Consider the following C-function in which a[n] and b[m] are two sorted…

2006

Consider the following C-function in which a[n] and b[m] are two sorted integer arrays and c[n + m] be another integer array. 

C

void xyz(int a[], int b [], int c[])
{
  int i, j, k;
  i = j = k = O;
  while ((i<n) && (j<m))
     if (a[i] < b[j]) c[k++] = a[i++];
     else c[k++] = b[j++];
}

Which of the following condition(s) hold(s) after the termination of the while loop?

(i) j < m, k = n+j-1, and a[n-1] < b[j] if i = n

(ii) i < n, k = m+i-1, and b[m-1] <= a[i] if j = m

Answer: D. neither (i) nor (ii) — Final answer: neither (i) nor (ii). Both statements contain an off-by-one error in the expression for k. Reasoning: The while loop merges elements one at a…

  1. A.

    only (i)

  2. B.

    only (ii)

  3. C.

    either (i) or (ii) but not both

  4. D.

    neither (i) nor (ii)

Attempted by 22 students.

Show answer & explanation

Correct answer: D

Final answer: neither (i) nor (ii). Both statements contain an off-by-one error in the expression for k.

Reasoning:

  • The while loop merges elements one at a time until one array is exhausted, so when the loop stops exactly one of these holds: i = n (first array exhausted) or j = m (second array exhausted). The other index is strictly less than its length.

  • If the first array is exhausted (i = n) then j < m. The total number of elements copied into c is k = i + j = n + j (k starts at 0 and increments once per copied element). The last step that made i reach n copied a[n-1], which required a[n-1] < b[j] at that time, so a[n-1] < b[j] holds.

  • If the second array is exhausted (j = m) then i < n. The total number of elements copied is k = i + j = i + m. The last step that made j reach m copied b[m-1], which required a[i] >= b[m-1], so b[m-1] <= a[i] holds.

  • The original statements gave k = n + j - 1 and k = m + i - 1, which are off by one. Because of those incorrect k expressions, neither statement (i) nor statement (ii) is fully correct.

Therefore the correct choice is the one that says neither (i) nor (ii).

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