# 基哥作業3

// Polynomial division provided that the quotient and remainder have integer coefficients

#include <iostream>
using std::cin;
using std::cout;
using std::endl;

#include <fstream>
using std::ifstream;
using std::ios;

// outputs the specified polynomial
void output( int polynomial[], int degree );

// returns true if and only if the specified polynomial is zero polynomial
bool isZero( int polynomial[], int degree );

// returns true if and only if polynomial1 == polynomial2
bool equal( int polynomial1[], int polynomial2[], int degree1, int degree2 );

// polynomial1 = -polynomial2
void minus( int polynomial1[], int polynomial2[], int &degree1, int degree2 );

// addend += adder
void addition( int addend[], int adder[], int &addendDegree, int adderDegree );

// minuend -= subtrahend
void subtraction( int minuend[], int subtrahend[], int &minuendDegree, int subtrahendDegree );

// product = multiplicand * multiplier
void multiplication( int multiplicand[], int multiplier[], int product[],
                     int multiplicandDegree, int multiplierDegree, int &productDegree );

// quotient = dividend / divisor; remainder = dividend % divisor
// provided that dividendDegree >= divisorDegree
void division( int dividend[], int divisor[], int quotient[], int remainder[],
               int dividendDegree, int divisorDegree, int &quotientDegree, int &remainderDegree );

const int numTestCases = 200; // the number of test cases
const int arraySize = 20;

int main()
{
   ifstream inFile( "Polynomials.dat", ios::in | ios::binary );


   //inFile.open("Polynomials.dat");/**/

   // exit program if ifstream could not open file
   if( !inFile )
   {
      cout << "File could not be opened\n";
      system( "pause" );
      exit( 1 );
   }

   
   int numErrors = numTestCases;
   for( int i = 0; i < numTestCases; i++ )
   {
      int dividend[ arraySize ] = {};
      int divisor[ arraySize ] = {};

      // input dividend and divisor from the file Polynomials.dat
      inFile.read( reinterpret_cast< char * >( dividend ), 80 );
      inFile.read( reinterpret_cast< char * >( divisor ), 80 );

      int dividendDegree = arraySize - 1;
      while( dividendDegree > 0 && dividend[ dividendDegree ] == 0 )
         dividendDegree--;

      int divisorDegree = arraySize - 1;
      while( divisorDegree > 0 && divisor[ divisorDegree ] == 0 )
         divisorDegree--;

      cout << "dividend: ";
      output( dividend, dividendDegree );
      cout << "divisor : ";
      output( divisor, divisorDegree );
      cout << endl;
      

      int quotient[ arraySize ] = {};
      int remainder[ arraySize ] = {};
      int quotientDegree = 0;
      int remainderDegree = 0;

      // quotient = dividend / divisor; remainder = dividend % divisor
      // thus, dividend == divisor * quotient + remainder
      division( dividend, divisor, quotient, remainder,
                dividendDegree, divisorDegree, quotientDegree, remainderDegree );

      if( quotientDegree != 0 && quotient[ quotientDegree ] == 0 )    //有bug
         cout << "Leading coefficient of quotient cannot be zero!\n";

      if( remainderDegree != 0 && remainder[ remainderDegree ] == 0 )
         cout << "Leading coefficient of remainder cannot be zero!\n";

      int buffer[ arraySize ] = {};
      int bufferDegree = 1;

      // buffer = divisor * quotient
      multiplication( divisor, quotient, buffer, divisorDegree, quotientDegree, bufferDegree );

      if( bufferDegree != 0 && buffer[ bufferDegree ] == 0 )
         cout << "Leading coefficient of buffer cannot be zero!\n";

      // buffer = buffer + remainder = divisor * quotient + remainder
      addition( buffer, remainder, bufferDegree, remainderDegree );
      

      if( bufferDegree != 0 && buffer[ bufferDegree ] == 0 )
         cout << "Leading coefficient of buffer cannot be zero!\n";

