Functional Decomposition

Functional decomposition refers to the process of considering a large problem, then breaking it down into smaller parts (decomposing it).

We can think of this as a top-down approach to identifying the smaller parts of a problem.

How to start

Begin by writing a single sentence.

One problem to solve might be:

Provide a patient with a way to make an appointment with a doctor.

For the RSA Numbers puzzle, we could summarize the problem as:

Find how many RSA numbers there are between the lower limit and upper limit provided.

Decompose

For the first example, from the top (general problem) down (to the smaller problems) we might have:

flowchart TD

id1["Book\nApointment"]
id1 --> id2["Register\nyourself"]
id1 --> id3["Search\ndoctor"]
id1 --> id4["Review\navailable times"]
id1 --> id5["Select\na\ntime"]
id1 --> id6["Provide\ntreatment\nhistory"]
id1 --> id7["Finalize\nbooking"]

Each step on the second level of the diagram represents a different function of the application we need to author.

With an unfamiliar problem, just doing a few examples by hand can be helpful. For the RSA Numbers puzzle:

From trying a few examples, we might realize there are three main functions, from most general, to most specific:

flowchart TD

id1["<b>Function A</b>\n(yellow)\nFind the count of RSA numbers in the provided range"]
id1 --> id2["<b>Function B</b>\n(green)\nIs this number an RSA number?"]
id2 --> id3["<b>Function C</b>\n(pink)\nIs this a divisor of the current number being considered?"]

Implementation

For the RSA Numbers puzzle, we might then begin with these function shells, and then fill in the necessary logic:

Function A:

func findCountOfRSANumbers(between lower: Int, and upper: Int) -> Int {
	// Loop over numbers in range
	for i in lower...upper {
		// Check whether current number is an RSA number
		let result = isRSA(number: i)
		// Do something based on result...
	}
	// Return count of RSA numbers in the range given...
}

Function B:

func isRSA(number: Int) -> Bool {
	// Loop over possible divisors
	for j in 1...number {
		// Check whether current number is a divisor of this number
		let result = isDivisor(dividend: number, divisor: j)
		// Do something based on result...
	}
	// Return whether this number is an RSA number...
}

Function C:

func isDivisor(dividend: Int, divisor: Int) -> Bool {
	// Add logic to determine whether provided divisor actually
	// goes evenly into the provided dividend
	// (e.g.: remainder is zero) 
 
	// Return the result...
}