2014年广工离散数学Anyview参考答案

广东工业大学离散数学Anyview习题答案——更新于2014年12月作者Seasand20141.00①试设计一算法，判断元素与集合之间的关系。实现下列函数：/***判断元素与集合之间的关系。元素和集合之间的关系只有两种。*@paramelem：元素*@parampA：集合*@return:如果elem∈pA，则返回TRUE，否则返回FALSE*/BooleanIsInSet(SetElemelem,pSetpA){//Addyourcodehere}//1.00BooleanIsInSet(SetElemelem,pSetpA){//AddyourcodehereSetElem*a=outToBuffer(pA);for(;*a!='\n';a++){if(elem==*a){returntrue;}}returnfalse;}1.01③试设计一算法，实现集合的并运算。实现下列函数：/***进行两个集合的并运算*@parampA：要进行并运算的集合*@parampB：要进行并运算的集合*@return:将pA和pB进行并运算后得到的集合*/pSetSetUnion(pSetpA,pSetpB){//Addyourcodehere}//1.01pSetSetUnion(pSetpA,pSetpB){SetElem*a=outToBuffer(pA);SetElem*b=outToBuffer(pB);pSetpC=createNullSet();inti=0;for(;*b!='\n';b++){directInsertSetElem(pC,*b);}for(a=outToBuffer(pA);*a!='\n';a++){if(isInSet(pB,*a)!=true){directInsertSetElem(pC,*a);}}returnpC;}1.02②试设计一算法，实现集合的交运算。实现下列函数：/***进行两个集合的交运算*@parampA：要进行交运算的集合*@parampB：要进行交运算的集合*@return:将pA和pB进行交运算后得到的集合*/pSetSetIntersection(pSetpA,pSetpB){//Addyourcodehere}//1.02pSetSetIntersection(pSetpA,pSetpB){SetElem*a=outToBuffer(pA);SetElem*b=outToBuffer(pB);pSetpC=createNullSet();for(;*b!='\n';b++){if(isInSet(pA,*b)==true){directInsertSetElem(pC,*b);}}returnpC;}1.03②试设计一算法，实现集合的差运算。实现下列函数：/***进行两个集合的差运算*@parampA：要进行差运算的集合，相当于A-B中的A*@parampB：要进行差运算的集合，相当于A-B中的B*@return:将pA和pB进行差运算后得到的集合*/pSetSetSubtraction(pSetpA,pSetpB){//Addyourcodehere}//1.03pSetSetSubtraction(pSetpA,pSetpB){SetElem*a=outToBuffer(pA);SetElem*b=outToBuffer(pB);pSetpC=createNullSet();for(;*a!='\n';a++){if(isInSet(pB,*a)==true)continue;directInsertSetElem(pC,*a);}returnpC;}1.04②试设计一算法，实现集合的求补集运算。实现下列函数：/***进行集合的求补集运算。*@parampA：要进行求补集运算的集合*@parampI：全集*@return:返回pA相对于pI的补集。注意：有可能存在pA不是PI的子集的情况，*在这种情况下pA的补集不存在，应当返回NULL*/pSetSetComplement(pSetpA,pSetpI){//Addyourcodehere}//1.04pSetSetComplement(pSetpA,pSetpI){SetElem*a=outToBuffer(pA);SetElem*i=outToBuffer(pI);pSetpC=createNullSet();intb=0,k=0;for(;*i!='\n';i++){if(isInSet(pA,*i)==true){b++;continue;}directInsertSetElem(pC,*i);}for(;*a!='\n';a++){if(isInSet(pI,*a)==true){continue;}k++;directInsertSetElem(pC,*i);}if((b==0&&isNullSet(pA)!=true)||(b!=0&&k!=0))returnNULL;if(isNullSet(pA)==true&&isNullSet(pI)!=true)returnpI;elsereturnpC;}1.05②试设计一算法，实现集合的对称差运算。实现下列函数：/***进行集合的对称差运算。*@parampA：需要进行对称差运算的集合*@parampB：需要进行对称差运算的集合*@return:返回pA与pB进行对称差运算后得到的集合。*/pSetSetSysmmetricDifference(pSetpA,pSetpB){//Addyourcodehere}//1.05pSetSetSysmmetricDifference(pSetpA,pSetpB){//AddyourcodeherepSetpS;pS=createNullSet();SetElem*pAElems;SetElem*pBElems;pAElems=outToBuffer(pA);pBElems=outToBuffer(pB);while(*pAElems!