      // if buffer != dividend, an error occurred!
      if( equal( buffer, dividend, bufferDegree, dividendDegree ) )
         numErrors--;
   }
   
   inFile.close();

   cout << "There are " << numErrors << " errors!\n\n";

   system( "pause" );
}

// outputs the specified polynomial
void output( int polynomial[], int degree )
{
   if( isZero( polynomial, degree ) ) // zero polynomial
      cout << 0;
   else
   {
      if( degree == 0 ) // constant polynomial
      {
         if( polynomial[ 0 ] < 0 )
            cout << "-" << -polynomial[ 0 ];
         else if( polynomial[ 0 ] > 0 )
            cout << polynomial[ 0 ];
      }
      else
      {
         if( degree == 1 ) // polynomial of degree 1
         {
            if( polynomial[ 1 ] < 0 )
               cout << "-" << -polynomial[ 1 ] << "x";
            else if( polynomial[ 1 ] > 0 )
               cout << polynomial[ 1 ] << "x";
         }
         else // polynomial of degree at least 2
         {
            // display the leading term
            if( polynomial[ degree ] < 0 )
               cout << "-" << -polynomial[ degree ] << "x^" << degree;
            else if( polynomial[ degree ] > 0 )
               cout << polynomial[ degree ] << "x^" << degree;

            // display all other terms
            for( int i = degree - 1; i > 1; i-- )
               if( polynomial[ i ] < 0 )
                  cout << " - " << -polynomial[ i ] << "x^" << i;
               else if( polynomial[ i ] > 0 )
                  cout << " + " << polynomial[ i ] << "x^" << i;

            // display the term of degree 1
            if( polynomial[ 1 ] < 0 )
               cout << " - " << -polynomial[ 1 ] << "x";
            else if( polynomial[ 1 ] > 0 )
               cout << " + " << polynomial[ 1 ] << "x";
         }

         // display the constant term
         if( polynomial[ 0 ] < 0 )
            cout << " - " << -polynomial[ 0 ];
         else if( polynomial[ 0 ] > 0 )
            cout << " + " << polynomial[ 0 ];
      }
   }

   cout << endl;
}

// returns true if and only if the specified polynomial is zero polynomial
bool isZero( int polynomial[], int degree )
{  // leading term is 0
   if( degree == 0 && polynomial[ 0 ] == 0 )
      return true;
   return false;
}

// returns true if and only if polynomial1 == polynomial2
bool equal( int polynomial1[], int polynomial2[], int degree1, int degree2 )
{
    //直接先判斷Degree
   if( degree1 != degree2 )
      return false;

   for( int i = 0; i <= degree1; i++ )
      if( polynomial1[ i ] != polynomial2[ i ] )
         return false;

   return true;
}

// polynomial1 = -polynomial2 (把多項式加負號)
void minus( int polynomial1[], int polynomial2[], int &degree1, int degree2 )
{
   degree1 = degree2;
   for( int i = 0; i <= degree1; i++ )
      polynomial1[ i ] = -polynomial2[ i ];
}

// addend += adder
void addition( int addend[], int adder[], int &addendDegree, int adderDegree ) //被加數的degree判斷
{   
    ////////////////////////(debug完成)
    //執行加法
    for (int i = 0; i <= addendDegree; i++)
    {
        addend[i] += adder[i];       
    }
    //判斷加法後的Degree
     //都是0的話

    int index = 0;
    for (int i = 0; i < 20; i++)
    {
        if (addend[i] == 0)
        {
            index++;
        }
    }
    if (index == 20)
    {
        addendDegree = 0;
    }
     //不為0
    for (int i = 19; i >= 0; i--)
    {
        if (addend[i] != 0)
        {
            addendDegree = i;
            break;
        }
    }
  
   if( addendDegree != 0 && addend[ addendDegree ] == 0 )   //最高次方不為0 and 最高次項係數為0
      cout << "Leading coefficient of addend cannot be zero!\n";
}

// minuend -= subtrahend (//remainder = remainder - buffer)
void subtraction( int minuend[], int subtrahend[], int &minuendDegree, int subtrahendDegree )
{
   int buffer[ arraySize ] = {};
   int bufferDegree = 0;

   // buffer = -subtrahend  (把buffer加上負號讓餘數去加)
   minus( buffer, subtrahend, bufferDegree, subtrahendDegree );

  

   // minuend = minuend + buffer = minuend - subtrahend  (餘數+(-buffer)) 
   addition( minuend, buffer, minuendDegree, bufferDegree );

   if( minuendDegree != 0 && minuend[ minuendDegree ] == 0 )
      cout << "Leading coefficient of minuend cannot be zero!\n";
}

