C Language | Set 6

3.7

Following questions have been asked in GATE CS 2006 exam.

1. Consider the following C-program fragment in which i, j and n are integer variables.

for (i = n, j = 0; i >0; i /= 2, j += i);

Let val(j) denote the value stored in the variable j after termination of the for loop. Which one of the following is true?
(A) val(j) = Θ(logn)
(B) vaI(j) = Θ(sqrt(n))
(C) val(j) = Θ(n)
(D) val(j) = Θ(nlogn)

Answer (C)

Note the semicolon after the for loop, so there is nothing in the body. The variable j is initially 0 and value of j is sum of values of i. i is initialized as n and is reduced to half in each iteration.

j = n/2 + n/4 + n/8 + .. + 1 = Θ(n)

2. 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.

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

(A) only (i)
(B) only (ii)
(C) either (i) or (ii) but not both
(D) neither (i) nor (ii)

Answer (C)
The condition (i) is true if the last inserted element in c[] is from a[] and condition (ii) is true if the last inserted element is from b[].


3. Consider this C code to swap two integers and these five statements: the code

void swap(int *px, int *py) 
{
   *px = *px - *py;
   *py = *px + *py;
   *px = *py - *px;
}

S1: will generate a compilation error
S2: may generate a segmentation fault at runtime depending on the arguments passed
S3: correctly implements the swap procedure for all input pointers referring to integers stored in memory locations accessible to the process
S4: implements the swap procedure correctly for some but not all valid input pointers
S5: may add or subtract integers and pointers.
(A) S1
(B) S2 and S3
(C) S2 and S4
(D) S2 and S5

Answer (C)
S2: May generate segmentation fault if value at pointers px or py is constant or px or py points to a memory location that is invalid
S4: May not work for all inputs as arithmetic overflow can occur.

Please write comments if you find any of the answers/explanations incorrect, or you want to share more information about the topics discussed above.

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