Can I can use Java to do"Seeking 1 + 2 ! + 3 ! + ... + 20 ! And"?

Question

I have this error：sum=-1490928446.You see:negative number.But I do not know what?I define Summation and a,I hope It can Compute"1 + 2 ! + 3 ! + ... + 20 ! ".I think my code has no problem,but it tell me negative number.Why?How can I solve it.Thank you very much.Here is my source code：

public static void main(String[] args) {

    //And to define a number of statistics accumulated result
    int sum=0;
    //An alternative definition of variable
    int a=1;
   //Two for loop
    for(int j=1;j<21;j++)
    {   
      for(int i=1;i<j+1;i++)
     {
        a=a*i;  
       sum +=a;
      }

     }
     //Print output results
    System.out.println("sum="+sum);
}

}

I want to know what logical error?Thank you very much.

Answer 1

int is not enough. Highest value into int (32 bit) can be 2^31 -1, that means 2147483647. Your sum is exceeding this. Use long instead.

long sum = 0;
long a = 1;
for (int j = 1; j < 21; j++) {
    for (int i = 1; i < j + 1; i++) {
        a = a * i;
        sum += a;
    }
}
System.out.println("sum=" + sum);

Answer 2

int is 32 bits, meaning it can only hold so much. The range is -2^31 ~ 2^31-1 to be exact. Per Integer Overflow from Wikipedia:

In computer programming, an integer overflow occurs when an arithmetic operation attempts to create a numeric value that is too large to be represented within the available storage space.

You're result is too large that it's overflowing and is giving you a negative result. Use a long which is 64 bits. Try this:

long sum = 0L;
long a = 1L;

Answer 3

int in Java has a range from +2,147,483,647 to -2,147,483,648. If your output exceeds this range, you can use long which has a range from +9,223,372,036,854,775,807 to -9,223,372,036,854,775,808.

If your output is even bigger than that, then try using the BigInteger. But in your case long would be enough to solve it.

Answer 4

As others have mentioned, you're overflowing the size of int. Changing to long can handle up to 20, but it will overflow too at any higher value, at which point you'd need BigInteger.

However, you have much bigger problems than that.
Your main problem is that your algorithm is bad.

You're supposed to be calculating this:

1 + 2 ! + 3 !    + 4 !          + 5 !                     + ...
1 + 1*2 + 1*2*3  + 1*2*3*4      + 1*2*3*4*5               + ...
1 + 2   + 6      + 24           + 120                     + ...

So let's add some print statements to see what you're really doing. See updated code and output below.

1 + 1+2 + 2+4+12 + 12+24+72+288 + 288+576+1728+6912+34560 + ...

WOW! That's not even close to the same thing.

I'll leave it to you to figure out where you went wrong.¹
Those print statements will help with that.
    ^{1) Hint: Remove i loop.}

Code

int sum = 0;
int a = 1;
System.out.printf("              a=%-11d   sum=%d%n", a, sum);
for (int j = 1; j < 21; j++) {
    for(int i=1;i<j+1;i++) {
        a = a * i;
        sum += a;
        System.out.printf("j=%-2d   i=%-2d   a=%-11d   sum=%d%n", j, i, a, sum);
    }
}
System.out.println("sum=" + sum);

Output

              a=1             sum=0
j=1    i=1    a=1             sum=1
j=2    i=1    a=1             sum=2
j=2    i=2    a=2             sum=4
j=3    i=1    a=2             sum=6
j=3    i=2    a=4             sum=10
j=3    i=3    a=12            sum=22
j=4    i=1    a=12            sum=34
j=4    i=2    a=24            sum=58
j=4    i=3    a=72            sum=130
j=4    i=4    a=288           sum=418
j=5    i=1    a=288           sum=706
j=5    i=2    a=576           sum=1282
j=5    i=3    a=1728          sum=3010
j=5    i=4    a=6912          sum=9922
j=5    i=5    a=34560         sum=44482
j=6    i=1    a=34560         sum=79042
j=6    i=2    a=69120         sum=148162
j=6    i=3    a=207360        sum=355522
j=6    i=4    a=829440        sum=1184962
j=6    i=5    a=4147200       sum=5332162
j=6    i=6    a=24883200      sum=30215362
j=7    i=1    a=24883200      sum=55098562
j=7    i=2    a=49766400      sum=104864962
j=7    i=3    a=149299200     sum=254164162
j=7    i=4    a=597196800     sum=851360962
j=7    i=5    a=-1308983296   sum=-457622334
j=7    i=6    a=736034816     sum=278412482
j=7    i=7    a=857276416     sum=1135688898

Here you can also see your overflow problem occurring (the first time) at j=7, i=5.

Answer 5

There is a mistake in your code. I think you should initialize a in the inner loop. Also as soon as the Factorial sum exceeds the maximum integer values it starts from negative.So use long.

Following code should work:

public static void main(String[] args) {

    long sum = 0;       

    for (int j = 1; j < 21; j++) {
        long a = 1;
        for (int i = 1; i < j + 1; i++) {
            a = a * i;
        }
        sum += a;
        /*//checks when the sum exceeds the Maximum int value
         * if(sum>Integer.MAX_VALUE){ System.out.println(sum+"---->"+j); }
         */
    }

    System.out.println("sum=" + sum);
}