import java.util.ArrayList;
import java.util.List;
public class PrimeFactors {
public static List<Integer> generate(int n) {
List<Integer> primes = new ArrayList<Integer>();
for (int candidate = 2; candidate <= n; candidate++) {
for (; n % candidate == 0; n /= candidate) {
primes.add(candidate);
}
}
return primes;
}
}Now the Java code is exactly the code Robert Martin showed, I was following his example. The Ruby version from back then looks pretty similar, just using while instead of for.module PrimeFactors
def generate(n)
prime_factors = []
candidate = 2
while n > 1 do
while n % candidate == 0 do
prime_factors << candidate
n /= candidate
end
candidate += 1
candidate = n if candidate > Math.sqrt(n) # performance fix
end
prime_factors
end
endIf you are wondering how I am still able to find the code, I organise my code katas to allow lookup and comparison. Since then I did the kata 141 times and it has many uses.Learn a language
Prime Factors is one of the first pieces of code I write - Test Driven of course - when revisiting old languages, like Commodore BASIC or looking at a new language, like Forth, using Gforth 0.7:
: prime_factors ( n -- n1 n2 n3 n4 ) DUP 1 > IF \ test for ?DO DUP 2 ?DO BEGIN DUP I MOD 0 = \ test candidate I WHILE I SWAP I / \ add candidate, reduce number REPEAT LOOP THEN DUP 1 = IF DROP THEN ; T{ 1 prime_factors -> }T T{ 2 prime_factors -> 2 }T T{ 3 prime_factors -> 3 }T T{ 4 prime_factors -> 2 2 }T T{ 6 prime_factors -> 2 3 }T T{ 8 prime_factors -> 2 2 2 }T T{ 9 prime_factors -> 3 3 }TGforth came with a modified testing framework based on John Hayes S1I's
tester.fs, defining the functions T{, -> and }T for testing. Note that the given function prime_factors is not realistic as the number of returned arguments is not known by the caller.When I had a look at Scala, of course I did Prime Factors:
import java.lang.Math.sqrt
object PrimeFactors {
def generate(number: Int): List[Int] = {
def fold(current: Pair[Int, List[Int]], candidate: Int): Pair[Int, List[Int]] = {
if (current._1 % candidate == 0)
fold((current._1 / candidate, candidate :: current._2), candidate)
else
current
}
val (remainder, factors) =
(2 to sqrt(number).intValue).foldLeft((number, List[Int]()))(fold)
if (remainder > 1)
(remainder :: factors).reverse
else
factors.reverse
}
}This is crazy. The code creates a sequence of all candidate primes and folds it starting from left by dividing by the candidate recursively, appending to the begin of the list, which is cheap. Because of that the list is reversed at the end. I have no idea why I created this, probably I was playing around with foldLeft. This is not a good example, please do not copy it. After all these years, the Forth solution seems easier to grasp. ;-)So which languages are missing? PowerShell looks much like my PHP (shown below) and my Python Prime Factors looks similar too, just with Python specific
range(2, number + 1) and //= inside. And of course JavaScript is missing:PrimeFactors = function() {
this.factors = [];
};
PrimeFactors.prototype.generate = function(num) {
var candidate;
for (candidate = 2; candidate <= num; candidate += 1) {
num = this.tryCandidate(num, candidate);
}
return this.factors;
};
PrimeFactors.prototype.tryCandidate = function(num, candidate) {
while (num % candidate === 0) {
num = this.reduceByFactor(num, candidate);
}
return num;
};
PrimeFactors.prototype.reduceByFactor = function(num, factor) {
this.factors.push(factor);
return num / factor;
};Isn't that lovely? Again this is not good code, please do not copy it. At least I showed some creativity using prototype functions.Learn a testing framework
Using TDD to write some known code is a perfect way to learn more about a testing framework. So I explored XSLTunit using Prime Factors in XSLT or NUnit in C#:
using NUnit.Framework;
[TestFixture]
public class PrimeFactorsTest
{
[TestCase(new int[0], 1)]
[TestCase(new int[] { 2 }, 2)]
[TestCase(new int[] { 3 }, 3)]
[TestCase(new int[] { 2, 2 }, 4)]
[TestCase(new int[] { 2, 2, 2 }, 8)]
[TestCase(new int[] { 3, 3 }, 9)]
public void TestFactors(int[] expected, int number)
{
CollectionAssert.AreEqual(expected, PrimeFactors.Generate(number));
}
[Test]
[Timeout(100)]
public void TestLarge()
{
CollectionAssert.AreEqual(new int[] { int.MaxValue },
PrimeFactors.Generate(int.MaxValue));
}
