# Algorithms | Searching | Question 4

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

 `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 < 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

Explanation:

The above program doesnâ€™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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