Expert: Zlatko - 10/28/2010

Question
QUESTION: Hi Zlatko,

Check out my code now, I think the polynomial printing works
now. I used all if statements to do it.

Thanks,
Mike


#include <iostream>
using namespace std;

class Polynomial
{
public:
  Polynomial(int t1 = 0, int t2 = 0, int t3 = 0, int t4 =
0, int t5 = 0);

   Polynomial calcSum(const Polynomial& p2);
   Polynomial calcDifference(const Polynomial& p2);
   Polynomial calcProduct(const Polynomial& p2);
  
  void printPolynomial();

private:
  int c4, c3, c2, c1, c0;
};

Polynomial :: Polynomial(int t1, int t2, int t3, int t4, int
t5)
{
  c4 = t1;
  c3 = t2;
  c2 = t3;
  c1 = t4;
  c0 = t5;
}

void Polynomial :: printPolynomial()
{
  cout << "\n-------------------------------\n";
  int coef[5] = {c0, c1, c2, c3, c4};
 
  for(int exp = 4; exp >= 0; --exp)
   {
    if(coef[exp] == 1)
       cout << "x^" << exp;
    
    if(coef[exp] == -1)
      cout << coef[exp] << "x^" << exp;
    
    if(coef[4] == 0 && coef[3] == 0 && coef[2] == 0 &&
coef[1] == 0 && coef[0] == 0 && exp == 4)
       cout << "0";

    if(coef[exp] > 0 && coef[exp] != 1 && (exp != 1 &&
exp != 0 && exp != 4))
       cout << "+" << coef[exp] << "x^" << exp;
         
    if(coef[exp] > 0 && coef[exp] != 1 && (exp == 1 ||
exp == 0))
       cout << "+" << coef[exp] << "x";

    if(coef[exp] > 0 && coef[exp] != 1 && exp == 4)
       cout << coef[exp] << "x^" << exp;
       
    if(coef[exp] < 0 && coef[exp] != -1 && (exp != 1
&& exp != 0))
       cout << coef[exp] << "x^" << exp;

    if(coef[exp] < 0 && coef[exp] != -1 && (exp == 1
|| exp == 0))
       cout << "+" << coef[exp] << "x";
  }
   cout << endl;
}

Polynomial Polynomial :: calcSum(const Polynomial& p2)
{
  Polynomial sum;
 
  sum.c4 = c4 + p2.c4;
  sum.c3 = c3 + p2.c3;
  sum.c2 = c2 + p2.c2;
  sum.c1 = c1 + p2.c1;
  sum.c0 = c0 + p2.c0;
 
  return sum;
}

Polynomial Polynomial :: calcDifference(const Polynomial&
p2)
{
  Polynomial difference;
 
  difference.c4 = c4 - p2.c4;
  difference.c3 = c3 - p2.c3;
  difference.c2 = c2 - p2.c2;
  difference.c1 = c1 - p2.c1;
  difference.c0 = c0 - p2.c0;
 
  return difference;
}

Polynomial Polynomial:: calcProduct(const Polynomial& p2)
{
  Polynomial product;
  product.c4 = c2*p2.c2;
  product.c3 = c2*p2.c1 + c1*p2.c2;
  product.c2 = c2*p2.c0 + c1*p2.c1 + c0*p2.c2;
  product.c1 = c1*p2.c0 + c0*p2.c1;
  product.c0 = c0*p2.c0;
  
  return product;
}

int main()
{
  Polynomial p1(1, 2, 3, -4, 5);
  Polynomial p2(-2, 3, -5, 6, 9);
  Polynomial p3(0, 0, 1, 2, 3);
  Polynomial p4(0, 0, 1, 2, 3);

  
  cout << "The first polynomial";
  p1.printPolynomial();
  cout << "\nThe second polynomial";
  p2.printPolynomial();

  Polynomial sum = p1.calcSum(p2);
  cout << "\nThe sum";
  sum.printPolynomial();

