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.
(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)
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.
i, j, k;
i = j = k = O;
((i<n) && (j<m))
(a[i] < b[j]) c[k++] = a[i++];
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)
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
*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.
(B) S2 and S3
(C) S2 and S4
(D) S2 and S5
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.
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