11609 - Teams

[sharath]

The problem says that output has to be printed result modulo 1000000007, I dont understand why this value and moreover for n=3, the number of ways the coach can choose his team is:
First for k = 1, He has 3 ways,
for k = 2, He has 6 * 2 (For different captains) ways,
for k = 3, He has 1 * 3 (For different captains) ways,

So totally he has 3+12+3 = 18 ways, then 18 modulo 1000000007 is 18 itself. I don't understand how the output is given as 1.
Let me know if I have understood the problem correctly.

[emotional blind]

The first line of the input represents the number of cases in the input.

[Psh]

Code: Select all

#include<stdio.h>
#include<math.h>
#define mod 1000000007

int main()
{
    int n,i;
    unsigned long m,p;
    scanf("%d",&n);
    for(i=1; i<=n; i++)
    {
         scanf("%lu",&m);
         p=pow(2,(m-1));
         printf("Case #%d: %lu\n",i,(m*p)%mod);
    }
    return 0;
}

[sohel]

What's your output for the input -> 1000000000
pow(2,(1000000000-1)) .. this statement won't work due to overflow.

[Psh]

Thanks!!
I've fixed it. Got that point.

[sazzadcsedu]

Can U imagine what is the value of pow(2,m-1) where m=1000000000. Value of pow(2,31) is 2147483648.So i think you
can understand what pow(2,999999999) will return. So you have to write your own power function
where the intermediate result is mod(%) by 1000000007. And you can't avoid TLE by iteratively
calculating power, like using a for loop till N.There is a nice divide and conquer algorithm for calculating (b^p)%m ,where
b is base,p is power and m is mod.Try this.

[Psh]

Yes, Bro..
I'm trying it now Bigmod method.

[Psh]

Now I've got Accepted.
Thanks for helping.

[nymo]

I think, the answer is: summation of k * nCk for k = 1 ... n [nCk = n Choose k]
Can someone tell me how to get a closed form?

[plamplam]

It's easy to derive this summation formula...after deriving this, why don't you write down all the values of this summation from n = 1 to n = 7 on paper? May be you will notice a pattern. If you do notice a pattern may be you will understand why and how such a pattern exists. Good luck.

[richatibrewal]

I am not getting the required output: I m using the summation of k*nCk

Code: Select all

#include<cstdio>
using namespace std;
#define mod 1000000007;
int main()
{
    int n,i,j,c=0,num,k;
    long long int sum,res;
    scanf("%d",&n);
    while(n--)
    {
        c++;
        sum=0;
        scanf("%d",&k);
        for(i=1;i<=k;i++)
        {
            res=i;
            num=k;
            for(j=1;j<=i;j++)
            {
                res=res*num;
                res=res/j;
                num--;
                res=res%mod;
            }

            sum=sum+res;
            sum=sum%mod;
             //printf("%d  %lld  %lld\n",i,sum,res);
        }
        printf("Case #%d: %lld\n",c,sum);
    }
    return 0;
}

[brianfry713]

Your code is getting TLE. Try input:

Code: Select all

1
1000000000