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Engineering Computer Science EBK DATA STRUCTURES AND ALGORITHMS IN C

Program Plan 1. Below-mentioned variables are used Term- Class consists of the powers and coefficients of variables. Variable- Class which consists of variables and their IDs. Polynomial - Class which consists of a structure that holds all the terms and variables of a polynomial expression. result - object of polynomial which holds the result of multiplication. p1, p2, p3 - objects of terms that hold the intermediate results. coeff - Has the coefficient of variable. power - has the power of variable. 2. Below Mentioned functions are used Operator*()-Operator overloading function which performs the polynomial multiplication. push_back()-a function that adds the variables, their coefficients and powers as terms into the storage stack. erase()-removes the variables, their coefficients and powers as terms from the storage stack. sort()-sorts the variables based on their powers. begin(), end()- functions used for traversing the polynomial expressions in the form of a stack. Program description: This is the modified function of the case study with the operator overloading function operator*. The function given in this exercise will give a special meaning (polynomial multiplication) for the operator “ * ”. Every term of polynomial 1 is multiplied with every term of polynomial 2 and stores the result in a first polynomial. Algorithm Define the classes Variable, Term and Polynomial Get the input polynomials Identify the variables, terms and coefficients of each polynomial Multiply each term of polynomial1 with every term of ploynomial2 Store the result in a new object of Term Add new terms to the object of resultant Polynomial Add the coefficients of the same terms and erase the duplicate terms in the resultant polynomial Return to main() Display the output Modified function #include <iostream> #include <cctype> #include <cstdlib> #include < vector > #include <list> #include <algorithm> using namespace std; class Variable { public: char id; intexp; Variable(){} Variable(char c, int i) { id = c; exp = i; } bool operator== (const Variable& v) const { return id == v.id &&exp == v.exp; } bool operator< (const Variable& v) const { return id < v.id; } }; class Term { public: Term() { coeff = 0; } intcoeff; vector<Variable>vars; bool operator== (const Term&) const; bool operator!= (const Term& term) const { return !(*this == term); } bool operator< (const Term&) const; bool operator> (const Term& term) const { return *this != term && (*this < term); } int min(int n, int m) const { return (n < m) ? n : m; } }; class Polynomial { public: Polynomial() { } Polynomial operator+ (Polynomial&); Polynomial operator* (Polynomial&); void error(char *s) { cerr<< s <<endl; exit(1); } private: list<Term> terms; friendistream& operator>> (istream& in, Polynomial&polyn) { charch, sign, coeffUsed, id; intexp; Term term; in>>ch; while (true) { coeffUsed = 0; if (!isalnum(ch) &&ch != ';' &&ch != '-' &&ch != '+') polyn.error("Wrong character entered2"); sign = 1; while (ch == '-' || ch == '+') { if (ch == '-') sign *= -1; ch = in.get(); if (isspace(ch)) in>>ch; } if (isdigit(ch)) { in.putback(ch); in>>term.coeff; ch = in.get(); term.coeff *= sign; coeffUsed = 1; } else term.coeff = sign; int i=0; for (int i = 0; isalnum(ch); i++) { id = ch; ch = in.get(); if (isdigit(ch)) { in.putback(ch); in>>exp>>ch; } else exp = 1; term.vars.push_back(Variable(id,exp)); } polyn.terms.push_back(term); term.vars.resize(0); if (isspace(ch)) in>>ch; if (ch == ';') if (coeffUsed || i> 0) break; else polyn.error("Term is missing"); else if (ch != '-' &&ch != '+') polyn.error("wrong character entered"); } for (list <Term> ::iterator it = polyn.terms.begin(); it != polyn.terms.end(); it++) if (it->vars.size() > 1) sort(it->vars.begin(),it->vars.end()); return in; } friendostream& operator<< (ostream& out, constPolynomial&polyn) { intafterFirstTerm = 0, i; for (list <Term> ::const_iterator pol = polyn.terms.begin(); pol != polyn.terms.end(); pol++) { out.put(' '); if (pol->coeff< 0) out.put('-'); else if (afterFirstTerm) out.put('+'); afterFirstTerm++; if (abs(pol->coeff) != 1) out<< ' ' << abs(pol->coeff); else if (pol->vars.size() == 0) out<< " 1"; else out.put(' '); for (i = 1; i<= pol->vars.size(); i++) { out<< pol->vars[i-1].id; if (pol->vars[i-1].exp != 1) out<< pol->vars[i-1].exp; } } out<<endl; return out; } }; bool Term::operator== (const Term& term) const { int i; for (i = 0; i< min(vars.size(),term.vars.size()) &&vars[i] == term.vars[i]; i++); return i == vars.size() &&vars.size() == term.vars.size(); } bool Term::operator< (const Term& term2) const { if (vars.size() == 0) return false; else if (term2.vars.size() == 0) return true; for (int i = 0; i< min(vars.size(),term2.vars.size()); i++) if (vars[i].id < term2.vars[i].id) return true; else if (term2.vars[i].id <vars[i].id) return false; else if (vars[i].exp< term2.vars[i].exp) return true; else if (term2.vars[i].exp<vars[i].exp) return false; return ((int)vars.size() - (int)term2.vars.size() < 0) ? true : false; } Polynomial Polynomial::operator+ (Polynomial& polyn2) { Polynomial result; list<Term>::iterator p1, p2; bool erased; for (p1 = terms.begin(); p1 != terms.end(); p1++) { result.terms.push_back(*p1); } for (p1 = polyn2.terms.begin(); p1 != polyn2.terms.end(); p1++) result.terms.push_back(*p1); for (p1 = result.terms.begin(); p1 != result.terms.end();) { for (p2 = p1, p2++, erased = false; p2 != result.terms.end(); p2++) { if (*p1 == *p2) { p1->coeff += p2->coeff; result.terms.erase(p2); if (p1->coeff == 0) result.terms.erase(p1); erased = true; break; } } if (erased) p1 = result.terms.begin(); else p1++; } result.terms.sort(); return result; } Polynomial Polynomial::operator* (Polynomial& polyn2) { Polynomial result; list<Term> ::iterator p1, p2,p3; bool erased; for (p1 = terms.begin(); p1 != terms.end(); p1++) { for (p2 = polyn2.terms.begin(); p2 != polyn2.terms.end(); p2++) // and { int max=p1->vars.size(),c1=0,c2=0; p1->coeff = p1->coeff*p2->coeff; for (vector <Variable> ::iterator it = p1->vars.begin() ; it != p1->vars.end(); ++it) { c2=0; for (vector <Variable> ::iterator it1 = p2->vars.begin() ; it1 != p2->vars.end(); ++it1) { if(p1->vars[c1].id==p2->vars[c2].id) { p1->vars[c1].exp=p1->vars[c1].exp+p2->vars[c2].exp; } c2++; } c1++; } result.terms.push_back(*p1); c1=0,c2=0; for (vector <Variable> ::iterator it = p1->vars.begin(); it != p1->vars.end(); ++it) { c2=0; for (vector <Variable> ::iterator it1 = p2->vars.begin() ; it1 != p2->vars.end(); ++it1) { if(p1->vars[c1].id==p2->vars[c2].id) { p1->vars[c1].exp=p1->vars[c1].exp-p2->vars[c2].exp; } c2++; } c1++; } p1->coeff = p1->coeff/p2->coeff; } } result.terms.sort(); return result; } int main() { Polynomial polyn1, polyn2; cout<< "Enter two polynomials, each ended with a semicolon:\n"; cin>> polyn1 >> polyn2; cout<< "The Sum is:\n" << polyn1 + polyn2; cout<<"The Product is:"<< polyn1 * polyn2; system("pause"); return 0; } Sample Output: Explanation: The program initially finds each term of polynomial 1 using for loop and then in the next for loop terms of polynomial 2 are identified. Since this is a nested for loop coefficient of each variable, in term is multiplied with that of the second polynomial and then coefficients of variables which are having the same term are added and then finally sorted based on the powers of terms to give the final polynomial expression.