='\n'){if(!isInSet(pB,*pAElems)){directInsertSetElem(pS,*pAElems);}pAElems++;}while(*pBElems!='\n'){if(!isInSet(pA,*pBElems)){directInsertSetElem(pS,*pBElems);}pBElems++;}returnpS;}1.06③试设计一算法，判断两个集合之间的包含关系。实现下列函数：/***判断两个集合之间的包含关系。规定集合之间的包含关系为：*真包含，被真包含于，相等。*@parampA：需要进行包含关系判断的集合*@parampB：需要进行包含关系判断的集合*@return:如果pA真包含pB，返回REALINCLUDING;*如果pA被真包含于pB，返回REALINCLUDED;*如果pA等于pB，返回EQUAL；*对于其它情况，返回NOT_INCLUSIVE。*/SetRelationshipStatusSetRelationship(pSetpA,pSetpB){//Addyourcodehere}//1.06SetRelationshipStatusSetRelationship(pSetpA,pSetpB){//AddyourcodeherepSetpS;pS=createNullSet();SetElem*pAElems;SetElem*pBElems;pAElems=outToBuffer(pA);pBElems=outToBuffer(pB);pS=pB;if(isNullSet(pA)&&!isNullSet(pB))returnREALINCLUDED;if(!isNullSet(pA)&&isNullSet(pB))returnREALINCLUDING;if(isNullSet(pA)&&isNullSet(pB))returnEQUAL;if(!isNullSet(pA)&&!isNullSet(pB)){while(*pAElems!='\n'){if(isInSet(pS,*pAElems))pAElems++;else{while(*pBElems!='\n'){if(isInSet(pA,*pBElems))pBElems++;elsereturnNOT_INCLUSIVE;if(*pBElems=='\n')returnREALINCLUDING;}}}if(*pAElems=='\n'){while(*pBElems!='\n')if(isInSet(pA,*pBElems))pBElems++;elsereturnREALINCLUDED;if(*pBElems=='\n')returnEQUAL;}}}1.07⑤试设计一个非递归算法，实现集合的求幂集运算。实现下列函数：/***求一个集合的幂集。*@parampA：需要进行幂集的集合*@return:返回pA的幂集*/pSetFamilyPowerSet(pSetpA){//Addyourcodehere}//1.07pSetmiji(pSetpB,pSetpC){SetElem*pBElems;SetElem*pCElems;pSetpS;pS=createNullSet();pBElems=outToBuffer(pB);pCElems=outToBuffer(pC);while(*pBElems!='\n'){directInsertSetElem(pS,*pBElems);pBElems++;}while(*pCElems!='\n'){if(!isInSet(pB,*pCElems)){directInsertSetElem(pS,*pCElems);}++pCElems;}returnpS;}pFamilyOfSetPowerSet(pSetpA){//Addyourcodehereinti;pSetpI=createNullSet();pFamilyOfSetpF=createNullFamilyOfSet();SetElem*pBElems=outToBuffer(pA);insertToFamilyOfSet(pF,pI);if(isNullSet(pA)==FALSE)while(*pBElems!='\n'){pSetpK=createNullSet();directInsertSetElem(pK,*pBElems);pSet*pS=outFamilyOfSetToBuffer(pF);for(i=0;*(pS+i)!=NULL;i++)insertToFamilyOfSet(pF,miji(pK,*(pS+i)));pBElems++;}returnpF;}1.08④试设计一个递归算法，实现集合的求幂集运算。实现下列函数：/***求一个集合的幂集。*@parampA：需要进行幂集的集合*@return:返回pA的幂集*/pFamilyOfSetPowerSet(pSetpA){//Addyourcodehere}//1.08pSetmiji(pSetpB,pSetpC){SetElem*pBElems;SetElem*pCElems;pSetpS;pS=createNullSet();pBElems=outToBuffer(pB);pCElems=outToBuffer(pC);while(*pBElems!='\n'){directInsertSetElem(pS,*pBElems);pBElems++;}while(*pCElems!='\n'){if(!isInSet(pB,*pCElems)){directInsertSetElem(pS,*pCElems);}++pCElems;}returnpS;}pFamilyOfSetPowerSet(pSetpA){//Addyourcodehereinti;pSetpI=createNullSet();pFamilyOfSetpF=createNullFamilyOfSet();SetElem*pBElems=outToBuffer(pA);insertToFamilyOfSet(pF,pI);if(isNullSet(pA)==FALSE)while(*pBElems!