"Equations" challenge on hackerrank

Question

I am having trouble on some test cases on the "Equations" challenge on hackerrank.com. This is where the problem is stated: https://www.hackerrank.com/challenges/equations.
I'm pretty sure I understand the logic, but there is still a bug in my program (or a flaw in my logic).

public class Solution
{
    public static void mark(boolean[] a, int i, int n) //sieve util
    {
        int num = i*2;
        while(num <= n)        
        {
            a[num] = true;
            num += i;
        }
    }
    public static long legendre(int n, int p) //get prime power   
    {
        long ans = 0;
        int k = p;
        while(n/k != 0)        
        {
            ans += (long)n/k;
            k *= p;
        }
        return ans;
    }
    public static void main(String[] args)
    {
       long mod = 1000007; 
       int n;
       Scanner input = new Scanner(System.in);
       n = input.nextInt();
       boolean[] a = new boolean[n+1];
       for(int i = 2; i <= n; ++i) //sieve
       {
           if(a[i] == false)
           {
               mark(a,i,n);
           }
       }      
       boolean isEven = true;
       long ans = 1, power = 1;
       for(int i = 2; i <= n; ++i)
       {
           if(a[i] == false)
           {
               power = legendre(n,i);
               if(power%2 == 1)
               {
                   isEven = false;
               }
               ans *= (2*power+1);
               ans %= mod;
           }
       }
       if(isEven == true) //symmetric solution
            ans -= 1;
       if(n == 1) //special case
            System.out.println(1);
       else
            System.out.println(ans);                  
    }
}

What I attempted to do: create a table of prime values and then get the power of each prime factor of n!. I used this formula: http://www.cut-the-knot.org/blue/LegendresTheorem.shtml. My program produced the correct output for n = 105387 (which is 629416), but for n = 131399, my output is 598995 (should be 856428).

This question has also been asked before here: Sample testcase for Interviewstreet: Equations Someone asked "what is the output for N=131399, I am getting 598995, but it's giving wrong. – peeyush May 26 '12 at 20:33" Apparently my particular bug is not unique.

Are you getting an overflow possibly? If you change your ints (the ones that may become large) to longs do you still see similar results? — takendarkk, Sep 07 '14 at 05:21
Wow. I honestly can not believe that worked. I've done so many math programming challenges and I'm constantly thinking about overflow, but I really thought I was safe here. Thanks for bearing with me — user2959071, Sep 07 '14 at 05:30
No problem. I'm glad it was really that simple, I don't have the brainpower for much more than that atm. — takendarkk, Sep 07 '14 at 05:31

barak manos · Answer 1 · 2014-09-07T05:38:14.307

1

When calling legendre(131399,46349), variable k overflows.

Change the type of this variable from int to long.

BTW, you could have easily tracked it by adding an assertion inside the loop:

if (k < 0)
    System.out.println(k);

edited Sep 07 '14 at 05:38

answered Sep 07 '14 at 05:31

barak manos

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score 0 · Answer 2 · edited Sep 07 '14 at 12:29

Changing to long won't work, I just tried. You need to use BigInteger.

Check out my solution...

public class Solutions {

    static boolean isPrime(int p) {
        boolean num = false;
        if (p == 2 || p == 3) {
            return true;
        }
        for (int j = 2; j <= Math.sqrt(p); j++) {
            if (p % j == 0) {
                num = false;
                break;
            } else {
                num = true;
            }
        }
        return num;
    }

    public static void main(String[] args) {
        long mod = 1000007;
        int n;
        Scanner input = new Scanner(System.in);
        n = input.nextInt();
        BigInteger bresult = BigInteger.ONE;
        long x = n;
        for (int i = 2; i <= x; i++) {
            if (isPrime(i)) {
                int k = 1;
                long power = 0;
                while ((Math.pow(i, k) <= x)) {

                    power += n / Math.pow(i, k);

                    k++;
                }
                bresult = bresult.multiply(BigInteger.valueOf(power * 2 + 1));
            }

        }
        System.out.println(bresult.mod(BigInteger.valueOf(mod)));

    }
}

"Equations" challenge on hackerrank

2 Answers2