// product = multiplicand * multiplier
void multiplication( int multiplicand[], int multiplier[], int product[],
                     int multiplicandDegree, int multiplierDegree, int &productDegree )
{
    /////
    //算出product(debug正確)
    for (int i = 0; i < arraySize; i++)
    {
        for (int j = 0; j < arraySize; j++)
        {
            product[i + j] += multiplicand[j] * multiplier[i];
        }
    }   
   
    //判斷乘法後值的Degree
     //值都是0
    int index = 0;
    for (int i = 0; i < 20; i++)
    {
        if (product[i] == 0)
        {
            index++;
        }
    }
    if (index == 20)
    {
        productDegree = 0;
    }
    //值不為0
    for (int i = 19; i >= 0; i--)
    {
        if (product[i] != 0)
        {
            productDegree = i;
            break;
        }
    }
    

   if( productDegree != 0 && product[ productDegree ] == 0 )
      cout << "Leading coefficient of product cannot be zero!\n";
}

// quotient = dividend / divisor; remainder = dividend % divisor
// provided that dividendDegree >= divisorDegree
void division( int dividend[], int divisor[], int quotient[], int remainder[],
               int dividendDegree, int divisorDegree, int &quotientDegree, int &remainderDegree )
{
   if( isZero( dividend, dividendDegree ) )
   {
      quotientDegree = 0;
      quotient[ 0 ] = 0;

      remainderDegree = 0;
      remainder[ 0 ] = 0;
      return;
   }

   //&quotientDegree餘數(固定值)
   quotientDegree = dividendDegree - divisorDegree;
   
   //被除數存入餘數做計算
   for (int i = 0; i < arraySize; i++)
   {
       remainder[i] = dividend[i];
   }
   remainderDegree = dividendDegree;
   //計算
   
   while (remainderDegree >= divisorDegree) //當餘數degree小於除數Degree跳出迴圈 (remainderDegree11 8 7 卡在9)
   {      
       int i = remainderDegree - divisorDegree; //目前要計算商的位置
       quotient[i] = remainder[remainderDegree] / divisor[divisorDegree]; //算出當前位置的商
       //算當前buffer
       int buffer2[arraySize] = {};
       int bufferDegree2 = 0;
       multiplication(divisor, quotient, buffer2,
           divisorDegree, i, bufferDegree2);
       //算餘數
       subtraction(remainder, buffer2, remainderDegree, bufferDegree2);

       //餘數為0跳出迴圈
       if (remainderDegree == 0 && remainder[0] == 0)
       {
           break;
       }
       //餘數Degree = 除數Degree = 0 且 餘數<除數 跳出迴圈
       if ( remainderDegree == 0 && divisorDegree == 0 && remainder[0] < divisor[0])
       {
           break;
       }
   }
    
   if( quotientDegree != 0 && quotient[ quotientDegree ] == 0 ) //有bug
      cout << "Leading coefficient of quotient cannot be zero!\n";

   if( remainderDegree != 0 && remainder[ remainderDegree ] == 0 )
      cout << "Leading coefficient of remainder cannot be zero!\n";
}

祥威改過的

// Polynomial division provided that the quotient and remainder have integer coefficients

#include <iostream>
using std::cin;
using std::cout;
using std::endl;

#include <fstream>
using std::ifstream;
using std::ios;

// outputs the specified polynomial
void output(int polynomial[], int degree);

// returns true if and only if the specified polynomial is zero polynomial
bool isZero(int polynomial[], int degree);

// returns true if and only if polynomial1 == polynomial2
bool equal(int polynomial1[], int polynomial2[], int degree1, int degree2);

// polynomial1 = -polynomial2
void minus(int polynomial1[], int polynomial2[], int& degree1, int degree2);

// addend += adder
void addition(int addend[], int adder[], int& addendDegree, int adderDegree);

// minuend -= subtrahend
void subtraction(int minuend[], int subtrahend[], int& minuendDegree, int subtrahendDegree);

// product = multiplicand * multiplier
void multiplication(int multiplicand[], int multiplier[], int product[],
    int multiplicandDegree, int multiplierDegree, int& productDegree);

