Recursion - Java Concepts - page 804

int smallerArea = smallerTriangle.getArea();

Now we can complete the getArea method:

public int getArea()
{
if (width == 1) return 1;
Triangle smallerTriangle = new Triangle(width
- 1);
int smallerArea = smallerTriangle.getArea();
return smallerArea + width;
}

A recursive computation solves a problem by using the solution of the same
problem with simpler values.

Here is an illustration of what happens when we compute the area of a triangle of
width 4.

ȗ The getArea method makes a smaller triangle of width 3.

ȗ It calls getArea on that triangle.

ȗ That method makes a smaller triangle of width 2.

ȗ It calls getArea on that triangle.

ȗ That method makes a smaller triangle of width 1.

ȗ It calls getArea on that triangle.

ȗ That method returns 1.

ȗ The method returns smallerArea + width = 1 + 2 = 3 .

ȗ The method returns smallerArea + width = 3 + 3 = 6 .

ȗ The method returns smallerArea + width = 6 + 4 = 10 .

This solution has one remarkable aspect. To solve the area problem for a triangle of a
given width, we use the fact that we can solve the same problem for a lesser width.
This is called a recursive solution.