  Polynomial difference = p1.calcDifference(p2);
  cout << "\nThe difference";
  difference.printPolynomial();
  cout << endl;

  cout << "\n===============================";
  cout << "\n\nThe first quadratic polynomial";
  p3.printPolynomial();
  cout << "\nThe second quadratic polynomial";
  p4.printPolynomial();

  Polynomial product = p3.calcProduct(p4);
  cout << "\nThe product";
  product.printPolynomial();
  cout << endl;
  return 0;
}

ANSWER: Mike !
I'm impressed. I really am. It's pretty good but I can make some suggestions. The program is printing out things like x^1 and x^0. Mathematically that is correct, but usually we write x and just the constant coefficient for x^0

Also there is an error here
-------------------------------
COEFF [0 0 0 0 -2]
+-2x

-------------------------------
COEFF [0 0 0 -2 0]
+-2x

Both polys print the same thing.

You will have an easier time with the code if you print characters like x and ^ individually instead of trying to print an entire term in one cout statement. By term, I mean the whole group consisting of sign, coefficient, x, ^, and the exponent number.

I can see you put a lot of though into the problem. Have a look at my solution if you like, then (as my professor used to say) go do something brainless for an hour (he said to watch Gilligan's Island). Then come back and try to redo it yourself. According to him, looking at other people's code was not cheating if you do something brainless for an hour before going back to coding. I agree with him. I learn a lot by reading other people's code.

void Polynomial :: printPolynomial()
{
   cout << "\n--------------------------\n";
   // Create an array of coefficients
   int coef[5] = {c0, c1, c2, c3, c4};
   // Print out the coefficients for debugging
   cout << "[Coeff " << c4 << " " << c3 << " " << c2 << " " << c1 << " " << c0 << "]" << endl;

   /* first is a flag. It is useful to know if the first
   coefficient has been printed out. Why ? Because if you're
   working on the first coefficient, and it is positive, you don't
   want the leading "+" being printed.
   Also, if you get to the end of the print function and
   first is still true, then it means that nothing has
   been printed so far
   */
   bool first = true;

   /* Work from the highest exponent to the lowest. Notice that
   the exp variable can also be used to print the number
   after the exponent sign "^"
   */
   for(int exp = 4; exp >= 0; --exp)
   {
       if (coef[exp] != 0) // don't print 0x
       {
         if (coef[exp] == -1 && exp != 0)
         {
         /* for -1, just print -, not -1,
         so we get -x instead of -1x, BUT, if
         the exponent is 0, then DO print -1. That is done
         at line AAA
         */
         cout << '-';
         }
         else if (coef[exp] > 0)
         {
         if (!first)
         {
         /* DO print leading + sign on a postitive
         coefficient, unless it is the first coefficient
         */
         cout << "+";
         }
         if (coef[exp] == 1 && exp == 0 || coef[exp] != 1)
         {
         /*
         for positive coefficient, print a coefficient of 1
         only if exponent is 0. This prevents printing things like 1x
         */
         cout << coef[exp];
         }
         }
         else
         {
         cout << coef[exp]; // This is line AAA
         }

         // finally print the x for non zero exponents
         if (exp >= 1) cout << "x";
         // print exponent for x^2 and greater, but not x^1 or x^0
         if (exp >= 2) cout << "^" << exp;
         first = false; // important to set first to false
       }
   }
   // if after all exponents, nothing has been printed, then just print 0
   if (first)
   {
       cout << "0";
   }
   cout << endl;
}


---------- FOLLOW-UP ----------

QUESTION: Hi Zlatko,

I think it really is a good idea if you do look at what
someone else did, especially if there are shorter / more
intuitive ways of solving the same problem.

Sometimes I feel that there are things that I did not think
of, and sometimes those little things make all the
difference when it's actually a really simple thing that you
could have thought of but you just didn't for whatever the
reason may be.