Program Plan 1. Below-mentioned variables are used Term- Class consists of the powers and coefficients of variables. Variable- Class which consists of variables and their IDs. Polynomial - Class which consists of a structure that holds all the terms and variables of a polynomial expression. result - object of polynomial which holds the result of multiplication. p1, p2, p3 - objects of terms that hold the intermediate results. coeff - Has the coefficient of variable. power - has the power of variable. 2. Below Mentioned functions are used Operator()-Operator overloading function which performs the polynomial multiplication. push_back()-a function that adds the variables, their coefficients and powers as terms into the storage stack. erase()-removes the variables, their coefficients and powers as terms from the storage stack. sort()-sorts the variables based on their powers. begin(), end()- functions used for traversing the polynomial expressions in the form of a stack. Program description: This is the modified function of the case study with the operator overloading function operator. The function given in this exercise will give a special meaning (polynomial multiplication) for the operator “ * ”. Every term of polynomial 1 is multiplied with every term of polynomial 2 and stores the result in a first polynomial. Algorithm Define the classes Variable, Term and Polynomial Get the input polynomials Identify the variables, terms and coefficients of each polynomial Multiply each term of polynomial1 with every term of ploynomial2 Store the result in a new object of Term Add new terms to the object of resultant Polynomial Add the coefficients of the same terms and erase the duplicate terms in the resultant polynomial Return to main() Display the output Modified function #include <iostream> #include <cctype> #include <cstdlib> #include < vector > #include <list> #include <algorithm> using namespace std; class Variable { public: char id; intexp; Variable(){} Variable(char c, int i) { id = c; exp = i; } bool operator== (const Variable& v) const { return id == v.id &&exp == v.exp; } bool operator< (const Variable& v) const { return id < v.id; } }; class Term { public: Term() { coeff = 0; } intcoeff; vector<Variable>vars; bool operator== (const Term&) const; bool operator!= (const Term& term) const { return !(this == term); } bool operator< (const Term&) const; bool operator> (const Term& term) const { return this != term && (this < term); } int min(int n, int m) const { return (n < m) ? n : m; } }; class Polynomial { public: Polynomial() { } Polynomial operator+ (Polynomial&); Polynomial operator (Polynomial&); void error(char s) { cerr<< s <<endl; exit(1); } private: list<Term> terms; friendistream& operator>> (istream& in, Polynomial&polyn) { charch, sign, coeffUsed, id; intexp; Term term; in>>ch; while (true) { coeffUsed = 0; if (!isalnum(ch) &&ch != ';' &&ch != '-' &&ch != '+') polyn.error("Wrong character entered2"); sign = 1; while (ch == '-' || ch == '+') { if (ch == '-') sign = -1; ch = in.get(); if (isspace(ch)) in>>ch; } if (isdigit(ch)) { in.putback(ch); in>>term.coeff; ch = in.get(); term.coeff = sign; coeffUsed = 1; } else term.coeff = sign; int i=0; for (int i = 0; isalnum(ch); i++) { id = ch; ch = in.get(); if (isdigit(ch)) { in.putback(ch); in>>exp>>ch; } else exp = 1; term.vars.push_back(Variable(id,exp)); } polyn.terms.push_back(term); term.vars.resize(0); if (isspace(ch)) in>>ch; if (ch == ';') if (coeffUsed || i> 0) break; else polyn.error("Term is missing"); else if (ch != '-' &&ch != '+') polyn.error("wrong character entered"); } for (list <Term> ::iterator it = polyn.terms.begin(); it != polyn.terms.end(); it++) if (it->vars.size() > 1) sort(it->vars.begin(),it->vars.end()); return in; } friendostream& operator<< (ostream& out, constPolynomial&polyn) { intafterFirstTerm = 0, i; for (list <Term> ::const_iterator