C++: STL linked list - representing a Polynomial - c++

Question

I'm working on a problem which requires me to use the STL linked list class to represent a polynomials. I've made a good start on getting the class definition, however I'm a little confused as to where to go next (novice programmer - please excuse my potential ignorance).
class Polynomial
{
public:
Polynomial(); //Default constructor
Polynomial(pair<double,int>); //Specified constructor
void add(Polynomial);
Polynomial multiply(Polynomial);
void print();
private:
list<int> order_terms;
list<double> coeffs;
};
I have two questions:
1) It seems more elegant to store the terms and coefficients as a pair - however I'm unsure how to get that working using the STL list.
2) Regarding the add member function, I'm unsure how to implement it such that I can define a Polynomial and then add terms to it like this:
Polynomial test(pair<3.14,0>);
Polynomial test_2(pair<2,1>);
test.add(test_2);
The main thing I'm having issues with understanding how to access the terms stored in the other object and linking it to the first Polynomial.
Any help greatly appreciated.
EDIT: Code for the add() function - currently not working
void Polynomial::add(const Polynomial& rhs)
{
//Perform some sort of sort here to make sure both lists are correctly sorted
//Traverse the list of terms to see if there's an existing nth order
//term in the list on the left-hand-side polynomial.
list<int>::iterator itr;
list<int>::iterator itl;
for(itr=rhs->terms.begin(); itr!=rhs->terms.end(); itr++)
{
bool match=0;
//See if there's an existing terms, if so add to it
for(itl=terms.begin(); itl!=terms.end(); itl++)
{
if(*itl->second)==*itr->second)
{
*itl->first+=*itr->first;
match = 1;
}
}
//If not, this is the first nth order term so just push it onto the list
if(!match){ terms.push_back(*itr); //Perform the sort again }
}

Answer 1

To use a pair in a list you can do:
list<pair<double, int> > - note the space between the >. It's also nice to do something like
typedef pair<double, int> TermCoeff;
list<TermCoeff> equation;
To sort a list:
list<TermCoeff> equation;
// insert items
equation.sort(coeff_compare);
There are pre-defined comparator functions for a pair in the <utility> header. They compare the first elements and then the second ones if first is equal.
For your second question you should remember that an object of a class can access the member variables of an object of the same class, even if they are private. If you don't leave any gaps in your coefficients (in the constructor fill in missing ones with the second value of the pair set to 0) this means your add method can look like:
Polynomial& Polynomial::add(const Polynomial& rhs) {
// constructor should sort all terms and enforce that all terms are present
// lhs = current object (left hand side of operator)
// rhs = other object (right hand side of operator)
// example: lhs.add(rhs)
list<TermCoeff>::const_iterator rhs_iter = rhs.terms.begin();
list<TermCoeff>::iterator lhs_iter = terms.begin();
while(rhs_iter != rhs.terms.end()) {
if (lhs_iter != terms.end()) {
// add because we aren't at the end of current object's terms
lhs_iter->second += rhs_iter->second;
++lhs_iter;
} else {
// insert because we are at the end of current object's terms
terms.push_back(*rhs_iter);
lhs_iter = terms.end(); // keep the iterator at the end
}
++rhs_iter;
}
return *this;
}
int main (int argc, const char * argv[])
{
list<TermCoeff> first, second;
first.push_back(TermCoeff(0, 0.0)); // empty
first.push_back(TermCoeff(1, 5.0));
first.push_back(TermCoeff(2, 5.0));
second.push_back(TermCoeff(0, 6.0));
second.push_back(TermCoeff(1, 0.0)); // empty
second.push_back(TermCoeff(2, 8.0));
second.push_back(TermCoeff(3, 9.0));
Polynomial first_eq(first);
Polynomial second_eq(second);
first_eq.add(second_eq);
first_eq.print();
return 0;
}
Note that I returned a reference to the current object. This is a nice thing to do in an addition method because then you can chain additions:
first.add(second).add(third);
or
first.add(second.add(third));

Answer 2

Others have explained list<pair<double, int> > (and I like shelleybutterfly's suggestion to derive Polynomial from the list, except that I'd make it protected, not public, so that outside code is not too free to mess with the contents of the list).
But the add function is a little tricky, because adding two polynomials doesn't generally mean concatenating them or adding their terms together. The operation is actually more like merging-- and you'll soon see that the lists must be sorted. (In fact, it's more natural to represent polynomials as vectors, but I guess that's not the assignment.)
I suggest you implement Polynomial::add(pair<double, int>), first, then implement the other one (add(Polynomial &)) in terms of that.
I don't want to spell it out too much, since this looks like homework. Is this enough to point you in the right direction?
EDIT:
Your new code looks correct (albeit inefficient) if you fix a couple of bugs:
void Polynomial::add(const Polynomial& rhs)
{
// Don't forget to implement the sorting routine.
// The iterators must be of the correct type. And itr must be const,
// since you have declared rhs to be a const reference. The compiler
// will not allow you to have an iterator with the power to alter
// a const thing.
list<pair<double,int> >::const_iterator itr;
list<pair<double,int> >::iterator itl;
for(itr=rhs->terms.begin(); itr!=rhs->terms.end(); itr++)
{
bool match=false;
for(itl=terms.begin(); itl!=terms.end(); itl++)
{
// You have an extra parenthesis here, and too much dereferencing.
if(itl->second == itr->second)
{
itl->first+=itr->first;
match = true;
}
}
if(!match)
{ terms.push_back(*itr); //Perform the sort again
} // Be careful not to catch the closing brace in a comment
}
}
Once it is working, you can think about ways to make it cleaner and more efficient. For example, if you insert the new term in the right place, the list will always be in the right order and there will be no need for a sort routine.

