Algorithms | Searching | Question 4

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Consider the following C program that attempts to locate an element x in an array Y[] using binary search. The program is erroneous. (GATE CS 2008)

C

   f(int Y[10], int x) {
     int i, j, k;
     i = 0; j = 9;
     do {
             k =  (i + j) /2;
             if( Y[k] < x)  i = k; else j = k;
         } while(Y[k] != x && i < j);
     if(Y[k] == x) printf (\"x is in the array \") ;
     else printf (\" x is not in the array \") ;
}

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 < 10

(B)

Y is [1 3 5 7 9 11 13 15 17 19] and x < 1

(C)

Y is [2 2 2 2 2 2 2 2 2 2] and x > 2

(D)

Y is [2 4 6 8 10 12 14 16 18 20] and 2 < x < 20 and x is even

Answer: (C)
Explanation:

The above program doesn’t work for the cases where the element to be searched is the last element of Y[] or greater than the last element (or maximum element) in Y[]. For such cases, the program goes in an infinite loop because i is assigned value as k in all iterations, and i never becomes equal to or greater than j. So while the condition never becomes false.

Hence Option (C) is the correct option.

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