// quotient = dividend / divisor; remainder = dividend % divisor
// provided that dividendDegree >= divisorDegree
void division(int dividend[], int divisor[], int quotient[], int remainder[],
    int dividendDegree, int divisorDegree, int& quotientDegree, int& remainderDegree);

const int numTestCases = 200; // the number of test cases
const int arraySize = 20;

int main()
{
    ifstream inFile("Polynomials.dat", ios::in | ios::binary);


    //inFile.open("Polynomials.dat");/**/

    // exit program if ifstream could not open file
    if (!inFile)
    {
        cout << "File could not be opened\n";
        system("pause");
        exit(1);
    }


    int numErrors = numTestCases;
    for (int i = 0; i < numTestCases; i++)
    {
        int dividend[arraySize] = {};
        int divisor[arraySize] = {};

        // input dividend and divisor from the file Polynomials.dat
        inFile.read(reinterpret_cast<char*>(dividend), 80);
        inFile.read(reinterpret_cast<char*>(divisor), 80);

        int dividendDegree = arraySize - 1;
        while (dividendDegree > 0 && dividend[dividendDegree] == 0)
            dividendDegree--;

        int divisorDegree = arraySize - 1;
        while (divisorDegree > 0 && divisor[divisorDegree] == 0)
            divisorDegree--;

        cout << "dividend: ";
        output(dividend, dividendDegree);
        cout << "divisor : ";
        output(divisor, divisorDegree);
        cout << endl;


        int quotient[arraySize] = {};
        int remainder[arraySize] = {};
        int quotientDegree = 0;
        int remainderDegree = 0;

        // quotient = dividend / divisor; remainder = dividend % divisor
        // thus, dividend == divisor * quotient + remainder
        division(dividend, divisor, quotient, remainder,
            dividendDegree, divisorDegree, quotientDegree, remainderDegree);

        if (quotientDegree != 0 && quotient[quotientDegree] == 0)    //有bug
            cout << "Leading coefficient of quotient cannot be zero!\n";

        if (remainderDegree != 0 && remainder[remainderDegree] == 0)
            cout << "Leading coefficient of remainder cannot be zero!\n";

        int buffer[arraySize] = {};
        int bufferDegree = 1;

        // buffer = divisor * quotient
        multiplication(divisor, quotient, buffer, divisorDegree, quotientDegree, bufferDegree);

        if (bufferDegree != 0 && buffer[bufferDegree] == 0)
            cout << "Leading coefficient of buffer cannot be zero!\n";

        // buffer = buffer + remainder = divisor * quotient + remainder
        addition(buffer, remainder, bufferDegree, remainderDegree);


        if (bufferDegree != 0 && buffer[bufferDegree] == 0)
            cout << "Leading coefficient of buffer cannot be zero!\n";

        // if buffer != dividend, an error occurred!
        if (equal(buffer, dividend, bufferDegree, dividendDegree))
            numErrors--;
    }

    inFile.close();

    cout << "There are " << numErrors << " errors!\n\n";

    system("pause");
}

// outputs the specified polynomial
void output(int polynomial[], int degree)
{
    if (isZero(polynomial, degree)) // zero polynomial
        cout << 0;
    else
    {
        if (degree == 0) // constant polynomial
        {
            if (polynomial[0] < 0)
                cout << "-" << -polynomial[0];
            else if (polynomial[0] > 0)
                cout << polynomial[0];
        }
        else
        {
            if (degree == 1) // polynomial of degree 1
            {
                if (polynomial[1] < 0)
                    cout << "-" << -polynomial[1] << "x";
                else if (polynomial[1] > 0)
                    cout << polynomial[1] << "x";
            }
            else // polynomial of degree at least 2
            {
                // display the leading term
                if (polynomial[degree] < 0)
                    cout << "-" << -polynomial[degree] << "x^" << degree;
                else if (polynomial[degree] > 0)
                    cout << polynomial[degree] << "x^" << degree;

                // display all other terms
                for (int i = degree - 1; i > 1; i--)
                    if (polynomial[i] < 0)
                        cout << " - " << -polynomial[i] << "x^" << i;
                    else if (polynomial[i] > 0)
                        cout << " + " << polynomial[i] << "x^" << i;

                // display the term of degree 1
                if (polynomial[1] < 0)
                    cout << " - " << -polynomial[1] << "x";
                else if (polynomial[1] > 0)
                    cout << " + " << polynomial[1] << "x";
            }