pol = polyn.terms.begin(); pol != polyn.terms.end(); pol++) { out.put(' '); if (pol->coeff< 0) out.put('-'); else if (afterFirstTerm) out.put('+'); afterFirstTerm++; if (abs(pol->coeff) != 1) out<< ' ' << abs(pol->coeff); else if (pol->vars.size() == 0) out<< " 1"; else out.put(' '); for (i = 1; i<= pol->vars.size(); i++) { out<< pol->vars[i-1].id; if (pol->vars[i-1].exp != 1) out<< pol->vars[i-1].exp; } } out<<endl; return out; } }; bool Term::operator== (const Term& term) const { int i; for (i = 0; i< min(vars.size(),term.vars.size()) &&vars[i] == term.vars[i]; i++); return i == vars.size() &&vars.size() == term.vars.size(); } bool Term::operator< (const Term& term2) const { if (vars.size() == 0) return false; else if (term2.vars.size() == 0) return true; for (int i = 0; i< min(vars.size(),term2.vars.size()); i++) if (vars[i].id < term2.vars[i].id) return true; else if (term2.vars[i].id <vars[i].id) return false; else if (vars[i].exp< term2.vars[i].exp) return true; else if (term2.vars[i].exp<vars[i].exp) return false; return ((int)vars.size() - (int)term2.vars.size() < 0) ? true : false; } Polynomial Polynomial::operator+ (Polynomial& polyn2) { Polynomial result; list<Term>::iterator p1, p2; bool erased; for (p1 = terms.begin(); p1 != terms.end(); p1++) { result.terms.push_back(p1); } for (p1 = polyn2.terms.begin(); p1 != polyn2.terms.end(); p1++) result.terms.push_back(p1); for (p1 = result.terms.begin(); p1 != result.terms.end();) { for (p2 = p1, p2++, erased = false; p2 != result.terms.end(); p2++) { if (p1 == p2) { p1->coeff += p2->coeff; result.terms.erase(p2); if (p1->coeff == 0) result.terms.erase(p1); erased = true; break; } } if (erased) p1 = result.terms.begin(); else p1++; } result.terms.sort(); return result; } Polynomial Polynomial::operator (Polynomial& polyn2) { Polynomial result; list<Term> ::iterator p1, p2,p3; bool erased; for (p1 = terms.begin(); p1 != terms.end(); p1++) { for (p2 = polyn2.terms.begin(); p2 != polyn2.terms.end(); p2++) // and { int max=p1->vars.size(),c1=0,c2=0; p1->coeff = p1->coeffp2->coeff; for (vector <Variable> ::iterator it = p1->vars.begin() ; it != p1->vars.end(); ++it) { c2=0; for (vector <Variable> ::iterator it1 = p2->vars.begin() ; it1 != p2->vars.end(); ++it1) { if(p1->vars[c1].id==p2->vars[c2].id) { p1->vars[c1].exp=p1->vars[c1].exp+p2->vars[c2].exp; } c2++; } c1++; } result.terms.push_back(p1); c1=0,c2=0; for (vector <Variable> ::iterator it = p1->vars.begin(); it != p1->vars.end(); ++it) { c2=0; for (vector <Variable> ::iterator it1 = p2->vars.begin() ; it1 != p2->vars.end(); ++it1) { if(p1->vars[c1].id==p2->vars[c2].id) { p1->vars[c1].exp=p1->vars[c1].exp-p2->vars[c2].exp; } c2++; } c1++; } p1->coeff = p1->coeff/p2->coeff; } } result.terms.sort(); return result; } int main() { Polynomial polyn1, polyn2; cout<< "Enter two polynomials, each ended with a semicolon:\n"; cin>> polyn1 >> polyn2; cout<< "The Sum is:\n" << polyn1 + polyn2; cout<<"The Product is:"<< polyn1 * polyn2; system("pause"); return 0; } Sample Output: Explanation: The program initially finds each term of polynomial 1 using for loop and then in the next for loop terms of polynomial 2 are identified. Since this is a nested for loop coefficient of each variable, in term is multiplied with that of the second polynomial and then coefficients of variables which are having the same term are added and then finally sorted based on the powers of terms to give the final polynomial expression.

Solution Summary: The author describes the operator overloading function operator*, which performs the polynomial multiplication.

EBK DATA STRUCTURES AND ALGORITHMS IN C

EBK DATA STRUCTURES AND ALGORITHMS IN C

4th Edition

ISBN: 9781285415017

Author: DROZDEK

Publisher: YUZU

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EBK DATA STRUCTURES AND ALGORITHMS IN C

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