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There is a general principle of software design called top-down design.
If, while writing a definition of function f, you find yourself wishing that you had other functions (say, g and h), then assume that you already have g and h and continue writing f, using them. You can write definitions of g and h later.
For example, the distance between two points (x1, y1) and (x2, y2) in the plane is √(x1 − x2)2 + (y1 − y2)2. Written in a program, that might look like this.
distance = sqrt((x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2));But if you assume that you have a function sqr(x) that returns x2, that becomes shorter.
distance = sqrt(sqr(x1 - x2) + sqr(y1 - y2));Top-down design tells you to write it in the shorter way and to think about writing sqr later.
Recursion can be viewed as a special case of top-down design. While you are writing a definition of power, imagine that you have a definition of power that you can use. Don't worry about whether it will be available; it will, because you are in the process of writing it!
But there is a catch. When writing a recursive definition, there are some limitations on the parameters that you can pass to recursive calls. We look at that issue in the next page.
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