            // display the constant term
            if (polynomial[0] < 0)
                cout << " - " << -polynomial[0];
            else if (polynomial[0] > 0)
                cout << " + " << polynomial[0];
        }
    }

    cout << endl;
}

// returns true if and only if the specified polynomial is zero polynomial
bool isZero(int polynomial[], int degree)
{  // leading term is 0
    if (degree == 0 && polynomial[0] == 0)
        return true;
    return false;
}

// returns true if and only if polynomial1 == polynomial2
bool equal(int polynomial1[], int polynomial2[], int degree1, int degree2)
{
    //直接先判斷Degree
    if (degree1 != degree2)
        return false;

    for (int i = 0; i <= degree1; i++)
        if (polynomial1[i] != polynomial2[i])
            return false;

    return true;
}

// polynomial1 = -polynomial2 (把多項式加負號)
void minus(int polynomial1[], int polynomial2[], int& degree1, int degree2)
{
    degree1 = degree2;
    for (int i = 0; i <= degree1; i++)
        polynomial1[i] = -polynomial2[i];
}

// addend += adder
void addition(int addend[], int adder[], int& addendDegree, int adderDegree) //被加數的degree判斷
{
    ////////////////////////(debug完成)
    //執行加法
    for (int i = 0; i <= addendDegree; i++)
    {
        addend[i] += adder[i];
    }
    //判斷加法後的Degree
     //都是0的話

    int index = 0;
    for (int i = 0; i < 20; i++)
    {
        if (addend[i] == 0)
        {
            index++;
        }
    }
    if (index == 20)
    {
        addendDegree = 0;
    }
    //不為0
    for (int i = 19; i >= 0; i--)
    {
        if (addend[i] != 0)
        {
            addendDegree = i;
            break;
        }
    }

    if (addendDegree != 0 && addend[addendDegree] == 0)   //最高次方不為0 and 最高次項係數為0
        cout << "Leading coefficient of addend cannot be zero!\n";
}

// minuend -= subtrahend (//remainder = remainder - buffer)
void subtraction(int minuend[], int subtrahend[], int& minuendDegree, int subtrahendDegree)
{
    int buffer[arraySize] = {};
    int bufferDegree = 0;

    // buffer = -subtrahend  (把buffer加上負號讓餘數去加)
    minus(buffer, subtrahend, bufferDegree, subtrahendDegree);



    // minuend = minuend + buffer = minuend - subtrahend  (餘數+(-buffer)) 
    addition(minuend, buffer, minuendDegree, bufferDegree);

    if (minuendDegree != 0 && minuend[minuendDegree] == 0)
        cout << "Leading coefficient of minuend cannot be zero!\n";
}

// product = multiplicand * multiplier
void multiplication(int multiplicand[], int multiplier[], int product[],
    int multiplicandDegree, int multiplierDegree, int& productDegree)
{
    /////
    //算出product(debug正確)
    for (int i = 0; i < arraySize; i++)
    {
        for (int j = 0; j < arraySize; j++)
        {
            product[i + j] += multiplicand[j] * multiplier[i];
        }
    }

    //判斷乘法後值的Degree
     //值都是0
    int index = 0;
    for (int i = 0; i < 20; i++)
    {
        if (product[i] == 0)
        {
            index++;
        }
    }
    if (index == 20)
    {
        productDegree = 0;
    }
    //值不為0
    for (int i = 19; i >= 0; i--)
    {
        if (product[i] != 0)
        {
            productDegree = i;
            break;
        }
    }


    if (productDegree != 0 && product[productDegree] == 0)
        cout << "Leading coefficient of product cannot be zero!\n";
}

// quotient = dividend / divisor; remainder = dividend % divisor
// provided that dividendDegree >= divisorDegree
void division(int dividend[], int divisor[], int quotient[], int remainder[],
    int dividendDegree, int divisorDegree, int& quotientDegree, int& remainderDegree)
{
    if (isZero(dividend, dividendDegree))
    {
        quotientDegree = 0;
        quotient[0] = 0;

        remainderDegree = 0;
        remainder[0] = 0;
        return;
    }

    //&quotientDegree餘數(固定值)
    quotientDegree = dividendDegree - divisorDegree;