='\n'){pSetpK=createNullSet();directInsertSetElem(pK,*pBElems);pSet*pS=outFamilyOfSetToBuffer(pF);for(i=0;*(pS+i)!=NULL;i++)insertToFamilyOfSet(pF,miji(pK,*(pS+i)));pBElems++;}returnpF;}3.01⑤试设计一个非递归算法，验证一个表达式是不是命题公式(statementformula)。实现下列函数：/***判断一个表达式是不是命题公式。*@parampFormula:要进行判断的表达式。该表达式的最后一个元素为“#”，而且规定*'#'仅用于指示该表达式的结尾，并不属于表达式的一部分。*@return:如果pFormula是命题公式，返回TRUE；否则返回FALSE。*/BooleanIsStatementFormula(pStatementFormulapFormula){//Addyourcodehere}BooleanIsStatementFormula(pStatementFormulapFormula){//AddyourcodehereStatementFormulaSymblespreS,currS,nextS;intleftNum=0,rightNum=0;preS=getCurrentSymbleType(pFormula);switch(preS){caseException:returnfalse;caseConjunction:caseDisjunction:caseImplication:caseEquivalence:caseLeftParenthesis:leftNum++;break;caseRightParenthesis:caseEndOfFormula:returntrue;}nextPos(pFormula);currS=getCurrentSymbleType(pFormula);switch(currS){caseLeftParenthesis:leftNum++;break;caseRightParenthesis:rightNum++;break;casePropositionalVariable:if(preS==PropositionalVariable)returnfalse;}while(nextS!=EndOfFormula){nextPos(pFormula);nextS=getCurrentSymbleType(pFormula);if(nextS==LeftParenthesis)leftNum++;if(nextS==RightParenthesis)rightNum++;if(preS==Exception||currS==Exception||nextS==Exception)returnfalse;if(currS==PropositionalVariable)if(nextS==PropositionalVariable||preS==PropositionalVariable)returnfalse;if(currS==Conjunction||currS==Disjunction||currS==Implication||currS==Equivalence)if((preS!=PropositionalVariable&&preS!=RightParenthesis)||(nextS!=PropositionalVariable&&nextS!=LeftParenthesis&&nextS!=Negation))returnfalse;if(nextS==Negation)if(currS==PropositionalVariable||currS==RightParenthesis)returnfalse;preS=currS;currS=nextS;}if(leftNum!=rightNum)returnfalse;returntrue;}3.02⑤试设计一个递归算法，验证一个表达式是不是命题公式(statementformula)。实现下列函数：/***判断一个表达式是不是命题公式。*@parampFormula:要进行判断的表达式。该表达式的最后一个元素为“#”，而且规定*'#'仅用于指示该表达式的结尾，并不属于表达式的一部分。*@return:如果pFormula是命题公式，返回TRUE；否则返回FALSE。*/BooleanIsStatementFormula(pStatementFormulapFormula){//Addyourcodehere}BooleanFunction(intleftNum,intrightNum,StatementFormulaSymblespreS,StatementFormulaSymblescurrS,StatementFormulaSymblesnextS,pStatementFormulapFormula){nextPos(pFormula);//解释同上题所示nextS=getCurrentSymbleType(pFormula);if(nextS==LeftParenthesis)leftNum++;if(nextS==RightParenthesis)rightNum++;if(preS==Exception||currS==Exception||nextS==Exception)returnfalse;if(currS==PropositionalVariable)if(nextS==PropositionalVariable||preS==PropositionalVariable)returnfalse;if(currS==Conjunction||currS==Disjunction||currS==Implication||currS==Equivalence)if((preS!