/**
* Polynomial multiplication
*
* @param a First polynomial to be multiplied.
* @param b Second polynomial to be multiplied.
* @return New polynomial as the product of polynomial a and polynomial b.
*/
// Example: The product of polynomial 2x0 + 3x1 and polynomial 1x2 + 1x3 should be 2x2 + 5x3 + 3x4
// 2x⁰ + 3x¹ X 1x² + 1x³ = 2x² + 5x³ + 3x⁴
// 2x⁰ + 3x¹
// 1x² + 1x³
// MULTIPLY
// (2x⁰ * 1x²) + (2x⁰ * 1x³) + (3x¹ * 1x²) + (3x¹ * 1x³)
// polyA.term0 * polyB.term0 = 2x⁰ * 1x²
// polyA.term0 * polyB.term1 = 2x⁰ * 1x³
// polyA.term1 * polyB.term0 = 3x¹ * 1x²
// polyA.term1 * polyB.term1 = 3x¹ * 1x³
// 2x² + 5x³ + 3x⁴
public static Polynomial Multiply(Polynomial a, Polynomial b)
{
// DO_NOT_EDIT_ANYTHING_ABOVE_THIS_LINE V
var degreeA = a.Degree();
var degreeB = b.Degree();
var degree = degreeA + degreeB;
var coefficients = new int[degree + 1];
var powers = new int[degree + 1];
var termA = a.Head; // 2x⁰
while (termA != null)
{
var termB = b.Head; // 1x²
while (termB != null)
{
// termA * termB => 2x⁰ * 1x²
var coefficientA = termA.Coefficient;
var coefficientB = termB.Coefficient;
var coefficientTotal = coefficientA * coefficientB;
coefficients[termA.Power + termB.Power] += coefficientTotal;
powers[termA.Power + termB.Power] = termA.Power + termB.Power;
termB = termB.Next;
}
termA = termA.Next;
}
while (termA != null)
{
var termB = b.Head; // 1x²
while (termB != null)
{
// termA * termB => 2x⁰ * 1x²
var coefficientA = termA.Coefficient;
var coefficientB = termB.Coefficient;
var coefficientTotal = coefficientA * coefficientB;
coefficients[termA.Power + termB.Power] += coefficientTotal;
powers[termA.Power + termB.Power] = termA.Power + termB.Power;
termB = termB.Next;
}
termA = termA.Next;
}
return(new Polynomial(coefficients, powers));
// DO_NOT_EDIT_ANYTHING_BELOW_THIS_LINE A
}
/**
* Polynomial addition
*
* @param a First polynomial to be added.
* @param b Second polynomial to be added.
* @return New polynomial as the sum of polynomial a and polynomial b.
*/
// Example: The result of addition of polynomial 2x0 + 0x1 + 3x2 and polynomial 0x0 + 1x1 + 0x2 should be 2x0 + 1x1 + 3x2
public static Polynomial Add(Polynomial a, Polynomial b)
{
// DO_NOT_EDIT_ANYTHING_ABOVE_THIS_LINE V
// TODO: for loops (i) unnecessary?
var degreeA = a.Degree();
var degreeB = b.Degree();
var degree = degreeA > degreeB ? degreeA : degreeB;
var coefficients = new int[degree + 1];
var powers = new int[degree + 1];
var term = a.Head;
while (term != null)
{
for (var i = 0; i <= degree; i++)
{
if (term.Power == i)
{
coefficients[i] = term.Coefficient;
powers[i] = term.Power;
term = term.Next;
break;
}
}
}
term = b.Head;
while (term != null)
{
for (var i = 0; i <= degree; i++)
{
if (term.Power == i)
{
coefficients[i] += term.Coefficient;
term = term.Next;
break;
}
}
}
return(new Polynomial(coefficients, powers));
// DO_NOT_EDIT_ANYTHING_BELOW_THIS_LINE A
}
