the element to the result. </li> <li>Repeat steps 1-4 on non-empty subsets on either side of elements A and B.</li> </ol> <p>;</p> <p><pre><code></p> <p>/* * baeza_intersect */ template&lt; template class Probe, class RandomAccessIterator, class OutputIterator> void baeza_intersect(RandomAccessIterator begin1, RandomAccessIterator end1, RandomAccessIterator begin2, RandomAccessIterator end2, OutputIterator out) { RandomAccessIterator probe1, probe2;</p> <p>if ( (end1 - begin1) &lt; ( end2 - begin2 ) ) { if ( begin1 == end1 ) return; probe1 = begin1 + ( ( end1 - begin1 ) >> 1 ); probe2 = lower_bound&lt; Probe >( begin2, end2, *probe1 ); baeza_intersect&lt; Probe >(begin1, probe1, begin2, probe2, out); // intersect left if (! (probe2 == end2 || *probe1 &lt; *probe2 )) *out++ = *probe2++; baeza_intersect&lt; Probe >(++probe1, end1, probe2, end2, out); // intersect right } else { if ( begin2 == end2 ) return; probe2 = begin2 + ( ( end2 - begin2 ) >> 1 ); probe1 = lower_bound&lt; Probe >( begin1, end1, *probe2 ); baeza_intersect&lt; Probe >(begin1, probe1, begin2, probe2, out); // intersect left if (! (probe1 == end1 || *probe2 &lt; *probe1 )) *out++ = *probe1++; baeza_intersect&lt; Probe >(probe1, end1, ++probe2, end2, out); // intersect right } }</p> <p>/* * with a comparator */ template&lt; template class Probe, class RandomAccessIterator, class OutputIterator, class Comparator > void baeza_intersect(RandomAccessIterator begin1, RandomAccessIterator end1, RandomAccessIterator begin2, RandomAccessIterator end2, OutputIterator out, Comparator cmp) { RandomAccessIterator probe1, probe2;</p> <pre><code> if ( (end1 - begin1) &lt; ( end2 - begin2 ) ) { if ( begin1 == end1 ) return; probe1 = begin1 + ( ( end1 - begin1 ) &gt;&gt; 1 ); probe2 = lower_bound&lt; Probe &gt;( begin2, end2, *probe1, cmp ); baeza_intersect&lt; Probe &gt;(begin1, probe1, begin2, probe2, out, cmp); // intersect left if (! (probe2 == end2 || cmp( *probe1, *probe2 ) )) *out++ = *probe2++; baeza_intersect&lt; Probe &gt;(++probe1, end1, probe2, end2, out, cmp); // intersect right } else { if ( begin2 == end2 ) return; probe2 = begin2 + ( ( end2 - begin2 ) &gt;&gt; 1 ); probe1 = lower_bound&lt; Probe &gt;( begin1, end1, *probe2, cmp ); baeza_intersect&lt; Probe &gt;(begin1, probe1, begin2, probe2, out, cmp); // intersect left if (! (probe1 == end1 || cmp( *probe2, *probe1 ) )) *out++ = *probe1++; baeza_intersect&lt; Probe &gt;(probe1, end1, ++probe2, end2, out, cmp); // intersect right } } </code></pre> <p>// probe.hpp</p> <p>/** * binary probe: pick the next element by choosing the halfway point between low and high */ template&lt; class RandomAccessIterator, class T > struct binary_probe { RandomAccessIterator operator()(RandomAccessIterator begin, RandomAccessIterator end, const T &amp; value) { return begin + ( (end - begin) >> 1); } };</p> <p>/** * lower_bound: like stl's lower_bound but with different kinds of probing * note the appearance of the rare template parameter template! */ template&lt; template class Probe, class RandomAccessIterator, class T > RandomAccessIterator lower_bound(RandomAccessIterator begin, RandomAccessIterator end, const T &amp; value) { RandomAccessIterator pit; Probe&lt; RandomAccessIterator, T > pfunc; // probe-functor (wants to get func'd up)</p> <p>while ( begin &lt; end ) { pit = pfunc(begin, end, value); if ( *pit &lt; value ) begin = pit + 1; else end = pit; } return begin; }</p> <p>/* * this time with a comparator! */ template&lt; template class Probe, class RandomAccessIterator, class T, class Comparator > RandomAccessIterator lower_bound(RandomAccessIterator begin, RandomAccessIterator end, const T &amp; value, Comparator cmp) { RandomAccessIterator pit; Probe&lt; RandomAccessIterator, T > pfunc;</p> <p>while ( begin &lt; end ) { pit = pfunc(begin, end, value); if ( cmp(*pit, value) ) begin = pit + 1; else end = pit; } return begin; } </pre></code></p>
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