=PropositionalVariable&&preS!=RightParenthesis)||(nextS!=PropositionalVariable&&nextS!=LeftParenthesis&&nextS!=Negation))returnfalse;if(nextS==Negation)if(currS==PropositionalVariable||currS==RightParenthesis)returnfalse;preS=currS;currS=nextS;if(nextS!=EndOfFormula){returnFunction(leftNum,rightNum,preS,currS,nextS,pFormula);}if(leftNum!=rightNum)returnfalse;returntrue;}BooleanIsStatementFormula(pStatementFormulapFormula){//AddyourcodehereStatementFormulaSymblespreS,currS,nextS;/intleftNum=0,rightNum=0;preS=getCurrentSymbleType(pFormula);switch(preS){caseException:returnfalse;//若取得了公式外的字符，则不是合法的命题公式caseConjunction:returnfalse;caseDisjunction:returnfalse;caseImplication:returnfalse;caseEquivalence:returnfalse;caseLeftParenthesis:leftNum++;break;//若为左括号，则leftNum的值自增一caseRightParenthesis:returnfalse;caseEndOfFormula:returntrue;//若命题公式只有结束符号‘#’，则为合法的命题公式}nextPos(pFormula);//指示器指向下一个字符currS=getCurrentSymbleType(pFormula);switch(currS){caseLeftParenthesis:leftNum++;break;//若为左括号，则leftNum的值自增一caseRightParenthesis:rightNum++;break;//若为有括号，则RightNum的值自增一casePropositionalVariable:if(preS==PropositionalVariable)//当currS为命题变元时，若preS也为命题变元returnfalse;}returnFunction(leftNum,rightNum,preS,currS,nextS,pFormula);//返回值的真假，同时调用函数Function}6.01③试设计一算法，实现集合的卡氏积运算。实现下列函数：/***进行两个集合的卡氏积运算*@parampA：要进行卡氏积运算的集合*@parampB：要进行卡氏积运算的集合*@return:将pA和pB进行卡氏积运算后得到的集合*/pCartersianSetCartesianProduct(pOriginalSetpA,pOriginalSetpB){//Addyourcodehere}CH06EX01pCartersianSetCartesianProduct(pOriginalSetpA,pOriginalSetpB){pOriginalSetElempX=NULL;pOriginalSetElempY=NULL;pOrderedCouplepOrder=NULL;pCartersianSetpCarter=createNullCartersianSet();//创建空的卡氏积集合if(!isNullOriginalSet(pA)&&!isNullOriginalSet(pB)){//判断集合是否为空resetOriginalSet(pA);//使A集合指针指向第一个元素while(!isEndOfOriginalSet(pA)){pX=getCurrentOriginalSetElem(pA);//取得A集合当前指针指向的元素resetOriginalSet(pB);//使B集合指针指向第一个元素while(!isEndOfOriginalSet(pB)){pY=getCurrentOriginalSetElem(pB);//取得B集合当前指针指向的元素pOrder=createOrderedCouple(pX,pY);//构造序偶对OrderedCoupleInsertToCartersianSet(pCarter,pOrder);//将序偶插入到卡氏积集合nextOriginalSetPos(pB);//指针后移}nextOriginalSetPos(pA);//指针后移}}returnpCarter;}6.02②试设计一算法，给定集合A、集合B和集合C，判断集合C是否为A到B的一个二元关系。实现下列函数：/***给定集合A、集合B和集合C，判断集合C是否为A到B的一个二元关系。*@parampA：集合A*@parampB：集合B*@parampC：集合C*@return:如果集合C是A到B的一个二元关系，则返回true，否则返回false。