Following questions have been asked in GATE CS 2008 exam.
1. The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1
(A) X[i, j] = X[i – 1, j] V X[i, j -ai]
(B) X[i, j] = X[i – 1, j] V X[i – 1, j – ai]
(C) X[i, j] = X[i – 1, j] V X[i, j – ai]
(D) X[i, j] = X[i – 1, j] V X[i -1, j – ai]
Answer (B)
X[I, j] (2 2. In question 1, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?
(A) X[1, W]
(B) X[n ,0]
(C) X[n, W]
(D) X[n -1, n]
Answer (C)
If we get the entry X[n, W] as true then there is a subset of {a1, a2, .. an} that has sum as W.
Reference: http://en.wikipedia.org/wiki/Subset_sum_problem
3. Consider the following C program that attempts to locate an element x in an array Y[] using binary search. The program is erroneous.
1. f(int Y[10], int x) {
2. int i, j, k;
3. i = 0; j = 9; 4. do {
5. k = (i + j) /2; 6. if( Y[k] < x) i = k; else j = k;
7. } while(Y[k] != x && i < j);
8. if(Y[k] == x) printf ("x is in the array ") ;
9. else printf (" x is not in the array ") ;
10. } |
On which of the following contents of Y and x does the program fail?
(A) Y is [1 2 3 4 5 6 7 8 9 10] and x 2
(D) Y is [2 4 6 8 10 12 14 16 18 20] and 2
4. In question 3, the correction needed in the program to make it work properly is
(A) Change line 6 to: if (Y[k] http://en.wikipedia.org/wiki/Binary_search_algorithm#Implementations
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