The following code for method minVal contains a logic error on a single line in the method body, on one of the four lines indicated by comments:

public static int minVal(int[] y, int first, int last)
{
/* This method returns the value of the minimum element in the
* subsection of the array "y", starting at position
* "first" and ending at position "last".
*/

int bestSoFar = y[first];

for (int i=first+1; i

Question

The following code for method minVal contains a logic error on a single line in the method body, on one of the four lines indicated by comments:

public static int minVal(int[] y, int first, int last) 
{
/* This method returns the value of the minimum element in the
 * subsection of the array "y", starting at position
 * "first" and ending at position "last".
 */
 
  int bestSoFar = y[first];          
 
  for (int i=first+1; i<=last; i++)  // line 1
  {
    if ( y[i] < y[bestSoFar] )       // line 2

bestSoFar = y[i];             // line 3

} // for

return bestSoFar;                  // line 4

} // method minVal

Which one of the four lines indicated by the comments contains the logic error?

BlackTom AI · Accepted Answer

The question asks us to identify which line among the four marked lines contains the logic error. We'll evaluate each option in turn, explaining why it is correct or incorrect, and how it affects the method.
Option 1 (line 1): for (int i=first+1; i<=last; i++) — This loop boundary is appropriate for scanning the subarray from first+1 up to last inclusive. The index progression i++ is correct, and the condition i <= last ensures the last element is considered. Therefore, line 1 is not the source of the bug.
Option 2 (line 2): if ( y[i] < y[bestSoFar] ) — Here is the heart of the problem. bestSoFar is initialized as bestSoFar = y[first], i.e., it already holds the value of the first element, not an index. Using y[bestSoFar] treats bestSoFar as an index into the array, which is incorrect and will access an unintended element (and can even go out of bounds). The comparison should compare the current element y[i] against the current minimum value, bestSoFar, i.e., if (y[i] < bestSoFar). This is the direct cause of the logic error.
Option 3 (line 3): bestSoFar = y[i]; — This line assigns the new minimum value found at index i to bestSoFar. Given the intended logic, this is correct only if bestSoFar is intended to hold the actual minimum value, which it does after line 2 is fixed. As written, with the incorrect line 2, this line would still perform the assignment of the value at i, which is consistent with the intended approach once line 2 is corrected.
Option 4 (line 4): return bestSoFar; — Returning the current value stored in bestSoFar is correct, as the method is supposed to yield the minimum value found in the specified subarray. This line correctly completes the method once the comparison logic is fixed.
In summary, the flawed logic stems from treating bestSoFar as an index in line 2. Since bestSoFar holds the minimum value itself, the code should compare y[i] to bestSoFar, not to y[bestSoFar]. Consequently, line 2 is the line containing the error. The remaining lines, when line 2 is corrected, align with the standard minimum-finding pattern in a subarray.

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