Question

Suppose that I have an array consisting of n elements.

1 2 3 4 5 6 ... n

I need to find a way to extract the sums of consecutive elements in this array using C++.
Like this:

1, 2, 3,...n, 1+2, 2+3, 3+4,...(n-1)+n, 1+2+3, 2+3+4,...(n-2)+(n-1)+n,...1+2+3...n

So far I figured out I need to iterate through this array by summing certain number of elements on each run. I am not sure if it is possible to implement the algorithm I explained above. There might be a better solution but this is the best I could come up with.

Answer 1

Let’s inspect case with 4 elements:

{1,3,4,5, // from original array
 4,7,9, // sum of 2 consecutive elements
 8,12, // sum of 3
 13} // sum of 4

As you can see every part for N sum array is of size lower from original array by (N-1). So you need target array of size: N + (N-1) + (N-2) + … 1 – which is N*(1+N)/2

int* createSumArray(int* arr, int size)
{
   int ti = 0; // target index
   int* ta = new int[size*(size+1)/2];
   for (int s = 1; s <= size; ++s) // how many elements to sum
   {
      for (int si = 0; si < size + 1 - s; ++si)
      {
          ta[ti] = 0;
          for (int i = si; i < si + s; ++i)
            ta[ti] += arr[i];
          ++ti;
      } 
   }
   return ta;
}

See test on ideone