Why does the base case in recursive solution to find the maximum subsequence in a given sequence return 0 if the number is negative?

Question

Below is a sample code in C++ written using recursion to solve the maximum subsequence problem - not exactly the subsequence, but the sum of the maximum subsequence.

int maxSumRec( const vector<int> & a, int left, int right )
{
  if( left == right ) // Base case
    if( a[ left]>0)
      return a[ left ];
    else
      return 0;

  int center = ( left + right ) / 2;
  int maxLeftSum = maxSumRec( a, left, center );
  int maxRightSum = maxSumRec( a, center + 1, right );
  int maxLeftBorderSum = 0, leftBorderSum = 0;
  for( int i = center; i >= left; --i )
  {
    leftBorderSum += a[ i ];
    if( leftBorderSum > maxLeftBorderSum )
      maxLeftBorderSum = leftBorderSum;
  }
  int maxRightBorderSum = 0, rightBorderSum = 0;
  for( int j = center + 1; j <= right; ++j )
  {
    rightBorderSum += a[ j ];
    if( rightBorderSum > maxRightBorderSum )
      maxRightBorderSum = rightBorderSum;
  }
  return max3( maxLeftSum, maxRightSum, maxLeftBorderSum + maxRightBorderSum );
}

Why does the base case have to return 0 if the single element left is negative? Will it not affect the sum if we return a higher value of 0 instead of the actual negative value? I searched the internet for the explanation of the base case and the problem statement but couldn't find out the explanation.

Answer 1

The empty sequence {} is a subsequence of {x}, and its sum is 0. The sum of the sequence {x} is x, which is obviously less than 0 if x is negative.