*/booleanisBinaryRelation(pOriginalSetpA,pOriginalSetpB,pCartersianSetpC){//Addyourcodehere}CH06EX02booleanisBinaryRelation(pOriginalSetpA,pOriginalSetpB,pCartersianSetpC){pOriginalSetElempX=NULL;pOriginalSetElempY=NULL;pOrderedCouplepZ=NULL;pOrderedCouplepOrder=NULL;pCartersianSetpCarter=createNullCartersianSet();//创建空的卡氏积集合booleanb=true;if(!isNullOriginalSet(pA)&&!isNullOriginalSet(pB)){//判断集合是否为空resetOriginalSet(pA);//使A集合指针指向第一个元素while(!isEndOfOriginalSet(pA)){pX=getCurrentOriginalSetElem(pA);//取得A集合当前指针指向的元素resetOriginalSet(pB);//使B集合指针指向第一个元素while(!isEndOfOriginalSet(pB)){pY=getCurrentOriginalSetElem(pB);//取得B集合当前指针指向的元素pOrder=createOrderedCouple(pX,pY);//构造序偶对OrderedCoupleInsertToCartersianSet(pCarter,pOrder);//将序偶插入到卡氏积集合nextOriginalSetPos(pB);//指针后移}nextOriginalSetPos(pA);//指针后移}}resetCartersianSet(pC);//使C集合指针指向第一个元素while(!isNullCartersianSet(pC)&&!isEndOfCartersianSet(pC)){pZ=getCurrentCartersianSetElem(pC);//取得C集合当前指针指向的元素b=isInCartersianSet(pCarter,pZ);//判断序偶是否在pCArter集合中if(b==false)break;nextCartersianSetPos(pC);//指针后移}returnb;}6.03②试设计一算法，求集合A上的恒等关系。实现下列函数：/***给定集合A，求集合A上的恒等关系。*@parampSet：原始集合*@return:集合A上的恒等关系。*/pCartersianSetIdentityRelation(pOriginalSetpSet){//Addyourcodehere}CH06EX03pCartersianSetIdentityRelation(pOriginalSetpSet){pOriginalSetElempX=NULL;pOrderedCouplepOrder=NULL;pCartersianSetpCarter=createNullCartersianSet();//创建空的卡氏积集合if(!isNullOriginalSet(pSet)){//判断集合是否为空resetOriginalSet(pSet);//使集合指针指向第一个元素while(!isEndOfOriginalSet(pSet)){pX=getCurrentOriginalSetElem(pSet);//取得集合当前指针指向的元素pOrder=createOrderedCouple(pX,pX);//构造序偶对OrderedCoupleInsertToCartersianSet(pCarter,pOrder);//将序偶插入到卡氏积集合nextOriginalSetPos(pSet);//指针后移}}returnpCarter;}6.04③试设计一算法，求两个卡氏积集合的复合运算。实现下列函数：/***给定两个集合，求该两个集合的复合运算。*@parampA：卡氏积集合*@parampB：卡氏积集合*@return:pA与pB的复合运算结果。*/pCartersianSetCompositeOperation(pCartersianSetpA,pCartersianSetpB){//Addyourcodehere}CH06EX04pCartersianSetCompositeOperation(pCartersianSetpA,pCartersianSetpB){pOriginalSetElempX;pOriginalSetElempY;pOriginalSetElempXX;pOriginalSetElempYY;pOrderedCouplepOrderA=NULL;pOrderedCouplepOrderB=NULL;pOrderedCouplepOrder=NULL;pCartersianSetpCarter=createNullCartersianSet();//创建空的卡氏积集合if(!isNullCartersianSet(pA)&&!isNullCartersianSet(pB)){resetCartersianSet(pA);//使A集合指针指向第一个元素while(!isEndOfCartersianSet(pA)){pOrderA=getCurrentCartersianSetElem(pA);//取得A集合当前指针指向的元素resetCartersianSet(pB);//使B集合指针指向第一个元素while(!isEndOfCartersianSet(pB)){pOrderB=getCurrentCartersianSetElem(pB);//取得B集合当前指针指向的元素pX=getFirstElemOfOrderedCouple(pOrderA);//取得A序偶的第一元pY=getSecondElemOfOrderedCouple(pOrderA);//取得A序偶的第二元pXX=getFirstElemOfOrderedCouple(pOrderB);//取得B序偶的第一元pYY=getSecondElemOfOrderedCouple(pOrderB);//取得B序偶的第二元if(pY==pXX){pOrder=createOrderedCouple(pX,pYY);//构造序偶对OrderedCoupleInsertToCartersianSet(pCarter,pOrder);//将序偶插入到卡氏积集合}nextCartersianSetPos(pB);//指针后移}nextCartersianSetPos(pA);//指针后移}}returnpCarter;}6.05②试设计一算法，求一个关系的逆运算。