Finding the sum of all subsets of a given set

Question

Suggest an algorithm for finding the sum of all subsets of a set.

For example, if k=3 and the subsets are {1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}

Answer 1

Answer:

Total no. of Subsets are 2^n.
As we don't require an empty set, so total required subsets are 2^n - 1. Now all we have to do is simply get all possible subsets.
This algorithm will help.

    void main()
    {
    //Total no. of elements in set = n;      
    //Let's say the Set be denoted as P[n]
    //declare a global variable sum and initialize to 0.
    for(int i=1;i<=n;i++)
    {
    int r = nCi;
    //here, r = nCi or you can say n combinations i
    //it's good to write an extra function named something like "nCi" to evaluate nCi and call it when required. 
   //define a new two dimensional array of size "r","i", say s[r][i]
   for(int k=0;k<r;k++)
    {
    //define a function to get all combination array for s[r][i] using "i" elements out of total "n"
    //This link will help you with best of code for this particular function
    //<http://www.geeksforgeeks.org/print-all-possible-combinations-of-r-elements-in-a-given-array-of-size-n/>
    //now for every particular s[r][i], do this
    for(int j=0;j<i;j++)
    {

    sum = sum + s[r][j];
    }
    }
        }
        //display total output
        printf("%d",sum);
        }

Answer 2

Each element appears the same number of times, which happens to be 2^n-1 where n is number of elements. So the answer is: count sum of elements in the set and multiply it by 2^n-1

Answer 3

For an input {x₁, …, x_n}, return 2^n-1 (x₁ + … + x_n), since each term appears in that many sums.