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# 基哥作業3
```cpp=
// 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 °ree1, 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 "ientDegree, 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 °ree1, 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 "ientDegree, int &remainderDegree )
{
if( isZero( dividend, dividendDegree ) )
{
quotientDegree = 0;
quotient[ 0 ] = 0;
remainderDegree = 0;
remainder[ 0 ] = 0;
return;
}
//"ientDegree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
```cpp=
// 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;
}
//"ientDegree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
```cpp=
// 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;
}
//"ientDegree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";
}
```
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