实现下列函数：/***求一个关系的逆运算。*@parampA：卡氏积集合*@return:pA的逆运算结果。*/pCartersianSetInverseOperation(pCartersianSetpA){//Addyourcodehere}CH06EX05pCartersianSetInverseOperation(pCartersianSetpA){pOriginalSetElempX;pOriginalSetElempY;pOrderedCouplepOrderA=NULL;pOrderedCouplepOrder=NULL;pCartersianSetpCarter=createNullCartersianSet();//创建空的卡氏积集合if(!isNullCartersianSet(pA)){resetCartersianSet(pA);//使A集合指针指向第一个元素while(!isEndOfCartersianSet(pA)){pOrderA=getCurrentCartersianSetElem(pA);//取得A集合当前指针指向的元素pX=getFirstElemOfOrderedCouple(pOrderA);//取得A序偶的第一元pY=getSecondElemOfOrderedCouple(pOrderA);//取得A序偶的第二元pOrder=createOrderedCouple(pY,pX);//构造序偶对OrderedCoupleInsertToCartersianSet(pCarter,pOrder);//将序偶插入到卡氏积集合nextCartersianSetPos(pA);//指针后移}}returnpCarter;}6.06④试设计一算法，对某集合A上的一个二元关系，求该关系的幂运算。实现下列函数：/***求一个关系的幂运算。*@parampA：原始集合*@parampBinaryRelationR：pA上的关系R*@paramn：幂运算的次数，且n>=0*@return:pBinaryRelationSet的n次幂运算结果。*/pCartersianSetPowOperation(pOriginalSetpA,pCartersianSetpBinaryRelationR,intn){//Addyourcodehere}CH06EX06pCartersianSetCompositeOperation(pCartersianSetpA,pCartersianSetpB){pCartersianSetpC=createNullCartersianSet();for(resetCartersianSet(pA);!isEndOfCartersianSet(pA);nextCartersianSetPos(pA)){for(resetCartersianSet(pB);!isEndOfCartersianSet(pB);nextCartersianSetPos(pB))if(isEqualOriginalSetElem(getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pA)),getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pB))))//获取A卡氏积中序偶的第二元//获取第二元OrderedCoupleInsertToCartersianSet(pC,createOrderedCouple(getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pA)),getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pB))));}returnpC;}pCartersianSetPowOperation(pOriginalSetpA,pCartersianSetpBinaryRelationR,intn){pCartersianSetpC=createNullCartersianSet();pC=copyCartersianSet(pBinaryRelationR);if(n==0){for(resetOriginalSet(pA);!isEndOfOriginalSet(pA);nextOriginalSetPos(pA)){for(resetOriginalSet(pA);!isEndOfOriginalSet(pA);nextOriginalSetPos(pA))OrderedCoupleInsertToCartersianSet(pC,createOrderedCouple(getCurrentOriginalSetElem(pA),getCurrentOriginalSetElem(pA)));}returnpC;}if(n==1){returnpBinaryRelationR;}for(inti=1;i<n;i++){pC=CompositeOperation(pC,pBinaryRelationR);}returnpC;}6.07②试设计一算法，对某集合A上的一个二元关系R，判断R是否具有自反性。实现下列函数：/***判断一个关系是否具有自反性。*@parampA：原始集合*@parampBinaryRelationR：卡氏积集合，该集合是一个pA上的二元关系*@return:如果pBinaryRelationSet具有自反性；则返回true，否则返回false。