    //被除數存入餘數做計算
    for (int i = 0; i < arraySize; i++)
    {
        remainder[i] = dividend[i];
    }
    remainderDegree = dividendDegree;
    //計算

    while (remainderDegree >= divisorDegree) //當餘數degree小於除數Degree跳出迴圈 (remainderDegree11 8 7 卡在9)
    {
        int i = remainderDegree - divisorDegree; //目前要計算商的位置
        //->
        int temp[arraySize] = {};
        temp[i] = remainder[remainderDegree] / divisor[divisorDegree];
        //<-
        quotient[i] = remainder[remainderDegree] / divisor[divisorDegree]; //算出當前位置的商
        //算當前buffer
        int buffer2[arraySize] = {};
        int bufferDegree2 = 0;
        //含有改這裡
        multiplication(divisor,temp, buffer2,
            divisorDegree, i, bufferDegree2);
        //算餘數
        subtraction(remainder, buffer2, remainderDegree, bufferDegree2);

        //餘數為0跳出迴圈
        if (remainderDegree == 0 && remainder[0] == 0)
        {
            break;
        }
        //餘數Degree = 除數Degree = 0 且 餘數<除數 跳出迴圈
        if (remainderDegree == 0 && divisorDegree == 0 && remainder[0] < divisor[0])
        {
            break;
        }
    }

    if (quotientDegree != 0 && quotient[quotientDegree] == 0) //有bug
        cout << "Leading coefficient of quotient cannot be zero!\n";

    if (remainderDegree != 0 && remainder[remainderDegree] == 0)
        cout << "Leading coefficient of remainder cannot be zero!\n";
}

e93e9eee改

// Polynomial division provided that the quotient and remainder have integer coefficients

#include <iostream>
using std::cin;
using std::cout;
using std::endl;

#include <fstream>
using std::ifstream;
using std::ios;

// outputs the specified polynomial
void output(int polynomial[], int degree);

// returns true if and only if the specified polynomial is zero polynomial
bool isZero(int polynomial[], int degree);

// returns true if and only if polynomial1 == polynomial2
bool equal(int polynomial1[], int polynomial2[], int degree1, int degree2);

// polynomial1 = -polynomial2
void minus(int polynomial1[], int polynomial2[], int& degree1, int degree2);

// addend += adder
void addition(int addend[], int adder[], int& addendDegree, int adderDegree);

// minuend -= subtrahend
void subtraction(int minuend[], int subtrahend[], int& minuendDegree, int subtrahendDegree);

// product = multiplicand * multiplier
void multiplication(int multiplicand[], int multiplier[], int product[],
    int multiplicandDegree, int multiplierDegree, int& productDegree);

// quotient = dividend / divisor; remainder = dividend % divisor
// provided that dividendDegree >= divisorDegree
void division(int dividend[], int divisor[], int quotient[], int remainder[],
    int dividendDegree, int divisorDegree, int& quotientDegree, int& remainderDegree);

const int numTestCases = 200; // the number of test cases
const int arraySize = 20;

int main()
{
    ifstream inFile("Polynomials.dat", ios::in | ios::binary);


    //inFile.open("Polynomials.dat");/**/

    // exit program if ifstream could not open file
    if (!inFile)
    {
        cout << "File could not be opened\n";
        system("pause");
        exit(1);
    }


    int numErrors = numTestCases;
    for (int i = 0; i < numTestCases; i++)
    {
        int dividend[arraySize] = {};
        int divisor[arraySize] = {};

        // input dividend and divisor from the file Polynomials.dat
        inFile.read(reinterpret_cast<char*>(dividend), 80);
        inFile.read(reinterpret_cast<char*>(divisor), 80);

        int dividendDegree = arraySize - 1;
        while (dividendDegree > 0 && dividend[dividendDegree] == 0)
            dividendDegree--;

        int divisorDegree = arraySize - 1;
        while (divisorDegree > 0 && divisor[divisorDegree] == 0)
            divisorDegree--;

        cout << "dividend: ";
        output(dividend, dividendDegree);
        cout << "divisor : ";
        output(divisor, divisorDegree);
        cout << endl;


        int quotient[arraySize] = {};
        int remainder[arraySize] = {};
        int quotientDegree = 0;
        int remainderDegree = 0;

