Write a function which computes the perfect sums in an array?

Question

Perfect sums is the sum of two or more number of elements of arrays whose sum is equal to a given number. Return 999 if not found.

my method signature is:

public static int persfectSum(int arr[], int input)

For example:

arr={2,3,5,6,8,10}
input = 10;

5+2+3= 10
2+8 = 10
So, the output is 2;

Answer 1

It is a variation of Subset-Sum problem - with an additional constraint on the size of the subset (larger then 1).

The problem is NP-Complete , but for relatively small integers can be solved using Dynamic Programming in pseudo-polynomial time .

A possibly simpler alternative which is feasible for small arrays is brute-force - just search all possible subsets, and verify for each if it matches the sum.

I believe these guidelines are more then enough as a starter for you to start programming the problem and solve your problem (HW?) on your own.

Good luck.

Answer 2

int PerfectSums(int n, int a[], int sum)
{

    int dp[n + 1][sum + 1] ;
    dp[0][0] = 1;

    for (int i = 1; i <= sum; i++)
        dp[0][i] = 0;

    for (int i = 1; i <= n; i++)
        dp[i][0] = 1;

    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= sum; j++)
        {

            if (a[i - 1] > j)
                dp[i][j] = dp[i - 1][j];

            else
            {
                dp[i][j] = dp[i - 1][j] + dp[i - 1][j - a[i - 1]];
            }
        }
    }

    return (dp[n][sum] == 0 ? 999 : dp[n][sum] ) ;
}