Rowanto Luo


Just another blog. or log.


Factorial function of 10000!

I have a friend who asked me to teach him Java programming. About a few days ago, he told me :

Programmers should work fast and efficient. Please give me a task which has a time limit. I'm not used to fast programming.

The part about fast and efficient is always universally true. It doesn't apply to only programming, but I am more in the direction of doing something right instead of fast. It's better to do it right, but slow, instead of fast, but horrible. Of course it's depending of the context also, but generally it should be like that in my opinion.

But nevermind all that, since he wanted a task, I gave it to him. I told him to make a program which can calculate factorial precisely (no float or double). The time limit was until sunday (3-4 days). I also gave some specification :

  1. A function which accept int as the factorial input, and returns the output as string (why string? since int won't be able to hold the value. I didn't tell him that though. It was a hint :) )
  2. Must at least be able to calculate 10000! (Factorial of 10000, which means 10000 x 9999 x 9998 x ... x 3 x 2 x 1)
  3. The class BigInteger must not be used.
  4. The output must be precise, no float or double or e+24 or something like that.
    He seems to be very confident. The moment he read that, he told me :

I have ever done this. I only needed 5 minutes, plus a worktime of 2-3 minutes. Please wait a moment..

I just laughed. :D
I replied, just try it first. Then he told me again :

My computer freeze. You are saved.

I just laughed again. Now it's been a few days, and he doesn't seem to be able to do it. Actually I don't expect him to be able to do it. I only expects him to come up with an idea how to solve it. He tends to start programming something which he doesn't understand. He didn't know what he's doing but he just type something. So it's actually a lesson for him to think up an algorithm to solve a problem.

I'm also not trying to embarrass him with this post. I'm not disclosing his name as well. Yes, sure, if people are always a little bit humbler, it would be good.

So actually the solution of this problem is to calculate everything using string. Do you still remember how you used to do calculation in elementary school?
As example, 241 x 24

    241
     23
   --------x
    723
   482
  ---------+
   5543

Yes, this is the solution, just put everything as string, and calculate all of them always a little by a little. String in Java has a maximum length of 2^32 (if I'm not wrong), so it should be enough to hold all of the result.

I've also finished a Java program to do that since I have a little time. I will have to do it later anyway since he will need a correct answer as well. But please beware, this is a 30-45 minutes work (I've done this before in pascal) and is not yet properly debugged. But I have tried with a number of examples and the result matched correctly. So it should be correct.

The funny part is, although the program is finished. I can't finish calculating 10000!, the program has been running for almost an hour now (on a single thread), and I've only calculated from 10000 to 5800. I think it will take days or maybe weeks to finish calculating 10000, since it will get slower and slower :D
I've also just told him, it'll be fine if he could calculate 200!

If my program is correct without any bugs, then answer for 200! (factorial of 200) is

788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000

for 500! (factorial of 500), the answer is

1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

for 1000! (factorial of 1000!), the answer is

402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

for 10000! (factorial of 10000!), the answer is..

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The code (comments are in Indonesian):

public class FaktorCalculator {

    /**
     * @param args
     */
    public static void main(String[] args) {
        System.out.println(calculateFactor(200));
    }

    public static String calculateFactor(int factor) {
        String result = "1";
        for (int i = factor; i > 0; i--) {
            System.out.println("Now calculating by " + i + "..");
            result = multiplyTwoString(result, Integer.toString(i));
        }
        return result;
    }

    /**
     * Perkalian antara dua string
     *
     * @param firstString string pertama
     * @param secondString string kedua
     * @return string pertama dikali string kedua
     */
    public static String multiplyTwoString(String firstString, String secondString) {
        // hasil yang akan kita balikan
        String result = "0";

        // string jumlah extra 0 dibelakang
        String endZero = "";
        for (int i = (secondString.length() - 1); i >= 0; i--) {
            // ambil angka terakhir yang teraktuel
            int number = Character.getNumericValue(secondString.charAt(i));

            // kalikan hasilnya
            String tempResult = multipleStringWithADigit(firstString, number);

            // tambahkan dengan hasil yang di simpan, namun dengan extra 0 nya.
            result = addTwoString(tempResult + endZero, result);

            endZero = endZero + "0";
        }
        return result;
    }

    /**
     * Perkalian antara string dengan 1 angka
     *
     * @param string String yang ingin dikali
     * @param digit dengan berapa string ini mesti dikali
     * @return Hasil dari perkaliannya dalam string
     */
    public static String multipleStringWithADigit(String string, int digit) {
        if (digit == 0) return "0";
        if (digit == 1) return string;

        String result = "0";
        for (int i = 0; i < digit; i++) {
            result = addTwoString(result, string);
        }
        return result;
    }

    /**
     * Methode untuk menambah dua string seperti anak sd
     *
     * @param firstString angka pertama nya
     * @param secondString angka kedua nya
     * @return hasil pertambahan dalam bentuk string
     */
    public static String addTwoString(String firstString, String secondString) {
        // definisikan dulu variabel yang akan kita pakai sebagai output
        String result = "";

        // kita simpan hasil tambah yang lebih di variabel rest ini
        int rest = 0;

        // kita cari angka terpendek ada berapa
        int shortestNumberLength;
        if (secondString.length() < firstString.length()) {
            shortestNumberLength = secondString.length();
        } else {
            shortestNumberLength = firstString.length();
        }

        // sekarang kita tambah-tambah kek anak sd dari belakang
        for (int i = 0; i < shortestNumberLength; i++) {
            // kita extract angkar terakhir aktuel jadi int
            int firstNumber = Character.getNumericValue(firstString.charAt(firstString.length() - 1 - i));
            int secondNumber = Character.getNumericValue(secondString.charAt(secondString.length() - 1 - i));

            // tambahkan, + juga kelebihan dari yang sebelumnya
            int totalledNumber = firstNumber + secondNumber + rest;

            // simpan angka yang lebih di rest
            rest = totalledNumber / 10;

            // simpang angka terakhirnya di awal variable result
            result = (totalledNumber % 10) + result;

            // kalau i sudah shortestNumberLength, berarti sudah terakir
            if (i == (shortestNumberLength - 1)) {
                // dan kalau panjang stringnya tidak sama, berarti depan ada angka sisa
                if (firstString.length() != secondString.length()) {
                    int differenceInLength = firstString.length() - secondString.length();

                    // kalau differenceInLength minus, berarti secondString lebih panjang, dan sebaliknya
                    // kita mesti ambil string yang lebih panjang
                    String stringWithRest;
                    if (differenceInLength < 0) {
                        stringWithRest = secondString;
                    } else {
                        stringWithRest = firstString;
                    }

                    // potong sisa stringnya
                    String restString = stringWithRest.substring(0, Math.abs(differenceInLength));

                    // ingat tambah dengan sisanya, bisa panggil methode ini lagi.
                    if (rest != 0) restString = addTwoString(restString, Integer.toString(rest));

                    // kita sambil sisanya dan tambahkan ke hasil
                    result = restString + result;
                }
                // ansonsten sisanya dari pertambahan mesti taruh depan juga
                else {
                    if (rest != 0) result = rest + result;
                }
            }
        }
        return result;
    }

}