        // quotient = dividend / divisor; remainder = dividend % divisor
        // thus, dividend == divisor * quotient + remainder
        division(dividend, divisor, quotient, remainder,
            dividendDegree, divisorDegree, quotientDegree, remainderDegree);

        if (quotientDegree != 0 && quotient[quotientDegree] == 0)    //有bug
            cout << "Leading coefficient of quotient cannot be zero!\n";

        if (remainderDegree != 0 && remainder[remainderDegree] == 0)
            cout << "Leading coefficient of remainder cannot be zero!\n";

        int buffer[arraySize] = {};
        int bufferDegree = 1;

        // buffer = divisor * quotient
        multiplication(divisor, quotient, buffer, divisorDegree, quotientDegree, bufferDegree);

        if (bufferDegree != 0 && buffer[bufferDegree] == 0)
            cout << "Leading coefficient of buffer cannot be zero!\n";

        // buffer = buffer + remainder = divisor * quotient + remainder
        addition(buffer, remainder, bufferDegree, remainderDegree);


        if (bufferDegree != 0 && buffer[bufferDegree] == 0)
            cout << "Leading coefficient of buffer cannot be zero!\n";

        // if buffer != dividend, an error occurred!
        if (equal(buffer, dividend, bufferDegree, dividendDegree))
            numErrors--;
    }

    inFile.close();

    cout << "There are " << numErrors << " errors!\n\n";

    system("pause");
}

// outputs the specified polynomial
void output(int polynomial[], int degree)
{
    if (isZero(polynomial, degree)) // zero polynomial
        cout << 0;
    else
    {
        if (degree == 0) // constant polynomial
        {
            if (polynomial[0] < 0)
                cout << "-" << -polynomial[0];
            else if (polynomial[0] > 0)
                cout << polynomial[0];
        }
        else
        {
            if (degree == 1) // polynomial of degree 1
            {
                if (polynomial[1] < 0)
                    cout << "-" << -polynomial[1] << "x";
                else if (polynomial[1] > 0)
                    cout << polynomial[1] << "x";
            }
            else // polynomial of degree at least 2
            {
                // display the leading term
                if (polynomial[degree] < 0)
                    cout << "-" << -polynomial[degree] << "x^" << degree;
                else if (polynomial[degree] > 0)
                    cout << polynomial[degree] << "x^" << degree;

                // display all other terms
                for (int i = degree - 1; i > 1; i--)
                    if (polynomial[i] < 0)
                        cout << " - " << -polynomial[i] << "x^" << i;
                    else if (polynomial[i] > 0)
                        cout << " + " << polynomial[i] << "x^" << i;

                // display the term of degree 1
                if (polynomial[1] < 0)
                    cout << " - " << -polynomial[1] << "x";
                else if (polynomial[1] > 0)
                    cout << " + " << polynomial[1] << "x";
            }

            // display the constant term
            if (polynomial[0] < 0)
                cout << " - " << -polynomial[0];
            else if (polynomial[0] > 0)
                cout << " + " << polynomial[0];
        }
    }

    cout << endl;
}

// returns true if and only if the specified polynomial is zero polynomial
bool isZero(int polynomial[], int degree)
{  // leading term is 0
    if (degree == 0 && polynomial[0] == 0)
        return true;
    return false;
}

// returns true if and only if polynomial1 == polynomial2
bool equal(int polynomial1[], int polynomial2[], int degree1, int degree2)
{
    //直接先判斷Degree
    if (degree1 != degree2)
        return false;

    for (int i = 0; i <= degree1; i++)
        if (polynomial1[i] != polynomial2[i])
            return false;

    return true;
}

// polynomial1 = -polynomial2 (把多項式加負號)
void minus(int polynomial1[], int polynomial2[], int& degree1, int degree2)
{
    degree1 = degree2;
    for (int i = 0; i <= degree1; i++)
        polynomial1[i] = -polynomial2[i];
}