So thank you very much for your help. I believe your way is
good too, maybe a bit better strategy than what I attempted,
but both seem logical so it's fine I guess

Here is my code once more, I believe it works now fine. The
bug that you've found, I tested and that combination does
work fine.  

#include <iostream>
using namespace std;

class Polynomial
{
public:
 Polynomial(int t1= 0, int t2= 0, int t3= 0, int t4= 0, int
t5= 0);

   Polynomial calcSum(const Polynomial& p2);
   Polynomial calcDifference(const Polynomial& p2);
   Polynomial calcProduct(const Polynomial& p2);
 
   void printPolynomial();

private:
 int c4, c3, c2, c1, c0;
};

Polynomial :: Polynomial(int t1, int t2, int t3, int t4, int
t5)
{
 c4 = t1;
 c3 = t2;
 c2 = t3;
 c1 = t4;
 c0 = t5;
}

void Polynomial :: printPolynomial()
{
 cout << "\n-------------------------------\n";
 int coef[5] = {c0, c1, c2, c3, c4};
 
 for(int exp = 4; exp >= 0; --exp)
   {
     if(coef[exp]==1)
         cout << "x^" << exp;
     
     if(coef[exp]==-1)
       cout << "-x^" << exp;

    if(coef[exp]>0 && exp==0)
       cout << "+" << coef[exp];
    else if (coef[exp] < 0 && exp==0)
       cout << coef[exp];
     
     if(coef[4]==0 && coef[3]==0 && coef[2]==0 &&
coef[1]==0 && coef[0]==0 && exp==4)
         cout << "0";

     if(coef[exp]>0 && coef[exp]!=1 && (exp!=1 && exp!=0 &&
exp!=4))
         cout << "+" << coef[exp] << "x^" << exp;
         
     if(coef[exp]>0 && coef[exp]!=1 && (exp==1))
         cout << "+" << coef[exp] << "x";
    else if(coef[exp]>0 && coef[exp]!=1 && exp==4)
       cout << coef[exp] << "x^" << exp;
       
     if(coef[exp]<0 && coef[exp]!=-1 && (exp!=1 && exp!=0))
         cout << coef[exp] << "x^" << exp;
    else if(coef[exp]<0 && coef[exp]!=-1 && (exp==1))
         cout << coef[exp] << "x";
   }
   cout << endl;
}

Polynomial Polynomial :: calcSum(const Polynomial& p2)
{
 Polynomial sum;
 
 sum.c4 = c4 + p2.c4;
 sum.c3 = c3 + p2.c3;
 sum.c2 = c2 + p2.c2;
 sum.c1 = c1 + p2.c1;
 sum.c0 = c0 + p2.c0;
 
 return sum;
}

Polynomial Polynomial :: calcDifference(const Polynomial&
p2)
{
 Polynomial difference;
 
 difference.c4 = c4 - p2.c4;
 difference.c3 = c3 - p2.c3;
 difference.c2 = c2 - p2.c2;
 difference.c1 = c1 - p2.c1;
 difference.c0 = c0 - p2.c0;
 
 return difference;
}

Polynomial Polynomial:: calcProduct(const Polynomial& p2)
{
 Polynomial product;
 product.c4 = c2*p2.c2;
 product.c3 = c2*p2.c1 + c1*p2.c2;
 product.c2 = c2*p2.c0 + c1*p2.c1 + c0*p2.c2;
 product.c1 = c1*p2.c0 + c0*p2.c1;
 product.c0 = c0*p2.c0;
 
 return product;
}

int main()
{
   Polynomial p1(0, 0, 0, 0, -2);
   Polynomial p2(-2, 3, -5, 6, 9);
   Polynomial p3(0, 0, 1, 2, 3);
   Polynomial p4(0, 0, 1, 2, 3);

   
   cout << "The first polynomial";
   p1.printPolynomial();
   cout << "\nThe second polynomial";
   p2.printPolynomial();

   Polynomial sum = p1.calcSum(p2);
   cout << "\nThe sum";
   sum.printPolynomial();

