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Polynomial synthetic division: Difference between revisions
I wrote it in C++ because I just learned how to do this in Algebra II.
MaiconSoft (talk | contribs) (Added Delphi example) |
(I wrote it in C++ because I just learned how to do this in Algebra II.) |
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[1, -12, 0, -42] / [1, -3] = [1, -9, -27] remainder [-123]
</pre>
=={{header|C++}}==
{{trans|Java}}
<lang cpp>/*
* C++ Polynomial Sythetic Division
* GNU Compile example for filename <synthdiv.cpp>
* g++ -std=c++11 -o synthdiv synthdiv.cpp
*/
#include <iostream>
#include <vector>
#include <string>
#include <cmath>
/*
* frmtPolynomial method
* Returns string for formatted
* polynomial from int vector of coefs.
* String looks like ax^2 + bx + c,
* a, b, and c being the integer
* coefs in the vector.
*/
std::string frmtPolynomial(std::vector<int> polynomial, bool remainder = false)
{
std::string r = "";
if (remainder)
{
r = " r: " + std::to_string(polynomial.back());
polynomial.pop_back();
}
std::string formatted = "";
int degree = polynomial.size() - 1;
int d = degree;
for (int i : polynomial)
{
if (d < degree)
{
if (i >= 0)
{
formatted += " + ";
}
else
{
formatted += " - ";
}
}
formatted += std::to_string(abs(i));
if (d > 1)
{
formatted += "x^" + std::to_string(d);
}
else if (d == 1)
{
formatted += "x";
}
d--;
}
return formatted;
}
/*
* syntheticDiv Method
* Performs Integer Polynomial Sythetic Division
* on polynomials expressed as vectors of coefs.
* Takes int vector param for dividend and
* divisor, and returns int vector quotient.
*/
std::vector<int> syntheticDiv(std::vector<int> dividend, std::vector<int> divisor)
{
std::vector<int> quotient;
quotient = dividend;
int normalizer = divisor[0];
for (int i = 0; i < dividend.size() - (divisor.size() - 1); i++)
{
quotient[i] /= normalizer;
int coef = quotient[i];
if (coef != 0)
{
for (int j = 1; j < divisor.size(); j++)
{
quotient[i + j] += -divisor[j] * coef;
}
}
}
return quotient;
}
/*
* Example of using the syntheticDiv method
* and the frmtPolynomial method.
* Assigns dividend and divisor polynomials:
* dividend: 1x^3 - 12x^2 + 0x - 42
* divisor: 1x - 3
* Outputs both to cout using frmtPolynomial.
* Printed polynomials look like above format.
* Processes dividend and divisor in the
* syntheticDiv method, returns quotient.
* Outputs quotient to cout using frmtPolynomial again.
* quotient: 1x^2 - 9x - 27 r: -123
*/
int main(int argc, char **argv)
{
std::vector<int> dividend{ 1, -12, 0, -42};
std::vector<int> divisor{ 1, -3};
std::cout << frmtPolynomial(dividend) << "\n";
std::cout << frmtPolynomial(divisor) << "\n";
std::vector<int> quotient = syntheticDiv(dividend, divisor);
std::cout << frmtPolynomial(quotient, true) << "\n";
}
</lang>
=={{header|C sharp|C#}}==
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