# Reduce algorithm complexity and promote modularity

Just about every developer has found himself in a situation where they had a complicated algorithm in a single, virtually unreadable method, that was entangled together with other methods in a class. For example, say you have a general-purpose class for solving equations:

```
public class EquationSolvers
{
public static Tuple<double, double> Quadratic(double a, double b, double c)
{
double disc = b*b - 4*a*c;
if (disc < 0)
throw new ArgumentException("Cannot solve equation with complex roots");
double sqrt = Math.Sqrt(disc);
return new Tuple<double, double>(
(-b + sqrt) / (2 * a), (-b - sqrt) / (2 * a));
}
// other solvers here
}
```

The above equation solver is hard-coded, meaning that to substitute a different solver, you would have to
manually replace each instance. Let’s start by taking it out into a separate class. To do this, we use the
Move to Another Type refactoring
(`F6`):

Then, we need to specify the class to move the method to.
In order to separate concerns better, we pick a separate class called
`QuadraticEquationSolver`

for this:

Now that the method has been moved, let’s try taking the discriminant out to a separate calculation.
This is easy – we simply select the discriminant calculation and invoke the
Extract Method refactoring (`Ctrl+Alt+M`):

Now, all we need to do is to give the new method a name:

And it’s done:

```
private static double CalculateDiscriminant(double a, double b, double c)
{
return b * b - 4 * a * c;
}
```

Now, let’s suppose that, after a while, we find a safer solver for quadratic equations. To factor it into the
program, we’ll first need to create an abstract base class
`QuadraticEquationSolverBase`

. We use the
Extract Superclass refactoring available in the
Refactor This menu
(`Ctrl+Shift+R`):

In the dialog that shows up, we get to pick which members will be promoted upwards. We only want the
`CalculateDiscriminant`

method:

We add an abstract definition of the
`Calculate()`

method (previously called
`Quadratic()`

) and end up with the
following base class:

```
public abstract class QuadraticEquationSolverBase
{
protected double CalculateDiscriminant(double a, double b, double c)
{
return b*b - 4*a*c;
}
public abstract Tuple<double, double> Calculate(double a, double b, double c);
}
```

We also got rid of the
`static`

keyword anywhere with the assumption that the implementations of
`QuadraticEquationSolverBase`

will be handled by a lifetime manager within our code. Consequently, ReSharper
reminds us to add the
`override`

keyword to the renamed
`Calculate`

method in our QuadraticEquationSolver class:

Now, let’s say we found a safer version of the quadratic equation solver. Let’s implement it. First, we use the Create derived type context action on our base class:

Then, we are asked to implement members on this type, which we do:

Finally, we provide an implementation, making use of the base class’
`CalculateDiscriminant()`

method:

```
class SafeQuadraticEquationSolver : QuadraticEquationSolverBase
{
public override Tuple<double, double> Calculate(double a, double b, double c)
{
double disc = CalculateDiscriminant(a, b, c);
if (disc < 0)
throw new ArgumentException("Cannot solve equation with complex roots");
double q = -0.5*(b + Math.Sign(b)*disc);
return new Tuple<double, double> (q/a, c/q);
}
}
```

And we’re done! Now the quadratic equation solver can be easily used, with its configuration and instantiation typically handled by an IoC container.