   Polynomial difference = p1.calcDifference(p2);
   cout << "\nThe difference";
   difference.printPolynomial();
   cout << endl;

   cout << "\n===============================\n";
   cout << "\n\nThe first quadratic polynomial";
   p3.printPolynomial();
   cout << "\nThe second quadratic polynomial";
   p4.printPolynomial();

   Polynomial product = p3.calcProduct(p4);
   cout << "\nThe product";
   product.printPolynomial();
   cout << endl;
   return 0;
}  

Answer
Hi Mike

Ok, I found 3 errors, and I made a minor change to fix them. The following are errors, because they are mathematically incorrect.

-------------------------------
[Coeff 0 0 0 0 1]
x^0+1

-------------------------------
[Coeff 0 0 0 0 -1]
-x^0-1

-------------------------------
[Coeff 1 1 1 1 1]
x^4x^3x^2x^1x^0+1

My 3 fixes are commented in the code below. Just look for zm

void Polynomial :: printPolynomial()
{
   cout << "\n-------------------------------\n";
   // cout << "[Coeff " << c4 << " " << c3 << " " << c2 << " " << c1 << " " << c0 << "]" << endl;

   int coef[5] = {c0, c1, c2, c3, c4};

   for(int exp = 4; exp >= 0; --exp)
   {
       if(exp != 0 && coef[exp]==1) // zm added exp != 0
       {
         cout << "+x^" << exp; // zm added + sign
       }

       if(exp != 0 && coef[exp]==-1) // zm added exp != 0
         cout << "-x^" << exp;

       if(coef[exp]>0 && exp==0)
         cout << "+" << coef[exp];
       else if (coef[exp] < 0 && exp==0)
         cout << coef[exp];

       if(coef[4]==0 && coef[3]==0 && coef[2]==0 &&
         coef[1]==0 && coef[0]==0 && exp==4)
         cout << "0";

       if(coef[exp]>0 && coef[exp]!=1 && (exp!=1 && exp!=0 &&
         exp!=4))
         cout << "+" << coef[exp] << "x^" << exp;

       if(coef[exp]>0 && coef[exp]!=1 && (exp==1))
         cout << "+" << coef[exp] << "x";
       else if(coef[exp]>0 && coef[exp]!=1 && exp==4)
         cout << coef[exp] << "x^" << exp;

       if(coef[exp]<0 && coef[exp]!=-1 && (exp!=1 && exp!=0))
         cout << coef[exp] << "x^" << exp;
       else if(coef[exp]<0 && coef[exp]!=-1 && (exp==1))
         cout << coef[exp] << "x";
   }
   cout << endl;
}


With the fixes, the polynomials all print mathematically correct, although there are some awkward constructs like leading plus signs and x^1, but that's OK. Mathematically it is correct.

For your reference, here is the full test output. My eyes glaze over from looking at it. You can see that programming is all about the details.



