CODEWITHSUNDEEP
javamathfactorial
user1313504
user1313504

Reputation:

Factorials Challenge.(Beginner's Challenge)

I tried the following challenge:

Given the first few factorials:

1! = 1

2! = 2 x 1 = 2

3! = 3 x 2 x 1 = 6

4! = 4 x 3 x 2 x 1 = 24

What is the sum of the first 15 factorials, NOT INCLUDING 0!?

My solution in Java is the following: 

public class Factorial
{
   public static void main(String[] args)
   {
     int sum = 0;    
     int multi = 1;
        for (int i=1;i<=15;i++)         
        {
        multi = multi*i;
        sum = multi+sum;     
        }     
     System.out.print(sum);
   }
}

I verified the solutions for the first 7 factorials but will it work for the first 15?

Upvotes: 2

Views: 2524

Answers (3)

zapl
zapl

Reputation: 63955

That

public static void printFactorials (int max) {
    long fac = 1;
    long sum = 0;
    for (int i = 1; i <= max; fac *= ++i) {
        System.out.println(String.format("Factorial(%2d)=%d", i, fac));
        sum += fac;
    }
    System.out.println(String.format("Sum of Factorials(1 to %2d)=%d", max, sum));
}

gives you

Factorial( 1)=1
Factorial( 2)=2
Factorial( 3)=6
Factorial( 4)=24
Factorial( 5)=120
Factorial( 6)=720
Factorial( 7)=5040
Factorial( 8)=40320
Factorial( 9)=362880
Factorial(10)=3628800
Factorial(11)=39916800
Factorial(12)=479001600
Factorial(13)=6227020800
Factorial(14)=87178291200
Factorial(15)=1307674368000
Sum of Factorials(1 to 15)=1401602636313

long starts to fail at 21, next step is BigInteger

public static void printRlyBigFactorials (int max) {
    BigInteger fac = BigInteger.ONE;
    BigInteger sum = BigInteger.ZERO;
    for (int i = 1; i <= max; ++i) {
        fac = fac.multiply(BigInteger.valueOf(i));
        sum = sum.add(fac);
        System.out.println(String.format("Factorial(%2d)=%d", i, fac));
    }
    System.out.println(String.format("Sum of Factorials(1 to %2d)=%d", max, sum));
}

That will work almost indefinitely and can give you fancy results like:

Sum of Factorials(1 to 500)=
1222581999810786173488382263893486121736784649845260488587055662127413631697
9142090995417259894466676137016242713788312106218384177808117660024733369428
7060019503701220190523381023699528466605036804597249531428694859689049295904
5138704466475196055082304091214424335155644013903958356823605973150159110295
5787828433482529258832635575855564789877227459384652114477297831606218655683
9245588828671235437927278554210732477499719243692398907465554636521289870187
5799458234466791378320221140358905721655475503366304295011345436395868843079
5463780536087239619245051615759218253091986494512882003123090598805090122753
7135918455294416676103707115038417384516670399033063650562275830354903359872
0775172343137459008549361297203752431405977559950082400276439557196120290170
5516606073135650288107937474531851451830365876392678959480905477335825506233
3795849463603798966643420966668878072957663827751761832039623225350606860709
6479320263132522604054741925038640750661849690108363701190203548476572823422
7743271977187818002695582046473911765828511673121820261887951566200568565033
40092247479478684738621107994804323593105039052556442336528920420940313

Upvotes: 1

Gyanendra Singh
Gyanendra Singh

Reputation: 1005

No, its not working for 15. Use long. Also, you could move the print statement inside the loop, to check from where it starts failing. I guess in this case it's 13.

Upvotes: 5

Jeffrey
Jeffrey

Reputation: 44808

It will not work for the first 15 factorials because of integer overflow. The correct answer is 1401602636313, which exceeds Java's int bound of 2147483647. You could either use a long which has a bound of 9223372036854775807 or a BigInteger.

Upvotes: 7

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