}Test your own testing frameworkSometimes, when I need to create my own unit testing framework, e.g. TPUnit for old Turbo Pascal, assert-scm (Scheme R5RS) or ASM Unit for Windows Assembly, I use Prime Factors as test cases:
_prime_factors: mov esi, 0 ; esi = number of factors mov edi, ebx ; edi = address of factors mov ecx, eax ; ecx = current number mov ebx, 1 ; ebx = candidate jmp .not_diviseable .loop_over_candidates: inc ebx ; next candidate .break_if_candidate_is_larger_than_square: ; if candidate * candidate <= number then try candidate mov eax, ebx mul ebx cmp eax, ecx jbe .try_candidate ; else number is a (large) prime and we are done mov [edi + esi * register_size], ecx add esi, 1 jmp .done .try_candidate: ; if number % candidate == 0 then add candidate mov eax, ecx xor edx, edx div ebx cmp edx, 0 ; remainder is 0 jne .not_diviseable .is_diviseable: mov [edi + esi * register_size], ebx ; store candidate in factors add esi, 1 ; we found a factor mov ecx, eax ; number is remainder of division jmp .try_candidate ; try current candidate again .not_diviseable: ; if number > 1 then try next candidate cmp ecx, 1 jne .loop_over_candidates .done: ; return number of factors mov eax, esi retThis piece of assembly calcultes the prime factors of the number passed in
EAX into in the dword array address EBX.TDD Demo
In 2012 I started practising Prime Factors as kata performance, minimising the number of keys I pressed. I ran it around 50 times. In the end I used the practice to calm down when I was anxious - it was like mediation. I still have to perform it somewhere, adding music and all... I have used it demoing TDD in uncounted presentations - actually around 40: during my university guest lectures, user group meetings and at my clients. Most demos were in Java and some in PHP,
<?php
class PrimeFactors {
static function generate($n) {
$factors = [];
for ($candidate = 2; $candidate <= $n; $candidate += 1) {
while ($n % $candidate == 0) {
$factors[]= $candidate;
$n /= $candidate;
}
}
return $factors;
}
}and a single demo of test driving R code,primeFactors <- function(number) {
factors <- vector(mode="integer")
candidate <- 2
while (candidate <= sqrt(number)) {
while (number %% candidate == 0) {
factors <- c(factors, candidate)
number <- number / candidate
}
candidate = candidate + 1
}
if (number > 1) {
factors <- c(factors, number)
}
factors
}It seems, most programming languages look the same. The last sentence is not true for NATURAL, Cobol's cousin, which is ugly. I will not show it here as it would destroy this lovely post.Conclusion
By writing this post, I learned that I still need to create Prime Factors in the programming languages Go, Kotlin, OpenOffice Basic, Oracle PL/SQL and of course TypeScript - I could - and I will, it is just a matter of time. So Prime Factors - in fact any small enough code kata - is a great tool for exploring, studying and practising programming languages, testing frameworks, IDE tools and Test Driven Development in general. I will leave you with my latest addition to my collection of Prime Factors, using C99. Have fun!
#include <math.h>
typedef struct {
unsigned char count;
unsigned int values[31];
} PrimeFactors;
void PrimeFactors_init(PrimeFactors* factors)
{
(*factors).count = 0;
}
void PrimeFactors_add(PrimeFactors* factors, const unsigned int factor)
{
int count = (*factors).count;
(*factors).values[count] = factor;
(*factors).count = count + 1;
}
void generate(const unsigned int number, PrimeFactors* factors)
{
PrimeFactors_init(factors);
unsigned int remaining = number;
for (unsigned int candidate = 2; candidate <= sqrtl(remaining); candidate += 1) {
while (remaining % candidate == 0) {
PrimeFactors_add(factors, candidate);
remaining /= candidate;
}
}
if (remaining > 1) {
PrimeFactors_add(factors, remaining);
}
}
Another company I worked with did not have any kind of time accounting. That was nice for a change, but I did not believe in it and kept using my macro infested Excel sheet. Later, when they started using their own tool based on Oracle Forms, I wrote a little application that imported the lines from my sheet into the database. It was quite simple (less than 100 lines) to read a CSV, do some translations and insert the data into a database. Unfortunately companies usually do not allow employees to write directly into their time accounting database (for obvious reasons).