-------------------------------
[Coeff 0 0 0 0 0]
0

-------------------------------
[Coeff 0 0 0 0 1]
+1

-------------------------------
[Coeff 0 0 0 1 0]
+x^1

-------------------------------
[Coeff 0 0 1 0 0]
+x^2

-------------------------------
[Coeff 0 1 0 0 0]
+x^3

-------------------------------
[Coeff 1 0 0 0 0]
+x^4

-------------------------------
[Coeff 0 0 0 0 -1]
-1

-------------------------------
[Coeff 0 0 0 -1 0]
-x^1

-------------------------------
[Coeff 0 0 -1 0 0]
-x^2

-------------------------------
[Coeff 0 -1 0 0 0]
-x^3

-------------------------------
[Coeff -1 0 0 0 0]
-x^4

-------------------------------
[Coeff 0 0 0 0 2]
+2

-------------------------------
[Coeff 0 0 0 2 0]
+2x

-------------------------------
[Coeff 0 0 2 0 0]
+2x^2

-------------------------------
[Coeff 0 2 0 0 0]
+2x^3

-------------------------------
[Coeff 2 0 0 0 0]
2x^4

-------------------------------
[Coeff 0 0 0 0 -2]
-2

-------------------------------
[Coeff 0 0 0 -2 0]
-2x

-------------------------------
[Coeff 0 0 -2 0 0]
-2x^2

-------------------------------
[Coeff 0 -2 0 0 0]
-2x^3

-------------------------------
[Coeff -2 0 0 0 0]
-2x^4

-------------------------------
[Coeff 1 1 1 1 1]
+x^4+x^3+x^2+x^1+1

-------------------------------
[Coeff 1 1 1 1 0]
+x^4+x^3+x^2+x^1

-------------------------------
[Coeff 1 1 1 0 0]
+x^4+x^3+x^2

-------------------------------
[Coeff 1 1 0 0 0]
+x^4+x^3

-------------------------------
[Coeff 1 0 0 0 0]
+x^4

-------------------------------
[Coeff 0 0 0 0 1]
+1

-------------------------------
[Coeff 0 0 0 1 1]
+x^1+1

-------------------------------
[Coeff 0 0 1 1 1]
+x^2+x^1+1

-------------------------------
[Coeff 0 1 1 1 1]
+x^3+x^2+x^1+1

-------------------------------
[Coeff -1 -1 -1 -1 -1]
-x^4-x^3-x^2-x^1-1

-------------------------------
[Coeff -1 -1 -1 -1 0]
-x^4-x^3-x^2-x^1

-------------------------------
[Coeff -1 -1 -1 0 0]
-x^4-x^3-x^2

-------------------------------
[Coeff -1 -1 0 0 0]
-x^4-x^3

-------------------------------
[Coeff -1 0 0 0 0]
-x^4

-------------------------------
[Coeff 0 0 0 0 -1]
-1

-------------------------------
[Coeff 0 0 0 -1 -1]
-x^1-1

-------------------------------
[Coeff 0 0 -1 -1 -1]
-x^2-x^1-1

-------------------------------
[Coeff 0 -1 -1 -1 -1]
-x^3-x^2-x^1-1

-------------------------------
[Coeff 2 2 2 2 2]
2x^4+2x^3+2x^2+2x+2

-------------------------------
[Coeff 2 2 2 2 0]
2x^4+2x^3+2x^2+2x

-------------------------------
[Coeff 2 2 2 0 0]
2x^4+2x^3+2x^2

-------------------------------
[Coeff 2 2 0 0 0]
2x^4+2x^3

-------------------------------
[Coeff 2 0 0 0 0]
2x^4

-------------------------------
[Coeff 0 0 0 0 2]
+2

-------------------------------
[Coeff 0 0 0 2 2]
+2x+2

-------------------------------
[Coeff 0 0 2 2 2]
+2x^2+2x+2

-------------------------------
[Coeff 0 2 2 2 2]
+2x^3+2x^2+2x+2

-------------------------------
[Coeff -2 -2 -2 -2 -2]
-2x^4-2x^3-2x^2-2x-2

-------------------------------
[Coeff -2 -2 -2 -2 0]
-2x^4-2x^3-2x^2-2x

-------------------------------
[Coeff -2 -2 -2 0 0]
-2x^4-2x^3-2x^2

-------------------------------
[Coeff -2 -2 0 0 0]
-2x^4-2x^3

-------------------------------
[Coeff -2 0 0 0 0]
-2x^4

-------------------------------
[Coeff 0 0 0 0 -2]
-2

-------------------------------
[Coeff 0 0 0 -2 -2]
-2x-2

-------------------------------
[Coeff 0 0 -2 -2 -2]
-2x^2-2x-2

-------------------------------
[Coeff 0 -2 -2 -2 -2]
-2x^3-2x^2-2x-2


And here is the full test code which you can call from main if you want to play with it further.