*/booleanIsReflexivity(pOriginalSetpA,pCartersianSetpBinaryRelationR){//Addyourcodehere}CH06EX07booleanIsReflexivity(pOriginalSetpA,pCartersianSetpBinaryRelationR){pOriginalSetElempX=NULL;pOrderedCouplepOrder=NULL;booleanb=false;if(!isNullOriginalSet(pA)){//判断集合是否为空resetOriginalSet(pA);//使集合指针指向第一个元素while(!isEndOfOriginalSet(pA)){pX=getCurrentOriginalSetElem(pA);//取得集合当前指针指向的元素pOrder=createOrderedCouple(pX,pX);//构造序偶对b=isInCartersianSet(pBinaryRelationR,pOrder);if(b==false){break;}nextOriginalSetPos(pA);//指针后移}}else{returntrue;}returnb;}6.08②试设计一算法，对某集合A上的一个二元关系R，判断R是否具有反自反性。实现下列函数：/***判断一个关系是否具有反自反性。*@parampA：原始集合*@parampBinaryRelationR：卡氏积集合，该集合是一个pA上的二元关系*@return:如果pBinaryRelationSet具有反自反性；则返回true，否则返回false。*/booleanIsAntiReflexivity(pOriginalSetpA,pCartersianSetpBinaryRelationR){//Addyourcodehere}CH06EX08booleanIsAntiReflexivity(pOriginalSetpA,pCartersianSetpBinaryRelationR){pOriginalSetElempX=NULL;pOrderedCouplepOrder=NULL;booleanb=true;if(!isNullOriginalSet(pA)){//判断集合是否为空resetOriginalSet(pA);//使集合指针指向第一个元素while(!isEndOfOriginalSet(pA)){pX=getCurrentOriginalSetElem(pA);//取得集合当前指针指向的元素pOrder=createOrderedCouple(pX,pX);//构造序偶对b=isInCartersianSet(pBinaryRelationR,pOrder);if(b==true){break;}nextOriginalSetPos(pA);//指针后移}}else{returntrue;}return!b;}6.09③试设计一算法，对某集合A上的一个二元关系R，判断R是否具有自反性或者反自反性。在实际运算中，A无需给出。实现下列函数：/***判断一个关系是否具有自反性或者反自反性。对一个关系R是否具有自反性或者反自反性，*有四种可能：是自反的；是反自反的；既是自反的也是反自反的、*既不是自反的也不是反自反的。*@parampA：原始集合*@parampBinaryRelationR：卡氏积集合，该集合是一个pA上的二元关系*@return:返回一个Reflexivity_Type枚举类型值。*如果pBinaryRelationSet具有自反性，则返回REFLEXIVITY;*如果pBinaryRelationSet具有反自反性，则返回ANTI_REFLEXIVITY;*如果pBinaryRelationSet既具有自反性，也具有反自反性，则返回*REFLEXIVITY_AND_ANTI_REFLEXIVITY;*如果pBinaryRelationSet既不具有自反性，也不具有反自反性，则返回*NOT_REFLEXIVITY_AND_NOT_ANTI_REFLEXIVITY;*/Reflexivity_TypeDetermineReflexivity0609(pOriginalSetpA,pCartersianSetpBinaryRelationR){//Addyourcodehere}CH06EX09Reflexivity_TypeDetermineReflexivity(pOriginalSetpA,pCartersianSetpBinaryRelationR){pOriginalSetElempX=NULL;pOrderedCouplepOrder=NULL;booleanb;inti=0,j=0;if(!isNullOriginalSet(pA)){//判断集合是否为空resetOriginalSet(pA);//使集合指针指向第一个元素while(!isEndOfOriginalSet(pA)){i++;pX=getCurrentOriginalSetElem(pA);//取得集合当前指针指向的元素pOrder=createOrderedCouple(pX,pX);//构造序偶对b=isInCartersianSet(pBinaryRelationR,pOrder);if(b==true){j++;}nextOriginalSetPos(pA);//指针后移}}else{returnREFLEXIVITY_AND_ANTI_REFLEXIVITY;}if(i==j){returnREFLEXIVITY;}elseif(j==0){returnANTI_REFLEXIVITY;}else{returnNOT_REFLEXIVITY_AND_NOT_ANTI_REFLEXIVITY;}returnREFLEXIVITY_AND_ANTI_REFLEXIVITY;}6.10④试设计一算法，对某集合A上的一个二元关系R，判断R是否具有对称性或者反对称性。实现下列函数：/***判断一个关系是否具有对称性或者反对称性。对一个关系R是否具有对称性或者反对称性，*有四种可能：是对称的；是反对称的；；既是对称的也是反对称的；既不是对称的也不是*反对称的。