#include #include #include #include #include #include //using namespace std; /* set Theory demonstrates common set operations using randomly generated int vector elements. it also displays some common stl functionalities. code by Synovicc Germain created on 25/01/18 */ std::ostream_iterator oitr(std::cout, " "); //universal set std::vector universalSet(20,0); //predicate int UsetElements() { static int value = 0; return value++; } //predicate inline int setABElm() { return rand()%20; } void setUnion(std::vector&,std::vector&,std::vector&); void setIntersection(std::vector&,std::vector&,std::vector&); void setComplement(std::vector&,std::vector&); void setDifference(std::vector&,std::vector&); void displaySet(std::vector&); void cardinality(std::vector&, const char*); int main() { srand(time(NULL)); //populate universalSet std::generate( universalSet.begin(), universalSet.end(), UsetElements ); std::cout<<"universal set:\n"; std::copy( universalSet.begin(), universalSet.end(), oitr ); std::vector setA(1+rand()%11,0); std::vector setB(1+rand()%11,0); std::vector csAuB; std::vector csAnB; std::generate( setA.begin(), setA.end(), setABElm ); std::generate( setB.begin(), setB.end(), setABElm ); std::cout<<"\n\nsetA:\n"; displaySet(setA); std::cout<<"\n\nsetB:\n"; displaySet(setB); std::cout<<"\n\nset A union set B\n"; setUnion(setA,setB,csAuB); std::cout<<"\n\nset A intersection set B\n"; setIntersection(setA,setB,csAnB); std::cout<<"\n\nset A complement:\n"; setComplement(universalSet,setA); std::cout<<"\n\nset B complement:\n"; setComplement(universalSet,setB); std::cout<<"\n\nset A - set B:\n"; setComplement(setA,setB); std::cout<<"\n\nset B - set A:\n"; setComplement(setB,setA); cardinality(universalSet,"U"); cardinality(setA,"A"); cardinality(setB,"B"); cardinality(csAuB,"AuB"); cardinality(csAnB,"AnB"); std::cout<<"\n\nMore operations coming soon!"; } void setUnion(std::vector& sA,std::vector& sB, std::vector& csAuB){ std::vector setAuB; std::set_union( sA.begin(), sA.end(), sB.begin(), sB.end(), std::back_inserter(setAuB) ); std::sort( setAuB.begin(), setAuB.end() ); std::copy( setAuB.begin(), std::unique( setAuB.begin(), setAuB.end() ), oitr ); std::copy( setAuB.begin(), std::unique( setAuB.begin(), setAuB.end() ), std::back_inserter(csAuB) ); } void setIntersection(std::vector& sA,std::vector& sB,std::vector& csAnB){ std::vector setAnB; std::set_intersection( sA.begin(), sA.end(), sB.begin(), sB.end(), std::back_inserter(setAnB) ); if(setAnB.size() == 0) std::cout<<"empty set"; else std::copy( setAnB.begin(), std::unique( setAnB.begin(), setAnB.end() ), oitr ); std::copy( setAnB.begin(), std::unique( setAnB.begin(), setAnB.end() ), std::back_inserter(csAnB) ); } void displaySet(std::vector& sX) { std::sort( sX.begin(), sX.end() ); std::copy( sX.begin(), sX.end(), oitr ); } void setComplement(std::vector&sU, std::vector&sX){ std::vector sXc; std::set_difference( sU.begin(), sU.end(), sX.begin(), sX.end(), std::back_inserter(sXc) ); std::sort( sXc.begin(), sXc.end() ); std::copy( sXc.begin(), sXc.end(), oitr ); } void cardinality(std::vector&sX, const char* nme){ std::cout<<"\n\nCardinality n( "<

Set Theory