// addend += adder
void addition(int addend[], int adder[], int& addendDegree, int adderDegree) //被加數的degree判斷
{
    ////////////////////////(debug完成)
    //執行加法
    for (int i = 0; i <= addendDegree; i++)
    {
        addend[i] += adder[i];
    }
    //判斷加法後的Degree
     //都是0的話

    int index = 0;
    for (int i = 0; i < 20; i++)
    {
        if (addend[i] == 0)
        {
            index++;
        }
    }
    if (index == 20)
    {
        addendDegree = 0;
    }
    //不為0
    for (int i = 19; i >= 0; i--)
    {
        if (addend[i] != 0)
        {
            addendDegree = i;
            break;
        }
    }

    if (addendDegree != 0 && addend[addendDegree] == 0)   //最高次方不為0 and 最高次項係數為0
        cout << "Leading coefficient of addend cannot be zero!\n";
}

// minuend -= subtrahend (//remainder = remainder - buffer)
void subtraction(int minuend[], int subtrahend[], int& minuendDegree, int subtrahendDegree)
{
    int buffer[arraySize] = {};
    int bufferDegree = 0;

    // buffer = -subtrahend  (把buffer加上負號讓餘數去加)
    minus(buffer, subtrahend, bufferDegree, subtrahendDegree);



    // minuend = minuend + buffer = minuend - subtrahend  (餘數+(-buffer)) 
    addition(minuend, buffer, minuendDegree, bufferDegree);

    if (minuendDegree != 0 && minuend[minuendDegree] == 0)
        cout << "Leading coefficient of minuend cannot be zero!\n";
}

// product = multiplicand * multiplier
void multiplication(int multiplicand[], int multiplier[], int product[],
    int multiplicandDegree, int multiplierDegree, int& productDegree)
{
    /////
    //算出product(debug正確)
    for (int i = 0; i < multiplicandDegree; i++)
    {
        product[multiplierDegree + i] += multiplicand[i] * multiplier[multiplicandDegree];
    }

    //判斷乘法後值的Degree
     //值都是0
    int index = 0;
    for (int i = 0; i < 20; i++)
    {
        if (product[i] == 0)
        {
            index++;
        }
    }
    if (index == 20)
    {
        productDegree = 0;
    }
    //值不為0
    for (int i = 19; i >= 0; i--)
    {
        if (product[i] != 0)
        {
            productDegree = i;
            break;
        }
    }


    if (productDegree != 0 && product[productDegree] == 0)
        cout << "Leading coefficient of product cannot be zero!\n";
}

// quotient = dividend / divisor; remainder = dividend % divisor
// provided that dividendDegree >= divisorDegree
void division(int dividend[], int divisor[], int quotient[], int remainder[],
    int dividendDegree, int divisorDegree, int& quotientDegree, int& remainderDegree)
{
    if (isZero(dividend, dividendDegree))
    {
        quotientDegree = 0;
        quotient[0] = 0;

        remainderDegree = 0;
        remainder[0] = 0;
        return;
    }

    //&quotientDegree餘數(固定值)
    quotientDegree = dividendDegree - divisorDegree;

    //被除數存入餘數做計算
    for (int i = 0; i < arraySize; i++)
    {
        remainder[i] = dividend[i];
    }
    remainderDegree = dividendDegree;
    //計算

    while (remainderDegree >= divisorDegree) //當餘數degree小於除數Degree跳出迴圈 (remainderDegree11 8 7 卡在9)
    {
        int i = remainderDegree - divisorDegree; //目前要計算商的位置
        quotient[i] = remainder[remainderDegree] / divisor[divisorDegree]; //算出當前位置的商
        //算當前buffer
        int buffer2[arraySize] = {};
        int bufferDegree2 = 0;
        multiplication(divisor, quotient, buffer2,
            divisorDegree, i, bufferDegree2);
        //算餘數
        subtraction(remainder, buffer2, remainderDegree, bufferDegree2);

        //餘數為0跳出迴圈
        if (remainderDegree == 0 && remainder[0] == 0)
        {
            break;
        }
        //餘數Degree = 除數Degree = 0 且 餘數<除數 跳出迴圈
        if (remainderDegree == 0 && divisorDegree == 0 && remainder[0] < divisor[0])
        {
            break;
        }
    }

    if (quotientDegree != 0 && quotient[quotientDegree] == 0) //有bug
        cout << "Leading coefficient of quotient cannot be zero!\n";

    if (remainderDegree != 0 && remainder[remainderDegree] == 0)
        cout << "Leading coefficient of remainder cannot be zero!\n";
}