*@parampBinaryRelationR：卡氏积集合，该集合是一个pA上的二元关系*@return:返回一个Symmetry_Type枚举类型值。*如果pBinaryRelationSet具有对称性，则返回SYMMETRY;*如果pBinaryRelationSet具有反对称性，则返回ANTI_SYMMETRY;*如果pBinaryRelationSet既具有对称性，也具有对称性，则返回*SYMMETRY_AND_ANTI_SYMMETRY;*如果pBinaryRelationSet既不具有对称性，也不具有反对称性，则返回*NOT_SYMMETRY_AND_NOT_ANTI_SYMMETRY;*/Symmetry_TypeDetermineSymmetry(pCartersianSetpBinaryRelationR){//Addyourcodehere}CH06EX10Symmetry_TypeDetermineSymmetry(pCartersianSetpBinaryRelationR){inta,b,c;a=b=c=0;if(!isNullCartersianSet(pBinaryRelationR)){for(resetCartersianSet(pBinaryRelationR);!isEndOfCartersianSet(pBinaryRelationR);nextCartersianSetPos(pBinaryRelationR)){if(isInCartersianSet(pBinaryRelationR,createOrderedCouple(getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR)),getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR))))&&!isEqualOriginalSetElem(getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR)),getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR)))){a++;}if(isInCartersianSet(pBinaryRelationR,createOrderedCouple(getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR)),getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR))))&&isEqualOriginalSetElem(getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR)),getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR)))){b++;}if(!isInCartersianSet(pBinaryRelationR,createOrderedCouple(getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR)),getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pBinaryRelationR))))){c++;}}{if(c==0&&a!=0)returnSYMMETRY;if(a==0&&c==0)returnSYMMETRY_AND_ANTI_SYMMETRY;if(a==0&&c!=0)returnANTI_SYMMETRY;elsereturnNOT_SYMMETRY_AND_NOT_ANTI_SYMMETRY;}}if(isNullCartersianSet(pBinaryRelationR))returnSYMMETRY_AND_ANTI_SYMMETRY;}6.11④试设计一算法，对某集合A上的一个二元关系R，判断R是否具有传递性。实现下列函数：/***判断一个关系是否具有传递性。*@parampA：原始集合*@parampBinaryRelationR：卡氏积集合，该集合是一个pA上的二元关系*@return:如果pBinaryRelationR具有传递性，则返回true，否则返回false*/booleanIsTransitive(pOriginalSetpA,pCartersianSetpBinaryRelationR){//Addyourcodehere}booleanIsTransitive(pOriginalSetpA,pCartersianSetpBinaryRelationR){pOriginalSetElemFirst1,Second1;pOriginalSetElemFirst2,Second2;pCartersianSetpB=copyCartersianSet(pBinaryRelationR);pCartersianSetpC=copyCartersianSet(pBinaryRelationR);if(!isNullCartersianSet(pBinaryRelationR)){for(resetCartersianSet(pC);!isEndOfCartersianSet(pC);nextCartersianSetPos(pC)){First1=getFirstElemOfOrderedCouple(getCurrentCartersianSetElem(pC));Second1=getSecondElemOfOrderedCouple(getCurrentCartersianSetElem(pC));for(resetCartersianSet(pB);!isEndOfCartersianSet(pB);nextCartersianSetPos(pB)){First2=getFirstElemOfOrderedC