Answer 3

As for using a pair, why not use a list<pair<double, int>> (list< pair<double, int> > for older compilers)? Or you could even define a separate class to hold your pair like so:
// example is implemented inline, you could always pull it out to
// your source file; although it's even possible that you could
// do everything inline if you want to allow just including a
// header but not having to link a separate file.
class CoeffAndTerm : public pair<double,int>
{
public:
// if you need it you should put extra functions here to
// provide abstractions:
double getTotalValue()
{
return first * second;
}
}
and then use
list<CoeffAndTerm> Polynomial;
as your variable, or even
// same stuff goes for this class RE: the inline function definitions
class Polynomial : public list<CoeffAndTerm>
{
public:
// same goes here for the abstraction stuff maybe things
// like in your current Polynomial class; assuming some
// functions here ...
Polynomial Multiply(Polynomial other)
{
Polynomial Result = new Polynomial();
for (int i=0; i < size(); ++i)
{
Result.addCoeffAndTerm(
new CoeffAndTerm(
other.first * first,
other.second * second
);
}
return Result;
}
}
so that you've got Polynomial being a derivation of the list itself. Not sure the exact usage of the Polynomial, so it's hard for me to speak to which makes more sense, but I like this way better as a general rule for a type such as this; seems to be that the polynomial "is a" list of coefficient and terms, it doesn't just "have" one. :) I'm sure that's debatable, and again it depends on the actual usage of your code.
for the operations, you could do reference returns, as in one of the other examples, but I have implemented the multiply without modifying the existing value, which you could also do for Add, Subtract, etc. so, assuming First, Second, Third, etc. are other polynomials
Polynomial Result = First.Multiply(Second).Add(Third).Subtract(Fourth);
you could also implement copy constructor, operator =, operator +, operator *, operator / and then do things that look like normal math:
Polynomial Result = First * Second + Third - Fourth;

Answer 4

While it's possible to use std::pair to group the term order and coefficient, I would recomment against it: it's not very readable - it's not clear what 'first' and 'second' means, and C++ will implicitly cast between numeric types - and you get no benefit from the added functionality of pair (ordering).
Instead, create a class like:
class Term {
double coeff_;
int exp_;
public:
Term(double coeff, int exp): coeff_(coeff), exp_(exp) {}
double coefficient() const { return coeff; }
int exponent() const { return exp; }
[...]
};
class Polynomial {
std::list<Term> terms;
[...]
Making fields public (e.g. by using struct or publicly deriving from pair) for performance reasons is not a good idea: inline constructor, getters and setters are just as fast as reading or writing the variable directly, and they have the advantage of encapsulating the implementation.
For that matter, you may want to create separate types to wrap polynomial coefficients and exponents themselves, in order to avoid mixing up numeric types, and performing nonsensical operations e.g.:
class Coefficient {
double val;
public:
explicit Coefficient(double value): val(value) {}
double getValue() { return val; }
double operator*(double rhs) { return val*rhs; }
Coefficient operator+(const Coefficient& rhs) {
return Coefficient(val+rhs.val);
}
[...]
};
etc.

Answer 5

Another possibility: instead of using a class, you could make as struct to represent the term and coefficient; you still can define methods on it just like a class, but the members are public by default which may make sense for efficiency reasons, especially if you're doing a lot of processing with these things. So, maybe:
struct CoeffAndTerm
{
int Term;
double Coeff;
private CoeffAndTerm(int parTerm, double parCoeff)
{
Term = parTerm;
Coeff = parCoeff;
}
public static CoeffAndTerm Make(int parTerm, double parCoeff)
{
return new CoeffAndTerm(parTerm, parCoeff);
}
// etc. and otherwise you can just do things as given in the example
// with the classes deriving from list<pair<int, double>>, e.g.,
// silly example again
public double getTotalValue()
{
return first * second;
}
}
and same applies otherwise as in the first example, again giving more direct access than that example had, but still allowing for the abstraction methods to be placed directly on the object
struct Polynomial : public list<CoeffAndTerm>
{
list<CoeffAndTerm> CoefficientsAndTerms;
Polynomial Multiply(Polynomial other)
{
Polynomial Result = new Polynomial();
for (int i=0; i < size(); ++i)
{
Result.addCoeffAndTerm(
new CoeffAndTerm(
other.first * first,
other.second * second
);
}
return Result;
}
// etc.
}