void PolynomialPrintTest()
{
   Polynomial().printPolynomial();

   Polynomial(0, 0, 0, 0, 1).printPolynomial();
   Polynomial(0, 0, 0, 1, 0).printPolynomial();
   Polynomial(0, 0, 1, 0, 0).printPolynomial();
   Polynomial(0, 1, 0, 0, 0).printPolynomial();
   Polynomial(1, 0, 0, 0, 0).printPolynomial();

   Polynomial(0, 0, 0, 0, -1).printPolynomial();
   Polynomial(0, 0, 0, -1, 0).printPolynomial();
   Polynomial(0, 0, -1, 0, 0).printPolynomial();
   Polynomial(0, -1, 0, 0, 0).printPolynomial();
   Polynomial(-1, 0, 0, 0, 0).printPolynomial();

   Polynomial(0, 0, 0, 0, 2).printPolynomial();
   Polynomial(0, 0, 0, 2, 0).printPolynomial();
   Polynomial(0, 0, 2, 0, 0).printPolynomial();
   Polynomial(0, 2, 0, 0, 0).printPolynomial();
   Polynomial(2, 0, 0, 0, 0).printPolynomial();

   Polynomial(0, 0, 0, 0, -2).printPolynomial();
   Polynomial(0, 0, 0, -2, 0).printPolynomial();
   Polynomial(0, 0, -2, 0, 0).printPolynomial();
   Polynomial(0, -2, 0, 0, 0).printPolynomial();
   Polynomial(-2, 0, 0, 0, 0).printPolynomial();

   Polynomial(1, 1, 1, 1, 1).printPolynomial();
   Polynomial(1, 1, 1, 1).printPolynomial();
   Polynomial(1, 1, 1).printPolynomial();
   Polynomial(1, 1).printPolynomial();
   Polynomial(1).printPolynomial();

   Polynomial(0, 0, 0, 0, 1).printPolynomial();
   Polynomial(0, 0, 0, 1, 1).printPolynomial();
   Polynomial(0, 0, 1, 1, 1).printPolynomial();
   Polynomial(0, 1, 1, 1, 1).printPolynomial();

   Polynomial(-1, -1, -1, -1, -1).printPolynomial();
   Polynomial(-1, -1, -1, -1).printPolynomial();
   Polynomial(-1, -1, -1).printPolynomial();
   Polynomial(-1, -1).printPolynomial();
   Polynomial(-1).printPolynomial();

   Polynomial(0, 0, 0, 0, -1).printPolynomial();
   Polynomial(0, 0, 0, -1, -1).printPolynomial();
   Polynomial(0, 0, -1, -1, -1).printPolynomial();
   Polynomial(0, -1, -1, -1, -1).printPolynomial();

   Polynomial(2, 2, 2, 2, 2).printPolynomial();
   Polynomial(2, 2, 2, 2).printPolynomial();
   Polynomial(2, 2, 2).printPolynomial();
   Polynomial(2, 2).printPolynomial();
   Polynomial(2).printPolynomial();
   Polynomial(0, 0, 0, 0, 2).printPolynomial();
   Polynomial(0, 0, 0, 2, 2).printPolynomial();
   Polynomial(0, 0, 2, 2, 2).printPolynomial();
   Polynomial(0, 2, 2, 2, 2).printPolynomial();

   Polynomial(-2, -2, -2, -2, -2).printPolynomial();
   Polynomial(-2, -2, -2, -2).printPolynomial();
   Polynomial(-2, -2, -2).printPolynomial();
   Polynomial(-2, -2).printPolynomial();
   Polynomial(-2).printPolynomial();
   Polynomial(0, 0, 0, 0, -2).printPolynomial();
   Polynomial(0, 0, 0, -2, -2).printPolynomial();
   Polynomial(0, 0, -2, -2, -2).printPolynomial();
   Polynomial(0, -2, -2, -2, -2).printPolynomial();
}


I think you can put this baby to bed.

Best regards
Zlatko